diff --git a/.ipynb_checkpoints/Muons_project-checkpoint.ipynb b/.ipynb_checkpoints/Muons_project-checkpoint.ipynb new file mode 100644 index 0000000..8ff992c --- /dev/null +++ b/.ipynb_checkpoints/Muons_project-checkpoint.ipynb @@ -0,0 +1,1480 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Simulation of a positron-induced Muon Source (part 1)\n", + "\n", + "\n", + "### Authors:\n", + "* Saverio Monaco\n", + "* Marianna Zeragic De Giorgio\n", + "* Gerardo Javier Carmona\n", + "* Hilario Capettini \n", + "\n", + "### Description\n", + "\n", + "The production of a high brillance muon beam is one of the most important challenge for the future of Particle Physics. A particularly interesting idea consists of shooting high energy positrons on a target, aiming at the production of muons by means of the process $e^+ + e^- \\rightarrow \\mu^+ + \\mu^-$. To mimize the divergence of the resulting \"muon beam\", the positrons energy is chosen so that the reaction occurs close to threshold (assuming the electrons in the target to be at rest). The main goal of this project is to produce a Monte Carlo simulation of such a process. \n", + "\n", + "\n", + "### References\n", + "\n", + "* [LEMMA](https://arxiv.org/pdf/1509.04454.pdf) paper. The original paper describing the positron-induced low emittance muon source, ehere all the relevant kinematic features of the process have been studied\n", + "* [Babayaga](https://www2.pv.infn.it/~hepcomplex/babayaga.html) event generator. You may want to install and run it as a comparison for your results.\n", + "* [2018 Experiment](https://arxiv.org/pdf/1909.13716.pdf): the paper describing the (very poor..) results of the experiment carried out in summer 2018\n", + "* [2021 proposal](https://cds.cern.ch/record/2712394?ln=en): the proposal for the experiment in 2021\n", + "\n", + "\n", + "### Contact\n", + "\n", + "* Marco Zanetti \n", + "* Camilla Curatolo \n", + "* Jacopo Pazzini \n", + "* Alberto Zucchetta " + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Analytical part\n", + "\n", + "1. Compute the process leading-order cross section, $\\sigma(\\theta; \\sqrt{s})$, as a function of the scattering angle $\\theta$ and with the center of mass energy $\\sqrt{s}$ as a parameter. Start by computing it in the center of mass system. N.B.: textbooks reports such cross section in the relativistic limit, i.e. for $\\sqrt{s}\\gg m_\\mu$, which is clearly not the case here ($\\sqrt{s}\\sim 2m_\\mu$);\n", + "\n", + "2. compute and display the angle and momentum components distributions of the emerging muon pairs;\n", + "\n", + "3. boost muons four-momenta in the laboratory frame, i.e. in the frame where the electron is at rest and the positron has enough energy to give rise to the process;" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Import the required packages\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import stats\n", + "import scipy.integrate as integrate\n", + "import csv\n", + "import pandas as pd\n", + "from matplotlib.ticker import FormatStrFormatter\n", + "import math" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Define the universal constants\n", + "muon_mass = 0.1056583745 #[GeV]\n", + "electron_mass = 0.00051099894 #[GeV]\n", + "alpha = 0.007297 #[] \n", + "Avogadro_number = 6.02214076e23 #[#/mol]" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The differential cross section was obtained from [MANDELN] and it is $$\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{CM}=\\frac{2\\,\\alpha^2}{s^2}\\frac{|p'|}{\\sqrt{s}}\\left(\\frac{s}{4}+p'^2\\cos^2\\vartheta+m_\\mu^2\\right)$$\n", + "\n", + "Using the relativistic total energy $$E_{CM}^2=4p'^2+4m_\\mu^2\\rightarrow p'^2=\\frac{E_{CM}^2}{4}-m_\\mu^2\\rightarrow p'^2=\\frac{s}{4}-m_\\mu^2$$\n", + "\n", + "The differential cross section can be rewritten as:\n", + "$$\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{CM}=\\frac{2\\,\\alpha^2}{s}\\sqrt{\\frac{1}{4}-\\frac{m_\\mu^2}{s}}\\left[\\left(\\frac{1}{4}+\\frac{m_\\mu^2}{s}\\right)+\\left(\\frac{1}{4}- \\frac{m_\\mu^2}{s}\\right)\\cos^2{\\theta}\\right]$$\n", + "\n", + "Integrating over the solid angle we obtain the total cross section as a function of the total center of mass energy:\n", + "$$\\sigma(s)=\\frac{8\\pi\\,\\alpha^2}{3\\,s}\\sqrt{\\frac{1}{4}-\\frac{m_\\mu^2}{s}}\\left[1 + 2\\frac{m_\\mu^2}{s}\\right]$$\n", + "\n", + "To obtain the Probability Density Function (PDF) the integration must be performed only over the azymuthal angle $\\phi$ and as a result we obtain a function of the polar angle $\\theta$ with the center of mass energy $\\sqrt{s}$ as a parameter.\n", + "$$PDF(\\theta)=\\frac{4\\pi\\,\\alpha^2}{s}\\sqrt{\\frac{1}{4}-\\frac{m_\\mu^2}{s}}\\left[\\left(\\frac{1}{4}+\\frac{m_\\mu^2}{s}\\right)+\\left(\\frac{1}{4}- \\frac{m_\\mu^2}{s}\\right)\\cos^2{\\theta}\\right]$$\n", + "\n", + "This PDF is not normalized but it is easily done dividing it through the total cross section. \n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#rs is the sqrt(s)= E\n", + "#The units are Barn so 1ub = 2.56819e-3 GeV^-2 \n", + "gev_to_ub = 389.379\n", + "\n", + "def cross_section(rs):\n", + " '''Takes the com energy rs in GeV and returns the total cross section in ub.'''\n", + " s = rs**2\n", + " sigma = 8 *np.pi * alpha**2 / (3*s) *\\\n", + " np.sqrt(1/4 - muon_mass**2 / s) *\\\n", + " (1 + 2 * muon_mass**2 / s)\n", + "\n", + " return sigma * gev_to_ub\n", + "\n", + "\n", + "def diff_cross_section(rs,theta):\n", + " '''Takes the com energy rs in GeV, an angle theta in radians and returns the corresponding differential cross section in ub.'''\n", + " s =rs**2\n", + " dsigma = 2 * alpha**2 / s *\\\n", + " np.sqrt(1/4 - muon_mass**2 / s) *\\\n", + " (1/4 + muon_mass**2 / s + (1/4 - muon_mass**2 / s)*np.cos(theta)**2)\n", + "\n", + " return dsigma * gev_to_ub\n", + "\n", + "def pdf_theta(rs,theta):\n", + " '''Gives the (not normalized) probability density for a scattering angle theta in radians for a scattering with com energy rs in GeV.'''\n", + " y = 2*np.pi *np.sin(theta)*diff_cross_section(rs,theta)\n", + "\n", + " return y\n", + " \n", + "def pdf_theta_normalized(rs,theta):\n", + " '''Gives the (normalized) probability density for a scattering angle theta in radians for a scattering with com energy rs in GeV.'''\n", + " y =pdf_theta(rs,theta)/cross_section(rs)\n", + "\n", + " return y\n", + " \n", + "def pdf_p_normalized(rs,theta):\n", + " y =pdf_p(rs,theta)/cross_section(rs)\n", + " return y" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Functions\n", + "def plot_momenta_hist(px,py,pz,title,color):\n", + " fig, (ax1,ax2,ax3) = plt.subplots(nrows=1, ncols=3, figsize=(12, 4))\n", + " \n", + " n, bins, _ = ax1.hist(px, bins=50,color=color, ec='grey')\n", + " ax1.set_xlabel(r'$p_x$ [GeV]', fontsize=15)\n", + " ax1.set_ylabel('Counts', fontsize=15)\n", + " ax1.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + " ax1.xaxis.set_major_formatter(FormatStrFormatter('%.2f'))\n", + "\n", + "\n", + " n, bins, _ = ax2.hist(py, bins=50,color=color, ec='grey')\n", + " ax2.set_title(title, fontsize=15)\n", + " ax2.set_xlabel(r'$p_y$ [GeV]', fontsize=15)\n", + " ax2.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + " ax2.xaxis.set_major_formatter(FormatStrFormatter('%.2f'))\n", + "\n", + "\n", + "\n", + " n, bins, _ = ax3.hist(pz, bins=50,color=color, ec='grey')\n", + " ax3.set_xlabel(r'$p_z$ [GeV]', fontsize=15)\n", + " ax3.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + " ax3.xaxis.set_major_formatter(FormatStrFormatter('%.2f'))\n", + "\n", + " plt.show() \n", + " \n", + "def plot_angles_hist(theta,phi,colort,colorp):\n", + " fig, (ax1,ax2) = plt.subplots(nrows=1, ncols=2, figsize=(12, 4))\n", + "\n", + " n, bins, _ = ax1.hist(theta, bins=50,color=colort, ec='black')\n", + " ax1.set_title(r'$\\mu^+$', fontsize=20)\n", + " ax1.set_xlabel(r'$\\theta$ [°]', fontsize=20)\n", + " ax1.set_ylabel('Counts', fontsize=20)\n", + " ax1.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + "\n", + " n, bins, _ = ax2.hist(phi, bins=50,color=colorp, ec='black')\n", + " ax2.set_title(r'$\\mu^+$', fontsize=20)\n", + " ax2.set_xlabel(r'$\\phi$ [°]', fontsize=20)\n", + " ax2.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + "\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#\n", + "###\n", + "####\n", + "#####\n", + "######\n", + "####### Analysis\n", + "######\n", + "#####\n", + "###\n", + "##\n", + "#" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "##################################################################################\n", + "#Analysis parameters\n", + "delta = 0.001\n", + "E = 2 * muon_mass + delta #This is the proposed energy just above the threshold\n", + "N = 10**7\n", + "deg=180/np.pi #Conversion radiants to degrees\n", + "\n", + "###################################################################################" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print(\"Momentum in the CM\", '%.5f' % np.sqrt(E**2/4-muon_mass**2), \"GeV\")\n", + "print(\"Total relativistic energy in the CM\", '%.5f' % E, \"GeV\")\n", + "print(\"Cross section\", '%.5f' % cross_section(E), \"barn\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "fig, ax = plt.subplots(figsize=(6,6))\n", + "theta = np.linspace(0,np.pi)\n", + "ax.plot(theta*deg, diff_cross_section(E,theta),color='blue', label='PDF')\n", + "\n", + "plt.title(r'Diferential cross section for $\\sqrt{s}=$'+str('%.5f' % E)+str(\" GeV\"), fontsize=15)\n", + "plt.xlabel(r'$ \\theta [°] $', fontsize=15)\n", + "plt.ylabel(r'$ \\frac{d\\sigma}{d\\Omega} [\\mu b]$', fontsize=15)\n", + "#plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "#import warnings\n", + "#warnings.filterwarnings(\"ignore\")\n", + "\n", + "fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(12, 6))\n", + "rs = np.linspace(2*muon_mass, 0.5)\n", + "ax1.plot(rs, cross_section(rs),color='blue', label='PDF')\n", + "\n", + "ax1.set_title('Total cross section', fontsize=15)\n", + "ax1.set_xlabel(r'$ \\sqrt{S} [GeV]$', fontsize=15)\n", + "ax1.set_ylabel(r'$ \\sigma [\\mu b]$', fontsize=15)\n", + "#plt.legend()\n", + "\n", + "rs = np.linspace(2*muon_mass, 0.23)\n", + "ax2.plot(rs, cross_section(rs),color='blue', label='PDF')\n", + "\n", + "ax2.set_title('Total cross section', fontsize=15)\n", + "ax2.set_xlabel(r'$ \\sqrt{S} [GeV]$', fontsize=15)\n", + "ax2.set_ylabel(r'$ \\sigma [\\mu b]$', fontsize=15)\n", + "ax2.set_xlim(0.21,0.23)\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": false + }, + "outputs": [], + "source": [ + "print('Angular distribution')\n", + "fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(12, 6))\n", + "\n", + "theta = np.linspace(0, np.pi)\n", + "\n", + "\n", + "ax1.plot(theta*deg, pdf_theta(E,theta),color='blue', label='PDF')\n", + "ax1.set_title(r'$ PDF(\\theta)$ for $\\sqrt{s}=$'+str('%.5f' % E)+str(\" GeV\"), fontsize=15)\n", + "ax1.set_xlabel(r'$ \\theta [°] $', fontsize=20)\n", + "ax1.set_ylabel(r'$ PDF$', fontsize=20)\n", + "#plt.legend()\n", + "\n", + "\n", + "\n", + "ax2.plot(theta*deg, pdf_theta_normalized(E,theta),color='blue', label='PDF')\n", + "ax2.set_title(r'Normalized $ PDF(\\theta)$ for $\\sqrt{s}=$'+str('%.5f' % E)+str(\" GeV\"), fontsize=15)\n", + "ax2.set_xlabel(r'$ \\theta [°] $', fontsize=20)\n", + "ax2.set_ylabel(r'$ PDF$', fontsize=20)\n", + "plt.show()\n", + "\n", + "print('Check the normalization')\n", + "x2 = lambda x: pdf_theta(E,x)\n", + "print('Integral of the PDF in [0,pi]', \"{:.5f}\".format(integrate.quad(x2, 0., np.pi)[0]))\n", + "x2 = lambda x: pdf_theta_normalized(E,x)\n", + "print('Integral of the normalized PDF in [0,pi]', \"{:.5f}\".format(integrate.quad(x2, 0., np.pi)[0]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Monte Carlo Simulation\n", + "\n", + "4. write a Monte Carlo simulation that generates scattering events following the distrubtions that you found analytically; \n", + "5. produce a synthetic dataset of about $N=10^5$ (or more) events. Events should be listed as rows in a file with columns representing the muons coordinates (keep in mind that in the lab frame muons are relativistic and thus the number of coordinates can be only 3 per muon);\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#\n", + "###\n", + "####\n", + "#####\n", + "######\n", + "#######\n", + "######\n", + "#####\n", + "###\n", + "##\n", + "#" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "# In order to sample theta angles, we have taken the inverse cumulative density function transform approach.\n", + "\n", + "def inv_cdf(rs,r):\n", + " '''Takes a CoM energy rs in GeV, and an array r of U(0,1) samples to generate an array of theta samples distributed according to the scattering pdf.\\n\n", + " Also admits an array of energies of the same size of the sample array.'''\n", + " s = rs**2\n", + " p = 3*(s+4*muon_mass**2)/(s-4*muon_mass**2)\n", + " q = 4*(2*r-1)*(s+2*muon_mass**2)/(s-4*muon_mass**2)\n", + " h = p**3/27+q**2/4\n", + " cos_t = np.cbrt(-q/2+np.sqrt(h))+np.cbrt(-q/2-np.sqrt(h))\n", + " rand_theta = np.arccos(cos_t)\n", + "\n", + " return rand_theta" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "# Plot scaled histogram\n", + "fig, ax = plt.subplots(figsize=(12,4))\n", + "\n", + "n, bins, _ = ax.hist(inv_cdf(E,np.random.random(N)), bins=50, color='orange', ec='black')\n", + "\n", + "d = (bins[1]-bins[0])\n", + "scaling = d * n.sum()\n", + "ax.plot(bins, pdf_theta_normalized(E,bins)*scaling, color='blue', label='PDF')\n", + "\n", + "plt.title('Histogram of accepted samples for'r'$ \\sqrt{S}=$'+str('%.5f' % E), fontsize=20)\n", + "plt.xlabel(r'$ \\theta [rad]$', fontsize=20)\n", + "plt.ylabel('Counts', fontsize=20)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To check that the distributions we are using are correct we compared them with Babayaga Event Generator [https://www2.pv.infn.it/~hepcomplex/babayaga.html] using as inputs the following values:\n", + "\n", + "* final state = mm \n", + "* ecms = 0.2200 GeV\n", + "* thmin = 0.0000 deg\n", + "* thmax = 180.0000 deg\n", + "* acoll. = 10.0000 deg\n", + "* emin = 0.0000 GeV\n", + "* ord = exp \n", + "* model = matched \n", + "* nphot mode = -1\n", + "* seed =700253512\n", + "* iarun = 1\n", + "* eps = .000500000\n", + "* darkmod = 0\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Comparison with BabaYaga algorithm\n", + "\n", + "file_data = np.loadtxt('matched_ep_th_exp_200.txt', usecols=(0,1,2))\n", + "\n", + "theta_bby,dcs = file_data[:,0],file_data[:,1]\n", + "centroid = theta_bby + (theta_bby[0] + theta_bby[1])/2\n", + "dcs = dcs / ((theta[1] - theta[0])*dcs).sum()\n", + "dcs =dcs/np.max(dcs)\n", + "\n", + "\n", + "\n", + "fig, ax = plt.subplots(figsize=(12,4))\n", + "\n", + "n, bins, _ = ax.hist(inv_cdf(E,np.random.random(N))*deg, bins=50, color='orange', ec='black')\n", + "ax.plot(theta_bby,dcs*np.max(n), linewidth=2.5, label='Babayaga results')\n", + "\n", + "plt.title('Comparison between project samples and Babayaga samples.', fontsize=20)\n", + "plt.xlabel(r'$ \\theta [°]$', fontsize=20)\n", + "plt.ylabel('Counts', fontsize=20)\n", + "plt.legend()\n", + "\n", + "\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#\n", + "###\n", + "####\n", + "#####\n", + "######\n", + "####### SIMULATION 1\n", + "######\n", + "#####\n", + "###\n", + "##\n", + "#" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "##################################################################################\n", + "#Simulation parameters\n", + "\n", + "delta = 0.001\n", + "E = 2 * muon_mass + delta #This is the proposed energy just above the threshold\n", + "N = 10**7\n", + "\n", + "###################################################################################" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Obtain the parameters distribution\n", + "theta_instances = inv_cdf(E,np.random.random(N))\n", + "#N_instances = len(theta_instances)\n", + "phi_instances = np.random.uniform(0., 2*np.pi, N)\n", + "\n", + "#The resulting space-momentum magnitude for each muon is the square of half the com energy minus the square of the muon mass.\n", + "p = np.sqrt(E**2/4-muon_mass**2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Obtain the muons momenta and build the file (Is it in the CoM frame?)\n", + "\n", + "def sph_to_cart(r,theta,phi):\n", + " '''Converts from spherical coordinates to cartesian coordinates'''\n", + " V = np.vstack([\n", + " r*np.sin(theta)*np.cos(phi),\n", + " r*np.sin(theta)*np.sin(phi),\n", + " r*np.cos(theta)\n", + " ])\n", + " return V\n", + "\n", + "pxm, pym, pzm = sph_to_cart(p, theta_instances, phi_instances)\n", + "\n", + "pxam = -pxm\n", + "pyam = -pym\n", + "pzam = -pzm" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "from IPython.display import Math\n", + "#Write the results to a file\n", + "\n", + "#print(r'$\\sqrt(s)$', '%.5f' % E, \"GeV\")\n", + "display(Math('\\sqrt s \\qquad\\qquad\\!\\!{} \\,\\,\\, GeV'.format(round(E,5))))\n", + "print('Norm of p ', '%.5f' % p, \"GeV\")\n", + "#file_name='muons_momentum_com.csv'\n", + "#data=pd.read_csv(file_name)\n", + "#data" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "plot_angles_hist(theta_instances*deg, phi_instances*deg,'orange','blue')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "plot_momenta_hist(pxm,pym,pzm,r'$\\mu^+$ momentum components in the center of mass frame','orange')\n", + "plot_momenta_hist(pxam,pyam,pzam,r'$\\mu^-$ momentum components in the center of mass frame','blue')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Lab frame is the frame where the electrons are at rest (in a target). In order to transpose the problem from the center of mass frame in this other frame, it is important to consider Special Relativity in the calculations, being the electron and positron highly energetic (in order to produce the muon pair).\n", + "\n", + "The generic boost in a frame moving with velocity $u$ in the z direction is:\n", + "\n", + "$$\\Lambda = \\left(\\begin{array}{c}\n", + " \\gamma & 0 & 0 & -u\\gamma \\\\\n", + " 0 & 1 & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " -u\\gamma & 0 & 0 & \\gamma \\\\ \n", + "\\end{array}\\right)$$\n", + "\n", + "In our case since the velocity is negative, the Lorentz Matrix for the electron moving at velocity $-v$ in the CoM frame is:\n", + "\n", + "$$\\Lambda = \\left(\\begin{array}{c}\n", + " \\gamma & 0 & 0 & v\\gamma \\\\\n", + " 0 & 1 & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " v\\gamma & 0 & 0 & \\gamma \\\\ \n", + "\\end{array}\\right)$$\n", + "\n", + "Since the electron is moving exclusively in the $z$ direction in the CoM frame, we can derive its velocity from the definition of relativistic momentum:\n", + "$$p=m_e\\gamma v\\to v\\gamma = \\frac{p}{m_e}\\to \\frac{v}{\\sqrt{1-v^2}}=\\frac{p}{m_e}\\to v= \\frac{p}{m_e\\sqrt{1+\\frac{p^2}{m_e^2}}}=\\frac{p}{\\sqrt{m_e^2 + p^2}}$$\n", + "\n", + "Notice that the energy of the particle in the COM is $E_p=\\sqrt{m_e^2+p^2}$ (the denominator)\n", + "\n", + "$$\\begin{cases}E_p^2=m_e^2+p^2\\\\ E^2_{CM}=4m_e^2+4p^2\\end{cases}$$\n", + "\n", + "then v becomes:\n", + "$$v=\\sqrt{ \\frac{E^2_{CM}-4m_e^2}{E^2_{CM}} }$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "################################################" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To boost from the CoM frame to the Lab frame the Lorentz matrix is the following:\n", + "\n", + "$$\\Lambda = \\left(\\begin{array}{c}\n", + " \\gamma & 0 & 0 & v\\gamma \\\\\n", + " 0 & 1 & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " v\\gamma & 0 & 0 & \\gamma \\\\ \n", + "\\end{array}\\right),\\qquad\\qquad v=\\sqrt{ \\frac{E^2_{CM}-4m_e^2}{E^2_{CM}} }$$\n", + "\n", + "To get the momenta of the muons in the Lab frame we need to apply the Lorentz matrix to their 4-momenta:\n", + "\n", + "$$\\Lambda^\\mu_\\nu P^\\nu = P'^\\mu$$\n", + "\n", + "Where $P^\\nu$ is the 4 momentum before the boosting (in the COM frame) and $P'^\\nu$ is the 4 momentum after the boosting (in the LAB frame)\n", + "\n", + "$$P=\\left(\\begin{array}{c}m\\gamma \\\\ p\\cos\\varphi \\\\ p\\sin\\varphi\\sin\\vartheta \\\\ p\\sin\\varphi\\cos\\vartheta\\end{array}\\right)$$\n", + "\n", + "\n", + "$$P'=\\left(\\begin{array}{c}\n", + " \\gamma & 0 & 0 & v\\gamma \\\\\n", + " 0 & 1 & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " v\\gamma & 0 & 0 & \\gamma \\\\ \n", + "\\end{array}\\right)\\left(\\begin{array}{c}m\\gamma \\\\ p\\cos\\varphi \\\\ p\\sin\\varphi\\sin\\vartheta \\\\ p\\sin\\varphi\\cos\\vartheta\\end{array}\\right)=\\left(\\begin{array}{c}m\\gamma^2 + \\gamma vp\\cos\\vartheta \\\\ p\\cos\\varphi \\\\ p\\sin\\vartheta\\\\ m\\gamma^2 v + \\gamma p\\cos\\vartheta \\end{array}\\right)$$\n", + "\n", + "During a Lorentz Boost in the z direction $\\varphi$ does not change, but $\\vartheta$ does. From the matricial equation above we can get the relationship $\\vartheta\\leftrightarrow\\vartheta'$ the angle of the scattered particle before and after the boosts:\n", + "\n", + "$$\\begin{cases}\n", + " m\\gamma^2v+\\gamma p\\cos\\vartheta = p'\\cos\\vartheta' \\\\\n", + " p\\sin\\vartheta = p\\sin\\vartheta'\n", + "\\end{cases}$$\n", + "\n", + "Writing $m\\gamma^2 v$ as $\\gamma p$ we have:\n", + "\n", + "$$\\begin{cases}\n", + " \\gamma p +\\gamma p\\cos\\vartheta = p'\\cos\\vartheta' \\\\\n", + " p\\sin\\vartheta = p\\sin\\vartheta'\n", + "\\end{cases}$$\n", + "\n", + "Dividing the first to the second we get:\n", + " $$\\tan\\vartheta'=\\frac{1}{\\gamma}\\left(\\frac{\\sin\\vartheta}{1+\\cos\\vartheta}\\right)$$" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Boost the results to the laboratory frame\n", + "def boost(v_i,x_0,x_i):\n", + " g = 1/np.sqrt(1-v_i**2)\n", + " b_x_0 = g*(x_0-v_i*x_i)\n", + " b_x_i = g*(x_i-v_i*x_0)\n", + " return b_x_0, b_x_i\n", + "\n", + "vz = -np.sqrt(1-4*electron_mass**2/E**2) \n", + "gamma = 1/np.sqrt(1-vz**2)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print('Gamma', '%.5f' % gamma)\n", + "print('Speed along z axis (vz)', '%.5f' % vz)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "pxm_lb = pxm\n", + "pym_lb = pym\n", + "E_lb, pzm_lb = boost(vz,E/2,pzm)\n", + "\n", + "pxam_lb = pxam \n", + "pyam_lb = pyam\n", + "_, pzam_lb = boost(vz,E/2,pzam)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Check the file\n", + "\n", + "#print(r'$\\sqrt(s)$', '%.5f' % E, \"GeV\")\n", + "display(Math('\\sqrt s \\qquad\\quad\\,{} \\,\\,\\, GeV'.format(round(E,5))))\n", + "print('Norm of p', '%.5f' % p, \"GeV\")\n", + "#file_name='/home/usuario/PoD/muons_momentum_lab.csv'\n", + "#data=pd.read_csv(file_name)\n", + "#data" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "plot_momenta_hist(pxm_lb,pym_lb,pzm_lb,r'$\\mu^+$ momentum components in the laboratory frame','orange')\n", + "plot_momenta_hist(pxm_lb,pym_lb,pzm_lb,r'$\\mu^-$ momentum components in the laboratory frame','blue')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "theta_lb = np.arccos(pzm_lb/np.sqrt(pxm_lb**2+pym_lb**2+pzm_lb**2))\n", + "phi_lb = np.arctan2(pym_lb,pxm_lb)\n", + "\n", + "plot_angles_hist(theta_lb*deg, phi_lb*deg, 'orange','blue')\n", + "\n", + "theta_max_t = 4 * electron_mass /E **2 * np.sqrt(E **2 /4. -muon_mass**2)\n", + "print('Maximum theta according to the theory [Antonelli]', \"{:.5f}\".format(theta_max_t*deg), \"deg\")\n", + "print('Maximum theta in the simulation ', \"{:.5f}\".format(np.max(theta_lb)*deg), \"deg\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "p_cm = -E**2/4 + pxm**2+pym**2+pzm**2\n", + "print('Squared four momentum in the CM frame',p_cm)\n", + "\n", + "p_lb = -E_lb**2 + pxm_lb**2+pym_lb**2+pzm_lb**2\n", + "print('Squared four momentum in the LB frame',p_lb)\n", + "\n", + "print('Muon energy in the laboratory frame',E_lb)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Visualization of the energy spread\n", + "\n", + "fig, ax = plt.subplots(figsize=(12,4))\n", + "\n", + "n, bins, _ = ax.hist(E_lb, bins=50, color='orange', ec='black')\n", + "plt.title(r'$\\mu^+$ energy spread in the laboratory frame.', fontsize=20)\n", + "plt.xlabel(' Energy [GeV]', fontsize=20)\n", + "plt.ylabel('Counts', fontsize=20)\n", + "plt.show()\n", + "\n", + "de_max_t = E / (2*electron_mass) * np.sqrt(E **2 /4 - muon_mass**2)\n", + "print('Difference between max and min energy of the muons according to the theory [Antonelli]', \"{:.5f}\".format(de_max_t), \"GeV\")\n", + "print('')\n", + "print('Difference between max and min energy of the muons', \"{:.5f}\".format(np.max(E_lb)-np.min(E_lb)), \"GeV\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Write the results to a file \n", + "\n", + "s1_muons_com = pd.DataFrame({'Theta' : theta_instances,'Phi' : phi_instances,'Muon px' : pxm, 'Muon py' : pym, 'Muon pz' : pzm})\n", + "#s1_muons_com.to_csv('s1_muons_momentum_com.csv', index=False)\n", + "\n", + "s1_muons_lab = pd.DataFrame({'Theta' : theta_lb,'Phi' : phi_lb,'Muon px' : pxm_lb, 'Muon py' : pym_lb, 'Muon pz' : pzm_lb})\n", + "#s1_muons_lab.to_csv('s1_muons_momentum_lab.csv', index=False)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#\n", + "###\n", + "####\n", + "#####\n", + "######\n", + "#######\n", + "######\n", + "#####\n", + "###\n", + "##\n", + "#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Properties of the target \n", + "6. assume a $3$ cm thick Beryllium block is used as target and a rate of positron on target of $10^6$ Hz. Compute the rescaling factor (weight) you need to apply to the $N$ simulated events such that they represent the statistics that would be gathered in a week of countinuous operations;\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The number of $\\mu^+ \\mu^-$ pairs produced per positron on the target is given by:\n", + "\n", + "\n", + "$$n(\\mu^+ \\mu^-) = n^+ \\rho^- l \\sigma(\\mu^+ \\mu^-)$$\n", + "\n", + "\n", + "where $n^+$ is the number of positrons, $\\rho^-$ is the electron density in the medium, $l$ is the thickness of the target, and $\\sigma(\\mu^+ \\mu^-)$ is the muon pairs production cross section. [Antonelli]\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "#We build a dataframe with some material properties to be analysed\n", + "\n", + "Material = ['H', 'He', 'Li', 'Be', 'B', 'C', 'Cu', 'W', 'Pb']\n", + "Z = [ 1 , 2, 3, 4, 5, 6, 29, 74, 82]\n", + "A = [1.00794, 4.0026, 6.941, 9.01218, 10.811, 12.0107, 63.546, 183.84, 207.2]\n", + "X0 = [900.6, 786, 156.2, 35.2, 22.2, 21.4, 1.4, 0.4, 0.6]\n", + "\n", + "properties_dic = {'Material': Material, 'Z': Z, 'A': A, 'X0': X0}\n", + "properties = pd.DataFrame(data=properties_dic)\n", + "properties\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "######\n", + "#Realistic target\n", + "positron_frequency = 1.e6 #[Hz]\n", + "target_length = 3 #[cm]\n", + "cs = cross_section(E)*10.e-31 #[uBarn]--> [cm^2]\n", + "time = 60 * 60 *24 *7 #[secconds]\n", + "\n", + "\n", + "properties['L'] = target_length\n", + "properties['Cross section'] = cs\n", + "\n", + "\n", + "#Number of positrons \n", + "N_positrons = positron_frequency * time \n", + "\n", + "#Number of muons\n", + "properties['N_muons'] = N_positrons * (properties['Z']*Avogadro_number/properties['A']) * properties['Cross section'] * properties['L']\n", + "\n", + "#Weight\n", + "rf = properties.at[3,'N_muons']/N\n", + "####" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "properties" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "print('Number of positrons produced in a week '\"{:.2e}\".format( N_positrons))\n", + "print('')\n", + "print('Number of simulated events '\"{:.2e}\".format( N ))\n", + "print('')\n", + "print('Rescaling factor if using Be as a target', '%.5f' % rf)\n", + "print('')\n", + "print('Number of muons produced after a week using Be as a target '\"{:.2e}\".format( properties.at[3,'N_muons']))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#\n", + "###\n", + "####\n", + "#####\n", + "######\n", + "####### \n", + "######\n", + "#####\n", + "###\n", + "##\n", + "#" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Properties of the beam\n", + "7. repeat what done so far simulating now the actual transverse shape and energy spread of the beam: for the former assume a flat distribution in a circle of radius $r=1$ cm and for the latter a gaussian distribution centered at the nominal beam energy and a width of $0.5$ GeV;" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "##################################################################################\n", + "#Simulation parameters\n", + "\n", + "N = 10**7 #Number of positrons\n", + "E_lab = 45 #GeV\n", + "sigma = 0.5 # mean and standard deviation\n", + "\n", + "###################################################################################" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Realistic beam\n", + "#Up to this point we have been assuming that the energy of the incident \n", + "#beam had a constant value, now we want to make a model where the energy\n", + "#of the beam has a gaussian distribution.\n", + "\n", + "E_lab_instances = np.random.normal(E_lab, sigma, N)\n", + "\n", + "#Now we need to boost them to the CoM frame\n", + "vz = np.sqrt((E_lab-electron_mass)/(E_lab+electron_mass))\n", + "gamma = 1/np.sqrt(1-vz**2)\n", + "\n", + "E_cm_instances = 2 *gamma*(E_lab_instances-vz*np.sqrt(E_lab_instances**2-electron_mass**2))" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "#Plot scaled histogram\n", + "fig, (ax1,ax2) = plt.subplots(nrows=2, ncols=1, figsize=(12, 10))\n", + "\n", + "n, bins, _ = ax1.hist(E_lab_instances, bins=90,color='orange', ec='black')\n", + "\n", + "d = (bins[1]-bins[0])\n", + "scaling = d * n.sum()\n", + "\n", + "ax1.plot(bins, scaling/(sigma * np.sqrt(2 * np.pi)) *np.exp( - (bins - E_lab)**2 / (2 * sigma**2) ),color='blue', label='Gaussian distribution media= sigma=')\n", + "\n", + "ax1.set_title('Positron beam energy distribution in the Lab frame', fontsize=15)\n", + "ax1.set_xlabel(' Energy [GeV]', fontsize=15)\n", + "ax1.set_ylabel('Counts', fontsize=15)\n", + "ax1.legend()\n", + "\n", + "n, bins, _ = ax2.hist(E_cm_instances, bins=90,color='orange', ec='black')\n", + "\n", + "d = (bins[1]-bins[0])\n", + "scaling = d * n.sum()\n", + "\n", + "ax2.axvline(x=2*muon_mass, label='Threshold energy')\n", + "#ax2.plot(bins, scaling/(sigma * np.sqrt(2 * np.pi)) *np.exp( - (bins - E_lab)**2 / (2 * sigma**2) ),color='blue', label='PDF')\n", + "ax2.set_title('Positron beam energy distribution in the CoM frame', fontsize=15)\n", + "ax2.set_xlabel(' Energy [GeV]', fontsize=15)\n", + "ax2.set_ylabel('Counts', fontsize=15)\n", + "ax2.legend()\n", + "\n", + "plt.subplots_adjust(top=0.8, wspace=0.4, hspace=0.4)\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "#Once we have the energy distribution plot a heatmap of the beam\n", + "\n", + "def circular_section(data):\n", + " \n", + " # specify circle parameters: centre ij and radius\n", + " pixels =len(data[0,:])\n", + " ci,cj = pixels/2 , pixels/2\n", + " cr=pixels/3\n", + "\n", + " # Create index arrays to z\n", + " I,J=np.meshgrid(np.arange(data.shape[0]),np.arange(data.shape[1]))\n", + "\n", + " # calculate distance of all points to centre\n", + " dist=np.sqrt((I-ci)**2+(J-cj)**2)\n", + "\n", + " # Assign value of 1 to those points where distcr)]=0\n", + " return data\n", + "\n", + "\n", + "\n", + "pixels=300\n", + "size =(-1.5,1.5,-1.5,1.5)\n", + "\n", + "# We randomly pick (pixel x pixels) elements of the energy distribution to plot the beam cross section\n", + "\n", + "z = np.random.choice(E_lab_instances, size=(pixels,pixels), replace=True, p=None) \n", + "\n", + "\n", + "plt.rcParams[\"figure.figsize\"] = (8,8)\n", + "plt.imshow(circular_section(z),cmap='plasma', extent=(size),origin='lower')\n", + "plt.title('Positron beam cross section',fontsize=17)\n", + "plt.ylabel(r'${y}$ [cm]',fontsize=17) \n", + "plt.xlabel(r'${x}$ [cm]',fontsize=17)\n", + "plt.colorbar()\n", + "plt.clim(np.min(E_lab_instances),np.max(E_lab_instances))\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#\n", + "###\n", + "####\n", + "#####\n", + "######\n", + "####### SIMULATION 2\n", + "######\n", + "#####\n", + "###\n", + "##\n", + "#" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "##################################################################################\n", + "#Simulation parameters\n", + "\n", + "N = 10**6 #Number of positrons \n", + "E_lab = 45 #GeV\n", + "sigma = 0.5 # mean and standard deviation\n", + "\n", + "###################################################################################" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "##Now that we have the energy distributions and also an idea of the shape\n", + "##we can repeat the previous part\n", + "\n", + "#Obtain the positron energy samples in the laboratory frame\n", + "E_lab_samples = np.random.normal(E_lab, sigma, N)\n", + "\n", + "#Boost of the positrons energy to the Center of Mass Frame\n", + "vz = np.sqrt((E_lab-electron_mass)/(E_lab+electron_mass))\n", + "gamma = 1/np.sqrt(1-vz**2)\n", + "\n", + "E_cm_samples = 2 *gamma*(E_lab_samples-vz*np.sqrt(E_lab_samples**2-electron_mass**2))\n", + "\n", + "#Filter the values below the threshold\n", + "E_cm_samples = E_cm_samples[E_cm_samples> 2* muon_mass]\n", + "\n", + "N_instances = len(E_cm_samples)\n", + "\n", + "theta_cm_instances = inv_cdf(E_cm_samples,np.random.random(N_instances))\n", + "\n", + "phi_cm_instances = np.random.uniform(0., 2*np.pi, N_instances)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Calculate the total momentum p CM\n", + "#Calculate the momentum components in CM\n", + "p_cm_instances = np.sqrt(E_cm_samples**2/4-muon_mass**2)\n", + "\n", + "pxm_cm, pym_cm, pzm_cm = sph_to_cart(p_cm_instances,theta_cm_instances,phi_cm_instances) \n", + "#Calculate the momentum components in LAB\n", + "vz = -np.sqrt(1-4*electron_mass**2/E_cm_samples**2) \n", + "gamma = 1/np.sqrt(1-vz**2)\n", + "\n", + "pxm_lb = pxm_cm\n", + "pym_lb = pym_cm\n", + "pzm_lb = gamma * pzm_cm - vz * gamma *E_cm_samples/2\n", + "\n", + "#Calculate the total momentum p LAB\n", + "#Obtain the angles thet and phi LAB\n", + "p_lb_instances = np.sqrt(pxm_lb**2 + pym_lb**2 + pzm_lb**2)\n", + "\n", + "theta_lb_instances = np.arccos(pzm_lb/p_lb_instances)\n", + "phi_lb_instances = np.arctan2(pym_lb,pxm_lb)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "plot_angles_hist(theta_cm_instances*deg,phi_cm_instances*deg,'orange','blue')\n", + "plot_angles_hist(theta_lb_instances*deg,phi_lb_instances*deg,'orange','blue')\n", + "\n", + "theta_max_t = 4 * electron_mass /np.max(E_cm_samples) **2 * np.sqrt(np.max(E_cm_samples) **2 /4. -muon_mass**2)\n", + "print('Maximum theta according to the theory [Antonelli]', \"{:.5f}\".format(theta_max_t*deg), \"deg\")\n", + "print('Maximum theta in the simulation ', \"{:.5f}\".format(np.max(theta_lb_instances)*deg), \"deg\")\n", + "print('The media for the theta angle ', \"{:.5f}\".format(np.average(theta_lb_instances)*deg), \"deg\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "plot_momenta_hist(pxm_cm,pym_cm,pzm_cm,r'$\\mu^+$ momentum components in the CoM frame','orange')\n", + "plot_momenta_hist(pxm_lb,pym_lb,pzm_lb,r'$\\mu^+$ momentum components in the LAB frame','dodgerblue')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Check of the four momenta\n", + "p_cm = -E_cm_samples**2/4 + pxm_cm**2+pym_cm**2+pzm_cm**2\n", + "print('Squared four momentum in the CM frame',p_cm)\n", + "\n", + "E_lb = gamma*(E_cm_samples/2-pzm_cm*vz)\n", + "p_lb = -E_lb**2 + pxm_lb**2+pym_lb**2+pzm_lb**2\n", + "print('Squared four momentum in the LB frame',p_lb)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Write the results to a file \n", + "\n", + "s2_muons_com = pd.DataFrame({'Theta' : theta_cm_instances,'Phi' : phi_cm_instances,'Muon px' : pxm_cm, 'Muon py' : pym_cm, 'Muon pz' : pzm_cm})\n", + "#s2_muons_com.to_csv('s2_muons_momentum_com.csv', index=False)\n", + "\n", + "s2_muons_lab = pd.DataFrame({'Theta' : theta_lb_instances,'Phi' : phi_lb_instances,'Muon px' : pxm_lb, 'Muon py' : pym_lb, 'Muon pz' : pzm_lb})\n", + "#s2_muons_lab.to_csv('s2_muons_momentum_lab.csv', index=False)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Aditional considerations\n", + "\n", + "8. given that the electrons traversing the target lose energy as $E(z)=E_0 \\exp{-z/X_0}$ (with z the longitudinal coordinate of the target, the one parallel to the beam direction and $X_0$ is the Beryllium radiation length), compute the nominal beam energy $E_0$ such that muon pairs can be generated along the whole length of the target;\n", + "9. (optional) take the former point into account when generating the events (i.e. the proccess $\\sqrt{s}$ depend on the position along the target where the $e^+ - e^-$ scattering occurrs.\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Plots of energy decay for different materials\n", + "x = np.linspace(0,3,num=100)\n", + "for i in range(0,8):\n", + " plt.plot(x, 45 * np.exp(-x/properties.at[i,'X0']),label = properties.at[i,'Material'])\n", + "plt.title('Energy decay for different materials', fontsize=15)\n", + "plt.xlabel('Penetration distance [cm]', fontsize=15)\n", + "plt.ylabel('Energy [Gev]', fontsize=15)\n", + "plt.legend()\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#\n", + "###\n", + "####\n", + "#####\n", + "######\n", + "####### SIMULATION 3\n", + "######\n", + "#####\n", + "###\n", + "##\n", + "#" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "##################################################################################\n", + "#Simulation parameters\n", + "\n", + "N = 10**6 #Number of positrons\n", + "E_lab = 45 #[GeV]\n", + "sigma = 0.5 # mean and standard deviation\n", + "\n", + "###################################################################################" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "E0_cm = 2 *muon_mass/np.exp(-target_length/properties.at[3,'X0'])\n", + "\n", + "print('Beryllium radiation length',properties.at[3,'X0'],'Cm')\n", + "print('Nominal beam energy in the CoM frame', '%.5f' % E0_cm, 'GeV')\n", + "\n", + "vz = -np.sqrt(1-4*electron_mass**2/E0_cm**2) \n", + "gamma = 1/np.sqrt(1-vz**2)\n", + "p = np.sqrt(E0_cm**2/4-muon_mass**2)\n", + "pzm = p * np.cos(0) \n", + "E0_lb = gamma*(E0_cm/2-pzm*vz)\n", + "\n", + "E0_lb =(2*muon_mass**2/electron_mass -electron_mass)*np.exp(target_length/properties.at[3,'X0']) ##CORRECT\n", + "print('Nominal beam energy in the Lab frame', '%.5f' % E0_lb, 'GeV')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#be generated along the whole length of the target as the media.\n", + "#E_lab = E0_lb \n", + "\n", + "#Obtain the positron energy samples in the laboratory frame\n", + "E_lab_samples = np.random.normal(E_lab, sigma, N)\n", + "\n", + "#We keep the distribution for ploting purposes\n", + "E_lab_plot = E_lab_samples \n", + "\n", + "#Now we distribute the energies according the position in the Beryllium plate\n", + "##########################################################################\n", + "x = np.random.uniform(low=0., high=target_length, size=(len(E_lab_samples),))\n", + "E_lab_samples = E_lab_samples*np.exp(-x/properties.at[3,'X0'])\n", + "##########################################################################\n", + "\n", + "#Boost of the positrons energy to the Center of Mass Frame\n", + "vz = np.sqrt((E_lab_samples-electron_mass)/(E_lab_samples+electron_mass)) \n", + "gamma = 1/np.sqrt(1-vz**2)\n", + "\n", + "E_cm_samples = 2 *gamma*(E_lab_samples-vz*np.sqrt(E_lab_samples**2-electron_mass**2))\n", + "\n", + "#Filter the values below the threshold\n", + "b = E_cm_samples[E_cm_samples> 2* muon_mass]\n", + "\n", + "N_instances = len(b)\n", + "\n", + "theta_cm_instances = inv_cdf(b,np.random.random(N_instances))\n", + "\n", + "phi_cm_instances = np.random.uniform(0., 2*np.pi, N_instances)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Energy distributions\n", + "fig, (ax1,ax2) = plt.subplots(nrows=1, ncols=2, figsize=(12, 4))\n", + "\n", + "n, bins, _ = ax1.hist(E_lab_plot, bins=50,color='orange', ec='grey')\n", + "ax1.set_title('Beam energy', fontsize=10)\n", + "ax1.set_xlabel(r'$Energy$ [GeV]', fontsize=15)\n", + "ax1.set_ylabel('Counts', fontsize=15)\n", + "#ax1.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + "ax1.xaxis.set_major_formatter(FormatStrFormatter('%.2f'))\n", + "\n", + "\n", + "n, bins, _ = ax2.hist(E_lab_samples, bins=50,color='orange', ec='grey')\n", + "ax2.set_title('Beam energy atenuation (material)', fontsize=10)\n", + "ax2.set_xlabel(r'$Energy$ [GeV]', fontsize=15)\n", + "#ax2.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + "ax2.xaxis.set_major_formatter(FormatStrFormatter('%.2f'))\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Calculate the total momentum p CM\n", + "#Calculate the momentum components in CM\n", + "p_cm_instances = np.sqrt(b**2/4-muon_mass**2)\n", + "\n", + "pxm_cm, pym_cm, pzm_cm = sph_to_cart(p_cm_instances, theta_cm_instances, phi_cm_instances)\n", + "\n", + "#Calculate the momentum components in LAB\n", + "vz = -np.sqrt(1-4*electron_mass**2/b**2) \n", + "gamma = 1/np.sqrt(1-vz**2)\n", + "\n", + "pxm_lb = pxm_cm\n", + "pym_lb = pym_cm\n", + "pzm_lb = gamma * pzm_cm - vz * gamma *b/2\n", + "\n", + "#Calculate the total momentum p LAB\n", + "#Obtain the angles thet and phi LAB\n", + "p_lb_instances = np.sqrt(pxm_lb**2 + pym_lb**2 + pzm_lb**2)\n", + "\n", + "theta_lb_instances = np.arccos(pzm_lb/p_lb_instances)\n", + "phi_lb_instances = np.arctan2(pym_lb,pxm_lb)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "plot_angles_hist(theta_cm_instances*deg,phi_cm_instances*deg,'orange','blue')\n", + "plot_angles_hist(theta_lb_instances*deg,phi_lb_instances*deg,'orange','blue')\n", + "\n", + "theta_max_t = 4 * electron_mass /np.max(b) **2 * np.sqrt(np.max(b) **2 /4. -muon_mass**2)\n", + "print('Maximum theta according to the theory [Antonelli]', \"{:.5f}\".format(theta_max_t*deg), \"deg\")\n", + "print('Maximum theta in the simulation ', \"{:.5f}\".format(np.max(theta_lb_instances)*deg), \"deg\")\n", + "print('The media for the theta angle ', \"{:.5f}\".format(np.average(theta_lb_instances)*deg), \"deg\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "scrolled": true + }, + "outputs": [], + "source": [ + "plot_momenta_hist(pxm_cm,pym_cm,pzm_cm,r'$\\mu^+$ momentum components in the CoM frame','orange')\n", + "plot_momenta_hist(pxm_lb,pym_lb,pzm_lb,r'$\\mu^+$ momentum components in the LAB frame','dodgerblue')" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Check of the four momenta\n", + "p_cm = -b**2/4 + pxm_cm**2+pym_cm**2+pzm_cm**2\n", + "print('Squared four momentum in the CM frame',p_cm)\n", + "\n", + "E_lb = gamma*(b/2-pzm_cm*vz)\n", + "p_lb = -E_lb**2 + pxm_lb**2+pym_lb**2+pzm_lb**2\n", + "print('Squared four momentum in the LB frame',p_lb)" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [ + "#Write the results to a file \n", + "\n", + "s3_muons_com = pd.DataFrame({'Theta' : theta_cm_instances,'Phi' : phi_cm_instances,'Muon px' : pxm_cm, 'Muon py' : pym_cm, 'Muon pz' : pzm_cm})\n", + "#s3_muons_com.to_csv('s3_muons_momentum_com.csv', index=False)\n", + "\n", + "s3_muons_lab = pd.DataFrame({'Theta' : theta_lb_instances,'Phi' : phi_lb_instances,'Muon px' : pxm_lb, 'Muon py' : pym_lb, 'Muon pz' : pzm_lb})\n", + "#s3_muons_lab.to_csv('s3_muons_momentum_lab.csv', index=False)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} diff --git a/.ipynb_checkpoints/theory-checkpoint.ipynb b/.ipynb_checkpoints/theory-checkpoint.ipynb new file mode 100644 index 0000000..08336b1 --- /dev/null +++ b/.ipynb_checkpoints/theory-checkpoint.ipynb @@ -0,0 +1,460 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 1) Differential cross section in the center of mass frame $\\sigma(\\vartheta,\\sqrt{s})$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Mandelstam variable s\n", + "The [Mandelstam variable](https://en.wikipedia.org/wiki/Mandelstam_variables) represents the squared of the 4-momenta for the in-going particles (and for the out-going particles too since the conservation of the 4 momentum)\n", + "\n", + "$$s=(p_1+p_2)^2=(p_3+p_4)^4$$\n", + "\n", + "Notice that $s$ represents the squared energy in the center of mass frame:\n", + "$$s=(E_{CM})^2$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This means that the function we are searching $\\sigma(\\vartheta,\\sqrt{s})\\equiv\\sigma(\\vartheta,E_{CM})$, after we find that we can apply a boost to the laboratory frame where the electron on the target are at rest (point 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Deriving the differential cross section" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Remember that we are in the center of mass frame, this means that the electron and positron will have opposite momentum in this frame" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The scattering equation can be found computing the scattering amplitude $\\mathcal{M}$ that can be seen as a sort of wave function sice its modulus squared is linked to the probability of the event to happend (for a given $\\vartheta$ and $\\sqrt{s}$).\n", + "$\\mathcal{M}$ depends on the spin interactions of the particles, we will just compute\n", + "$$X=\\frac{1}{4}\\sum M$$ that represent the mean $\\mathcal{M}$ between all types of spin interactions (unpolarized cross section approximation)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are 3 possible versions of the differential cross section depending on the approximation you can make:\n", + "* $\\textbf{No approximations}$: this formula is pretty ugly and not necessary as the second one is way easier to implement and still be a good approximation\n", + "* $\\textbf{Neglecting $m_e$ in the energy term}$ this can make sense since the rest mass energy is $2 m_\\mu $: the contribution of the energy of the rest mass of electrons is way smaller\n", + "$$\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{CM}=\\frac{\\alpha^2}{16\\, s^2}\\frac{|p'|}{\\sqrt{s}}\\left(s+p'^2\\cos^2\\vartheta+m_\\mu^2\\right)$$\n", + "* In $\\textbf{ultrarelativistic limit}$, the muons are so energetic that we can neglet their rest mass energy, this means:\n", + "$E>>m_\\mu\\rightarrow s>>m_\\mu^2\\\\\n", + "|p|\\approx E$\n", + "\n", + " The formula from before becomes: $$\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{CM}=\\frac{\\alpha^2}{16 s}(1+\\cos^2\\vartheta)$$\n", + " However in the assignment it is clearly stated that the energy we are dealing with are in the order of $m_\\mu$ $(\\sqrt{s}\\sim m_\\mu)$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The differential cross section we choosed is then $$\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{CM}=\\frac{\\alpha^2}{16\\, s^2}\\frac{|p'|}{\\sqrt{s}}\\left(s+p'^2\\cos^2\\vartheta+m_\\mu^2\\right)$$\n", + "The relativistic total energy is $$E_{CM}^2=2p'^2c^2+4m_\\mu^2c^4\\rightarrow p'^2=\\frac{E_{CM}^2}{2c^2}-2m_\\mu^2c^2\\rightarrow p'^2=\\frac{s}{2c^2}-2m_\\mu^2c^2$$\n", + "Then our differential cross section becomes:\n", + "$$\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{CM}=\\frac{\\alpha^2}{16\\, s^2}\\sqrt{\\frac{{\\frac{s}{2c^2}-2m_\\mu^2c^2}}{{s}}}\\left(s+\\left(\\frac{s}{2c^2}-2m_\\mu^2c^2\\right)\\cos^2\\vartheta+m_\\mu^2\\right)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 2) The energy and angle distributions $\\sigma\\left(\\sqrt{s}\\right)$ and $\\sigma(\\vartheta)$\n", + "\n", + "We can see $\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{CM}\\equiv \\sigma(\\vartheta,\\sqrt{s})$ as a [joint probability distribution](https://en.wikipedia.org/wiki/Joint_probability_distribution) i.e the probability of the event to happend with a specific $\\vartheta$ AND $\\sqrt{s}$.\n", + "If we integrate $\\sigma(\\vartheta,\\sqrt{s})$ in one of the two variable, we get the [marginal distribution](https://en.wikipedia.org/wiki/Marginal_distribution) for the other variable: for example if we integrate $\\sigma(\\vartheta,\\sqrt{s})$ in $\\sqrt{s}$ we obtain a certain function (distribution) for the other variable:\n", + "\n", + "$$\\int\\sigma(\\vartheta,\\sqrt{s})\\,d(\\sqrt{s})\\equiv \\sigma(\\vartheta)$$\n", + "\n", + "$\\sigma(\\vartheta)$ represents the probability for the event to happend according to a certain $\\vartheta$ independing of the energy $\\sqrt{s}$\n", + "\n", + "(and $\\sigma(\\sqrt{s})$ is obtained integrating in $\\vartheta$ and represents the probabiliy for the event to happend at a certain energy ($\\sqrt{s}$) for any given $\\vartheta$)\n", + "\n", + "Let's obtain those two distributions:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Deriving $\\sigma(\\vartheta)$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Oh God" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Deriving $\\sigma\\left(\\sqrt{s}\\right)$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By integrating in $\\vartheta\\in[0,2\\pi]$ we get\n", + "$$\\sigma(\\sqrt{s})=\\frac{\\pi\\alpha^2}{8}\\frac{1}{(\\sqrt{s})^5}\\left[\\sqrt{\\frac{1}{2c^2}(\\sqrt{s})^2-2m_\\mu^2c^2}\\left((\\sqrt{s})^2\\left(1+\\frac{1}{4c^2}\\right)-m_\\mu^2\\left(1+c^2\\right)\\right)\\right]$$\n", + "Note that the argument in the $\\sqrt{\\quad}$ must be positive, this means:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\\sqrt{\\frac{1}{2c^2}(\\sqrt{s})^2-2m_\\mu^2c^2}\\geq0$$\n", + "\n", + "$$\\sqrt{\\frac{1}{2c^2}(E)^2-2m_\\mu^2c^2}\\geq0$$\n", + "\n", + "$$\\sqrt{(E)^2-4m_\\mu^2c^4}\\geq0$$\n", + "\n", + "$$ \\sqrt{s}=E_{CM}\\geq 2m_\\mu c^2$$" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "import math\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": {}, + "outputs": [], + "source": [ + "def sigma_of_sqrts(e):\n", + " alpha = 1\n", + " m_mu = 1\n", + " c = 1\n", + "\n", + " return ((math.pi*alpha*alpha)/8)/(math.pow(e,5))*math.sqrt( ((e*e)/(2*c*c)) - 2*m_mu*m_mu*c*c )*( e*e*(1+1/(4*c*c)) - m_mu*m_mu*(1+c*c) )" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": {}, + "outputs": [], + "source": [ + "m_mu = 1\n", + "c = 1\n", + "energies = np.arange(20)\n", + "energies = energies/30 + 2*m_mu*c*c\n", + "\n", + "ss = []\n", + "for i in range(np.size(energies)):\n", + " ss.append(sigma_of_sqrts(energies[i]))" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(1.5, 0.02, 'threshold energy')" + ] + }, + "execution_count": 18, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "plt.figure(figsize=(10, 3))\n", + "plt.plot(energies, ss, '-o')\n", + "plt.xlim(0,)\n", + "plt.plot([2, 2], [0, .025], color='r', linestyle='-', linewidth=1, alpha = 0.5)\n", + "plt.xlabel(\"centre of mass energy\")\n", + "plt.ylabel(\"cross section\")\n", + "plt.text(1.5, .02, 'threshold energy', fontsize=10, color='r')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 3) Bosting to the laboratory frame" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have to apply a boost for the resulting momenta to get the result in the laboratory frame, that is the frame where the electron are at rest (in a target).\n", + "To get the boost application we have to find the electrons momentum in the centre of mass frame, not a problem since we know its energy and mass." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Deriving the Lorentz matrix $\\Lambda$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have to boost in a frame where the electron $e^-$ is at rest, this means that we have to find the velocity of the electron in the COM frame and since the velocity is negative we will find a Lorentz matrix of the following form:\n", + "$$\\left(\\begin{array}\n", + " &\\gamma &-v\\gamma & 0 & 0 \\\\\n", + " -v\\gamma & \\gamma & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " 0 & 0 & 0 & 1 \\\\ \n", + "\\end{array}\\right)\\Rightarrow\\left(\\begin{array}\n", + " &\\gamma &v\\gamma & 0 & 0 \\\\\n", + " v\\gamma & \\gamma & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " 0 & 0 & 0 & 1 \\\\ \n", + "\\end{array}\\right)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since the particle $e^-$ is moving in the direction $\\hat{x}$, we can easily find the velocity using the definition of the relativistic momentum:\n", + "$$p=m_e\\gamma v\\to v\\gamma = \\frac{p}{m_e}\\to \\frac{v}{\\sqrt{1-v^2}}=\\frac{p}{m_e}\\to v= \\frac{p}{m_e\\sqrt{1+\\frac{p^2}{m_e^2}}}=\\frac{p}{\\sqrt{m_e^2 + p^2}}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the energy of the particle in the COM is $E_p=\\sqrt{m_e^2+p^2}$ (the denominator)\n", + "\n", + "$$\\begin{cases}E_p^2=m_e^2+p^2\\\\ E^2_{CM}=4m_e^2+4p^2\\end{cases}$$\n", + "\n", + "v then becomes:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$v=\\sqrt{ \\frac{E^2_{CM}-4m_e^2}{E^2_{CM}} }$$" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": {}, + "outputs": [], + "source": [ + "def velocity(ecm):\n", + " me = 1\n", + " k = 0.05 # just for plotting purposes\n", + " return k*math.sqrt(ecm*ecm - 4*me*me)/ecm\n", + "\n", + "ecm = np.arange(2,2.6,0.1)\n", + "v = []\n", + "for i in range(np.size(ecm)):\n", + " v.append(velocity(ecm[i]))\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'cross section')" + ] + }, + "execution_count": 40, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 3))\n", + "plt.plot(energies, ss, '-o',color = 'g')\n", + "plt.plot(ecm, v, '-o',color='b')\n", + "plt.plot([2, 2], [0, .02], color='r', linestyle='-', linewidth=1, alpha = 0.5)\n", + "plt.xlabel(\"centre of mass energy\")\n", + "plt.ylabel(\"cross section\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Lorentz transformation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Lorentz matrix is then:\n", + "$$\\left(\\begin{array}\n", + " &\\gamma &v\\gamma & 0 & 0 \\\\\n", + " v\\gamma & \\gamma & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " 0 & 0 & 0 & 1 \\\\ \n", + "\\end{array}\\right),\\qquad\\qquad v=\\sqrt{ \\frac{E^2_{CM}-4m_e^2}{E^2_{CM}} }$$\n", + "Let's see how a boost work:\n", + "$$\\Lambda^\\mu_\\nu P^\\nu = P'^\\mu$$\n", + "Where $P^\\nu$ is the 4 momentum before the boosting (in the COM frame) and $P'^\\nu$ is the 4 momentum after the boosting (in the LAB frame)\n", + "\n", + "$$P^\\mu=\\left(\\begin{array}{c}m\\gamma \\\\ p\\cos\\vartheta \\\\ p\\sin\\vartheta\\\\ 0 \\end{array}\\right)$$\n", + "\n", + "$m\\gamma$ is the total energy of the particle $E_p$ (you can write $E_p$ either as $m\\gamma$ or the formula with the squared root, that is the same)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$P'=\\left(\\begin{array}\n", + " &\\gamma &v\\gamma & 0 & 0 \\\\\n", + " v\\gamma & \\gamma & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " 0 & 0 & 0 & 1 \\\\ \n", + "\\end{array}\\right)\\left(\\begin{array}{c}m\\gamma \\\\ p\\cos\\vartheta \\\\ p\\sin\\vartheta\\\\ 0 \\end{array}\\right)=\\left(\\begin{array}{c}m\\gamma^2 + \\gamma vp\\cos\\vartheta \\\\ m\\gamma^2 v + \\gamma p\\cos\\vartheta \\\\ p\\sin\\vartheta\\\\ 0 \\end{array}\\right)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can check that $P^2=P'^2=-m^2$ since it is a scalar it is invariant under lorentz boost, it is just to check if the boost is done correctly (I already checked)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From here we can get the relationship $\\vartheta\\leftrightarrow\\vartheta'$ the angle of the scattered particle before and after the boosts (yes it changes using special relativity!)\n", + "\n", + "$$\\begin{cases}\n", + " m\\gamma^2v+\\gamma p\\cos\\vartheta = p'\\cos\\vartheta' \\\\\n", + " p\\sin\\vartheta = p\\sin\\vartheta'\n", + "\\end{cases}$$\n", + "\n", + "Writing $m\\gamma^2 v$ as $\\gamma p$ we have\n", + "\n", + "$$\\begin{cases}\n", + " \\gamma p +\\gamma p\\cos\\vartheta = p'\\cos\\vartheta' \\\\\n", + " p\\sin\\vartheta = p\\sin\\vartheta'\n", + "\\end{cases}$$\n", + "\n", + "Dividing the first to the second we get:\n", + " $$\\tan\\vartheta'=\\frac{1}{\\gamma}\\left(\\frac{\\sin\\vartheta}{1+\\cos\\vartheta}\\right)$$\n", + " \n", + "Here you can play with an [interactive desmos graph](https://www.desmos.com/calculator/n1ldtauxer), g is the $gamma$ factor, for $g=1$ we have no boost and the transformation $\\vartheta\\leftrightarrow\\vartheta'$ is indeed identical" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/Muons_project.ipynb b/Muons_project.ipynb new file mode 100644 index 0000000..81777b2 --- /dev/null +++ b/Muons_project.ipynb @@ -0,0 +1,2625 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Simulation of a positron-induced Muon Source (part 1)\n", + "\n", + "## Laboratory of Computational Physics Mod. A, Professor Marco Zanetti\n", + "\n", + "### Authors:\n", + "* Saverio Monaco\n", + "* Marianna Zerajic De Giorgio\n", + "* Javier Gerardo Carmona\n", + "* Hilario Capettini \n", + "\n", + "### Description\n", + "\n", + "The production of a high brillance muon beam is one of the most important challenge for the future of Particle Physics. A particularly interesting idea consists of shooting high energy positrons on a target, aiming at the production of muons by means of the process $e^+ + e^- \\rightarrow \\mu^+ + \\mu^-$. To mimize the divergence of the resulting \"muon beam\", the positrons energy is chosen so that the reaction occurs close to threshold (assuming the electrons in the target to be at rest). The main goal of this project is to produce a Monte Carlo simulation of such a process. \n" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "#Import the required packages\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "from scipy import stats\n", + "import scipy.integrate as integrate\n", + "import csv\n", + "import pandas as pd\n", + "from matplotlib.ticker import FormatStrFormatter\n", + "import math\n", + "from IPython.display import Math\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Analytical part\n", + "\n", + "1. Compute the process leading-order cross section, $\\sigma(\\theta; \\sqrt{s})$, as a function of the scattering angle $\\theta$ and with the center of mass energy $\\sqrt{s}$ as a parameter. Start by computing it in the center of mass system. N.B.: textbooks reports such cross section in the relativistic limit, i.e. for $\\sqrt{s}\\gg m_\\mu$, which is clearly not the case here ($\\sqrt{s}\\sim 2m_\\mu$);\n", + "\n", + "2. compute and display the angle and momentum components distributions of the emerging muon pairs;\n", + "\n", + "3. boost muons four-momenta in the laboratory frame, i.e. in the frame where the electron is at rest and the positron has enough energy to give rise to the process;" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Derivation of the Probability Density for Scattering Angle\n", + "\n", + "The center of mass frame differential cross section was obtained following [MANDL]:\n", + "\n", + "$$\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{CM}=\\frac{2\\,\\alpha^2}{s^2}\\frac{|p'|}{\\sqrt{s}}\\left(\\frac{s}{4}+p'^2\\cos^2\\vartheta+m_\\mu^2\\right)$$\n", + "\n", + "Using the relativistic total energy expression $$E_{CM}^2=4p'^2+4m_\\mu^2\\rightarrow p'^2=\\frac{E_{CM}^2}{4}-m_\\mu^2\\rightarrow p'^2=\\frac{s}{4}-m_\\mu^2$$\n", + "\n", + "The differential cross section can be rewritten as:\n", + "$$\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{CM}=\\frac{2\\,\\alpha^2}{s}\\sqrt{\\frac{1}{4}-\\frac{m_\\mu^2}{s}}\\left[\\left(\\frac{1}{4}+\\frac{m_\\mu^2}{s}\\right)+\\left(\\frac{1}{4}- \\frac{m_\\mu^2}{s}\\right)\\cos^2{\\vartheta}\\right]$$\n", + "\n", + "Integrating over the solid angle we obtain the total cross section as a function of the total center of mass energy:\n", + "$$\\sigma(s)=\\frac{8\\pi\\,\\alpha^2}{3\\,s}\\sqrt{\\frac{1}{4}-\\frac{m_\\mu^2}{s}}\\left[1 + 2\\frac{m_\\mu^2}{s}\\right]$$\n", + "\n", + "To obtain the Probability Density Function (PDF) the integration must be performed only over the azymuthal angle $\\varphi$ and as a result we obtain a function of the polar angle $\\vartheta$ with the center of mass energy $\\sqrt{s}$ as a parameter.\n", + "$$PDF(\\vartheta)=\\frac{4\\pi\\,\\alpha^2}{s}\\sqrt{\\frac{1}{4}-\\frac{m_\\mu^2}{s}}\\left[\\left(\\frac{1}{4}+\\frac{m_\\mu^2}{s}\\right)+\\left(\\frac{1}{4}- \\frac{m_\\mu^2}{s}\\right)\\cos^2{\\vartheta}\\right]\\sin(\\vartheta)$$\n", + "\n", + "Which becomes a normalized expression once it's divided by the total cross-section:\n", + "$$\\text{pdf}(\\vartheta)=\\frac{PDF(\\vartheta)}{\\sigma(s)}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Lab frame is the frame where the electrons are at rest, and thus considered to be the target. It is by means of Lorentz boosts that we will transform the simulated data from the center of mass frame to the laboratory frame.\n", + "\n", + "The generic boost in a frame moving with velocity $u$ in the $Z$ direction is:\n", + "\n", + "$$\\Lambda = \\left(\\begin{array}{c c c c}\n", + " \\gamma & 0 & 0 & -u\\gamma \\\\\n", + " 0 & 1 & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " -u\\gamma & 0 & 0 & \\gamma \\\\ \n", + "\\end{array}\\right)$$\n", + "\n", + "In this case, the electron's rest reference frame moves with speed $v$ in the negative $Z$ direction of the Center of mass frame. Therefore, the Lorentz Matrix becomes:\n", + "\n", + "$$\\Lambda = \\left(\\begin{array}{c c c c}\n", + " \\gamma & 0 & 0 & v\\gamma \\\\\n", + " 0 & 1 & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " v\\gamma & 0 & 0 & \\gamma \\\\ \n", + "\\end{array}\\right)$$\n", + "\n", + "We can derive the magnitude of this velocity from the definition of relativistic momentum:\n", + "\n", + "$$p=m_e\\gamma v\\to v\\gamma = \\frac{p}{m_e}\\to \\frac{v}{\\sqrt{1-v^2}}=\\frac{p}{m_e}\\to v= \\frac{p}{m_e\\sqrt{1+\\frac{p^2}{m_e^2}}}=\\frac{p}{\\sqrt{m_e^2 + p^2}}$$\n", + "\n", + "Notice that the energy of the particle in the CoM, namely, $E_p=\\sqrt{m_e^2+p^2}$, is half of the total energy in the CoM frame. Thus\n", + "\n", + "$$\\begin{align}E^2_{CM}&=4m_e^2+4p^2\\end{align}$$\n", + "\n", + "then $v$ becomes:\n", + "$$v=\\sqrt{ \\frac{E^2_{CM}-4m_e^2}{E^2_{CM}} }$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To boost from the CoM frame to the Lab frame the Lorentz matrix is the following:\n", + "\n", + "$$\\Lambda = \\left(\\begin{array}{c c c c}\n", + " \\gamma & 0 & 0 & v\\gamma \\\\\n", + " 0 & 1 & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " v\\gamma & 0 & 0 & \\gamma \\\\ \n", + "\\end{array}\\right),\\qquad\\qquad v=\\sqrt{ \\frac{E^2_{CM}-4m_e^2}{E^2_{CM}} }$$\n", + "\n", + "To get the momenta of the muons in the Lab frame we need to apply the Lorentz matrix to their 4-momenta:\n", + "\n", + "$$\\Lambda^\\mu_\\nu P^\\nu = P'^\\mu$$\n", + "\n", + "Where $P^\\nu$ is the 4 momentum before the boosting (in the COM frame) and $P'^\\nu$ is the 4 momentum after the boosting (in the LAB frame)\n", + "\n", + "$$P=\\left(\\begin{array}{c}m\\gamma \\\\ p\\cos\\varphi\\sin\\vartheta \\\\ p\\sin\\varphi\\sin\\vartheta \\\\ p\\cos\\vartheta\\end{array}\\right)$$\n", + "\n", + "\n", + "$$P'=\\left(\\begin{array}{c c c c}\n", + " \\gamma & 0 & 0 & v\\gamma \\\\\n", + " 0 & 1 & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " v\\gamma & 0 & 0 & \\gamma \\\\ \n", + "\\end{array}\\right)\\left(\\begin{array}{c}m\\gamma \\\\ p\\cos\\varphi\\sin\\vartheta \\\\ p\\sin\\varphi\\sin\\vartheta \\\\ p\\cos\\vartheta\\end{array}\\right)=\\left(\\begin{array}{c}m\\gamma^2 + \\gamma vp\\cos\\vartheta \\\\ p\\cos\\varphi\\sin\\vartheta \\\\ p\\sin\\varphi\\sin\\vartheta\\\\ m\\gamma^2 v + \\gamma p\\cos\\vartheta \\end{array}\\right)$$\n", + "\n", + "During a Lorentz Boost in the z direction $\\varphi$ does not change, but $\\vartheta$ does. From the tensorial equation above we can get the relation between $\\vartheta$ and $\\vartheta'$, the angle of the scattered particle before and after the boosts:\n", + "\n", + "$$\\begin{cases}\n", + " m\\gamma^2v+\\gamma p\\cos\\vartheta = p'\\cos\\vartheta' \\\\\n", + " p\\sin\\vartheta = p'\\sin\\vartheta'\n", + "\\end{cases}$$\n", + "\n", + "Writing $m\\gamma^2 v$ as $\\gamma p$ we have:\n", + "\n", + "$$\\begin{cases}\n", + " \\gamma p +\\gamma p\\cos\\vartheta = p'\\cos\\vartheta' \\\\\n", + " p\\sin\\vartheta = p'\\sin\\vartheta'\n", + "\\end{cases}$$\n", + "\n", + "Dividing the first to the second we get:\n", + " $$\\tan\\vartheta'=\\frac{1}{\\gamma}\\left(\\frac{\\sin\\vartheta}{1+\\cos\\vartheta}\\right)$$" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "#Define the universal constants\n", + "muon_mass = 0.1056583745 #[GeV]\n", + "electron_mass = 0.00051099894 #[GeV]\n", + "alpha = 0.007297 #[]\n", + "Avogadro_number = 6.02214076e23 #[#/mol]\n", + "#Conversion constants\n", + "gev_to_ub = 389.379 #[GeV^{-2}]\n", + "deg = 180/np.pi #[deg/rad]\n" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "#rs is the sqrt(s)= E\n", + "#The units are Barn so 1ub = 2.56819e-3 GeV^-2\n", + "\n", + "def cross_section(rs):\n", + " '''Takes the com energy rs in GeV and returns the total cross section in ub.'''\n", + " s = rs**2\n", + " sigma = 8 *np.pi * alpha**2 / (3*s) *\\\n", + " np.sqrt(1/4 - muon_mass**2 / s) *\\\n", + " (1 + 2 * muon_mass**2 / s)\n", + "\n", + " return sigma * gev_to_ub\n", + "\n", + "\n", + "def diff_cross_section(rs,theta):\n", + " '''Takes the com energy rs in GeV, an angle theta in radians and returns the corresponding differential cross section in ub.'''\n", + " s =rs**2\n", + " dsigma = 2 * alpha**2 / s *\\\n", + " np.sqrt(1/4 - muon_mass**2 / s) *\\\n", + " (1/4 + muon_mass**2 / s + (1/4 - muon_mass**2 / s)*np.cos(theta)**2)\n", + "\n", + " return dsigma * gev_to_ub\n", + "\n", + "def pdf_theta(rs,theta):\n", + " '''Gives the (not normalized) probability density for a scattering angle theta in radians for a scattering with com energy rs in GeV.'''\n", + " y = 2*np.pi *np.sin(theta)*diff_cross_section(rs,theta)\n", + "\n", + " return y\n", + " \n", + "def pdf_theta_normalized(rs,theta):\n", + " '''Gives the (normalized) probability density for a scattering angle theta in radians for a scattering with com energy rs in GeV.'''\n", + " y =pdf_theta(rs,theta)/cross_section(rs)\n", + "\n", + " return y\n", + "\n", + "# Following the boost discussion, we also define a simple boost function\n", + "def boost(v_i,x_0,x_i):\n", + " '''Returns the temporal coordinate and the spatial coordinate that result from a boost with velocity v_i, assumed to be on the axis of the x_i coordinate.'''\n", + " g = 1/np.sqrt(1-v_i**2) # Gamma\n", + " b_x_0 = g*(x_0-v_i*x_i) # Boosted temporal coordinate\n", + " b_x_i = g*(x_i-v_i*x_0) # Boosted spatial coordinate\n", + "\n", + " return b_x_0, b_x_i\n" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [], + "source": [ + "#Functions\n", + "def plot_momenta_hist(px,py,pz,title,color):\n", + " '''Takes the momentum components samples (px, py, pz) and plots a histogram for each component.'''\n", + " fig, (ax1,ax2,ax3) = plt.subplots(nrows=1, ncols=3, figsize=(12, 4))\n", + " \n", + " n, bins, _ = ax1.hist(px, bins=50,color=color, ec='grey')\n", + " ax1.set_xlabel(r'$p_x$ [GeV]', fontsize=15)\n", + " ax1.set_ylabel('Counts', fontsize=15)\n", + " ax1.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + " ax1.xaxis.set_major_formatter(FormatStrFormatter('%.2f'))\n", + "\n", + "\n", + " n, bins, _ = ax2.hist(py, bins=50,color=color, ec='grey')\n", + " ax2.set_xlabel(r'$p_y$ [GeV]', fontsize=15)\n", + " ax2.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + " ax2.xaxis.set_major_formatter(FormatStrFormatter('%.2f'))\n", + "\n", + "\n", + "\n", + " n, bins, _ = ax3.hist(pz, bins=50,color=color, ec='grey')\n", + " ax3.set_xlabel(r'$p_z$ [GeV]', fontsize=15)\n", + " ax3.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + " ax3.xaxis.set_major_formatter(FormatStrFormatter('%.2f'))\n", + " \n", + " fig.suptitle(title, fontsize=20)\n", + "\n", + " plt.show() \n", + " \n", + "def plot_angles_hist(theta,phi,colort,colorp,title):\n", + " '''Takes the angular components samples (theta, phi) and plots a histogram for each component.'''\n", + " fig, (ax1,ax2) = plt.subplots(nrows=1, ncols=2, figsize=(12, 4))\n", + "\n", + " n, bins, _ = ax1.hist(theta, bins=50,color=colort, ec='black')\n", + " ax1.set_xlabel(r'$\\theta$ [°]', fontsize=20)\n", + " ax1.set_ylabel('Counts', fontsize=20)\n", + " ax1.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + "\n", + " n, bins, _ = ax2.hist(phi, bins=50,color=colorp, ec='black')\n", + " ax2.set_xlabel(r'$\\phi$ [°]', fontsize=20)\n", + " ax2.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + " \n", + " fig.suptitle(title, fontsize=20)\n", + " plt.show()\n", + "\n", + "def circular_section(data):\n", + " \n", + " # specify circle parameters: centre ij and radius\n", + " pixels =len(data[0,:])\n", + " ci,cj = pixels/2 , pixels/2\n", + " cr=pixels/3\n", + "\n", + " # Create index arrays to z\n", + " I,J=np.meshgrid(np.arange(data.shape[0]),np.arange(data.shape[1]))\n", + "\n", + " # calculate distance of all points to centre\n", + " dist=np.sqrt((I-ci)**2+(J-cj)**2)\n", + "\n", + " # Assign value of 1 to those points where distcr)]=0\n", + " return data\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Analysis" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "##################################################################################\n", + "#Analysis parameters\n", + "delta = 0.001\n", + "E = 2 * muon_mass + delta #This is the proposed energy just above the threshold\n", + "N = 10**7\n", + "\n", + "###################################################################################" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Total relativistic energy in CoM: 0.21232 GeV\n", + "Cross section: 0.27927 $micro barn\n" + ] + } + ], + "source": [ + "print(\"Total relativistic energy in CoM: \", '%.5f' % E, \"GeV\")\n", + "print(\"Cross section:\", '%.5f' % cross_section(E), '$micro barn')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(6,6))\n", + "theta = np.linspace(0,np.pi)\n", + "ax.plot(theta*deg, diff_cross_section(E,theta),color='blue', label='PDF')\n", + "\n", + "plt.title(r'Differential cross section for $\\sqrt{s}=$'+str('%.3f' % E)+str(\" GeV\"),\\\n", + " fontsize=15, pad = 20)\n", + "plt.xlabel(r'$ \\theta \\,[°] $', fontsize=15)\n", + "plt.ylabel(r'$ \\frac{d\\sigma}{d\\Omega} \\,[\\mu b]$', fontsize=15)\n", + "plt.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(-3,-3))\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(12, 6))\n", + "rs = np.linspace(2*muon_mass, 0.5)\n", + "ax1.plot(rs, cross_section(rs),color='blue', label='PDF')\n", + "\n", + "ax1.set_title('Total cross section', fontsize=15)\n", + "ax1.set_xlabel(r'$ \\sqrt{S}\\,[GeV]$', fontsize=15)\n", + "ax1.set_ylabel(r'$ \\sigma\\,[\\mu b]$', fontsize=15)\n", + "\n", + "rs = np.linspace(2*muon_mass, 0.23)\n", + "ax2.plot(rs, cross_section(rs),color='blue', label='PDF')\n", + "\n", + "ax2.set_title('Total cross section', fontsize=15)\n", + "ax2.set_xlabel(r'$ \\sqrt{S}\\,[GeV]$', fontsize=15)\n", + "ax2.set_ylabel(r'$ \\sigma\\,[\\mu b]$', fontsize=15)\n", + "ax2.set_xlim(0.21,0.23)\n", + "ax2.xaxis.set_major_formatter(FormatStrFormatter('%.3f'))\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 9, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Angular distribution\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Check the normalization\n", + "Integral of the PDF in [0,pi] 0.27927\n", + "Integral of the normalized PDF in [0,pi] 1.00000\n" + ] + } + ], + "source": [ + "print('Angular distribution')\n", + "fig, (ax1, ax2) = plt.subplots(nrows=1, ncols=2, figsize=(12, 6))\n", + "\n", + "theta = np.linspace(0, np.pi)\n", + "\n", + "\n", + "ax1.plot(theta*deg, pdf_theta(E,theta),color='blue', label='PDF')\n", + "ax1.set_title(r'$ PDF(\\theta)$ for $\\sqrt{s}=$'+str('%.5f' % E)+str(\" GeV\"), fontsize=15)\n", + "ax1.set_xlabel(r'$ \\theta [°] $', fontsize=20)\n", + "ax1.set_ylabel(r'$ PDF$', fontsize=20)\n", + "#plt.legend()\n", + "\n", + "\n", + "\n", + "ax2.plot(theta*deg, pdf_theta_normalized(E,theta),color='blue', label='PDF')\n", + "ax2.set_title(r'Normalized $ PDF(\\theta)$ for $\\sqrt{s}=$'+str('%.5f' % E)+str(\" GeV\"), fontsize=15)\n", + "ax2.set_xlabel(r'$ \\theta [°] $', fontsize=20)\n", + "ax2.set_ylabel(r'$ PDF$', fontsize=20)\n", + "plt.show()\n", + "\n", + "print('Check the normalization')\n", + "x2 = lambda x: pdf_theta(E,x)\n", + "print('Integral of the PDF in [0,pi]', \"{:.5f}\".format(integrate.quad(x2, 0., np.pi)[0]))\n", + "x2 = lambda x: pdf_theta_normalized(E,x)\n", + "print('Integral of the normalized PDF in [0,pi]', \"{:.5f}\".format(integrate.quad(x2, 0., np.pi)[0]))\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Monte Carlo Simulation\n", + "\n", + "4. write a Monte Carlo simulation that generates scattering events following the distrubtions that you found analytically; \n", + "5. produce a synthetic dataset of about $N=10^5$ (or more) events. Events should be listed as rows in a file with columns representing the muons coordinates (keep in mind that in the lab frame muons are relativistic and thus the number of coordinates can be only 3 per muon);\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### Inverse cumulative transform\n", + "In order to sample $\\theta$ distributed according to the differential cross section, we will use the inverse cumulative density approach. [DEVROYE]\n", + "\n", + "We start from the (analytical) normalized expresion for the probability density of the scattering angle:\n", + "$$\\text{pdf}(\\theta)=\\frac{3}{8}\\frac{\\sin{\\theta}}{s+2m_\\mu^2}\\left(s+4m_\\mu^2+(s-4m_\\mu^2)\\cos^2{\\theta}\\right)$$\n", + "After integration over the interval $[0,\\vartheta]$, we find the cumulative density function:\n", + "\n", + "$$\\text{cdf}(\\vartheta)=\n", + "\\frac{3}{8}\\frac{\\sin{\\theta}}{s+2m_\\mu^2}\\left(s+4m_\\mu^2+(s-4m_\\mu^2)\\cos^2{\\theta}\\right)$$\n", + "\n", + "Which after some reordering leads to the following expression:\n", + "\n", + "$$\\cos^3{\\vartheta}+3\\frac{s+4m_\\mu^2}{s-4m_\\mu^2}\\cos{\\vartheta}+4\\frac{s+2m_\\mu^2}{s-4m_\\mu^2}(2\\text{cdf}(\\vartheta)\n", + "-1)=0$$\n", + "\n", + "A depressed cubic equation, which may be solved for $\\cos\\vartheta$ with the real root[CARDANO]:\n", + "$$\n", + "\\left(-\\frac{q}{2}+\\sqrt{\\frac{q^2}{4}+\\frac{p^3}{27}}\\right)^{\\frac{1}{3}}+\\left(-\\frac{q}{2}-\\sqrt{\\frac{q^2}{4}+\\frac{p^3}{27}}\\right)^{\\frac{1}{3}}\n", + "$$\n", + "after identifying:\n", + "$$\n", + "\\cases{q = 4\\frac{s+2m_\\mu^2}{s-4m_\\mu^2}(2\\text{cdf}(\\vartheta)-1)\\\\\n", + "p = 3\\frac{s+4m_\\mu^2}{s-4m_\\mu^2}\n", + "}\n", + "$$\n", + "\n", + "An angle $\\vartheta$ obtained in this way is will be sampled according to the scattering angle distribution given $cdf(\\vartheta)$ is substituted by a uniformly distributed unit random variable." + ] + }, + { + "cell_type": "code", + "execution_count": 10, + "metadata": {}, + "outputs": [], + "source": [ + "# In order to sample theta angles, we have taken the inverse cumulative density function transform approach.\n", + "\n", + "def inv_cdf(rs,r):\n", + " '''Takes a CoM energy rs in GeV, and an array r of U(0,1) samples to generate an array of theta samples distributed according to the scattering pdf.\\n\n", + " Also admits an array of energies of the same size of the sample array.'''\n", + " s = rs**2\n", + " p = 3*(s+4*muon_mass**2)/(s-4*muon_mass**2)\n", + " q = 4*(2*r-1)*(s+2*muon_mass**2)/(s-4*muon_mass**2)\n", + " h = p**3/27+q**2/4\n", + " cos_t = np.cbrt(-q/2+np.sqrt(h))+np.cbrt(-q/2-np.sqrt(h))\n", + " rand_theta = np.arccos(cos_t)\n", + "\n", + " return rand_theta\n" + ] + }, + { + "cell_type": "code", + "execution_count": 11, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# Plot scaled histogram\n", + "fig, ax = plt.subplots(figsize=(12,4))\n", + "\n", + "n, bins, _ = ax.hist(inv_cdf(E,np.random.random(N)), bins=50, color='orange', ec='black')\n", + "\n", + "d = (bins[1]-bins[0])\n", + "scaling = d * n.sum()\n", + "ax.plot(bins, pdf_theta_normalized(E,bins)*scaling, color='blue', label='PDF')\n", + "\n", + "plt.title(r'$\\theta$ samples for CoM energy $ \\sqrt{S}=$'+str('%.5f' % E)+' GeV', fontsize=20)\n", + "plt.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + "plt.xlim(0.,np.pi)\n", + "plt.xlabel(r'$ \\theta\\, [rad]$', fontsize=20)\n", + "plt.ylabel('Counts', fontsize=20)\n", + "plt.legend()\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In order to validate the distributions, we compared them with the outcome of [Babayaga Event Generator](https://www2.pv.infn.it/~hepcomplex/babayaga.html) under the following inputs:\n", + "\n", + "* final state = mm \n", + "* ecms = 0.2120 GeV\n", + "* thmin = 0.0000 deg\n", + "* thmax = 180.0000 deg\n", + "* acoll. = 10.0000 deg\n", + "* emin = 0.0000 GeV\n", + "* ord = exp \n", + "* model = matched \n", + "* nphot mode = -1\n", + "* seed = 700253512\n", + "* iarun = 1\n", + "* eps = .000500000\n", + "* darkmod = 0\n" + ] + }, + { + "cell_type": "code", + "execution_count": 12, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Comparison with BabaYaga algorithm\n", + "\n", + "file_data = np.loadtxt('matched_ep_th_exp_200.txt', usecols=(0,1,2))\n", + "\n", + "theta_bby,dcs = file_data[:,0],file_data[:,1]\n", + "centroid = theta_bby + (theta_bby[0] + theta_bby[1])/2\n", + "dcs = dcs / ((theta[1] - theta[0])*dcs).sum()\n", + "dcs =dcs/np.max(dcs)\n", + "\n", + "\n", + "\n", + "fig, ax = plt.subplots(figsize=(12,4))\n", + "\n", + "n, bins, _ = ax.hist(inv_cdf(E,np.random.random(N))*deg, bins=100, color='orange', ec='black')\n", + "ax.plot(theta_bby,dcs*np.max(n), linewidth=2.5, label='Babayaga results')\n", + "\n", + "plt.title('Comparison between project samples and Babayaga samples.', fontsize=20)\n", + "plt.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + "plt.xlim(0.,180)\n", + "plt.xlabel(r'$ \\theta\\, [°]$', fontsize=20)\n", + "plt.ylabel('Counts', fontsize=20)\n", + "plt.legend()\n", + "\n", + "\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### SIMULATION 1" + ] + }, + { + "cell_type": "code", + "execution_count": 13, + "metadata": {}, + "outputs": [], + "source": [ + "##################################################################################\n", + "#Simulation parameters\n", + "\n", + "delta = 0.001\n", + "E = 2 * muon_mass + delta #This is the proposed energy just above the threshold\n", + "N = 10**7\n", + "\n", + "###################################################################################" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": {}, + "outputs": [], + "source": [ + "#Obtain the parameters distribution\n", + "theta_instances = inv_cdf(E,np.random.random(N))\n", + "#N_instances = len(theta_instances)\n", + "phi_instances = np.random.uniform(0., 2*np.pi, N)\n", + "\n", + "#The resulting space-momentum magnitude for each muon is the square of half the com energy minus the square of the muon mass.\n", + "p = np.sqrt(E**2/4-muon_mass**2)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 15, + "metadata": {}, + "outputs": [], + "source": [ + "#Obtain the muons momenta and build the file\n", + "\n", + "def sph_to_cart(r,theta,phi):\n", + " '''Converts from spherical coordinates to cartesian coordinates'''\n", + " V = np.vstack([\n", + " r*np.sin(theta)*np.cos(phi),\n", + " r*np.sin(theta)*np.sin(phi),\n", + " r*np.cos(theta)\n", + " ])\n", + " return V\n", + "\n", + "pxm, pym, pzm = sph_to_cart(p, theta_instances, phi_instances)\n", + "\n", + "pxam = -pxm\n", + "pyam = -pym\n", + "pzam = -pzm" + ] + }, + { + "cell_type": "code", + "execution_count": 16, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/latex": [ + "$\\displaystyle \\sqrt s \\qquad\\qquad\\!\\!0.21232 \\,\\,\\, GeV$" + ], + "text/plain": [ + "" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Norm of p 0.01029 GeV\n" + ] + } + ], + "source": [ + "display(Math('\\sqrt s \\qquad\\qquad\\!\\!{} \\,\\,\\, GeV'.format(round(E,5))))\n", + "print('Norm of p ', '%.5f' % p, \"GeV\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 17, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_angles_hist(theta_instances*deg, phi_instances*deg,'coral','royalblue','Muon angle distribution in the CoM frame')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 18, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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IG2+pddzGSjOq0YI7M6/PzG+Vj28Fvgfs0dFtLfChLFwI7BIRDwEOADZl5jWZeSdwWtlXUj3ceEst4jZWml1T++ObiFgF/CfgGx1NewDXVZ5vLod1G35gjSG2zrv+/m3cctsdAOx8/5141WtmZ6diNTYYPL7Fxpvl19x2mXk9cH35+NaIWNh4f7fS7Zcbb+DCiFjYeK+i3HgDRMTCxrs6riZgUjlgLi0ts7KN7bcOH3W7sNg8drjPdu76j+UDTdPP/dIwqc9SnaZScEfE/YHTgVdl5s86m7uMkn2Gd5v+Ooq9baxcuXKo2PolbvUx9H9Dh5nOqG2d87/ltjt40z7HA/A3m97ACSec0LVvv9jqihX4ZWyd8fVbjtXX1O11Vafb2TaJ11HX8uj3fNTP1WLjjmNWNt6zbpiV/qh9++XWCf96/Mix9ptOHYVRvy/PMFzRNKpB42lb0VbnNnbY7eti6/B+bYNu/zrnccK/Hj/QdqEzhlG3IcN8lsepI0b9sjLq53Oc9VnT203o/VlqYts8iMYL7ojYgWJF8JHM/FSXLpuBvSrP9wS2ADv2GH4vmbkeWA+wevXqrkV5VecHpVfiVh9D/zd0mOmM2tat+Fxwd+4w8EpuUvEs1tYrvkFWiL1eV3W63drGfR2Tms4w81hseSw2nUmbtS/IoxZtTXzpgsFX+qP27feeL4u7+n52Fvss9ZpOv77DLPPqdPp9ee58nf2+AIzz3g0azzBF2zCx1lGc172NHXb72qm6nu63XVhoH2X7N+g0O2MYdRsy7Gd5EuuIfm2jfqno9nyWap7F+lZ1fs7qmMewGi24IyKAfwK+l5n/0KPbWcAx5U/QBwK3ZOb1EXEDsE9E7A38CDgSeP4k4qp+Ox5mgS72htatX/HZr28TsQ1jsZXcvJml5TGLX5D7/ZIDk1/pDzudqmHWEZNYnwxSXAzyWVps3dJZkI/yxXuY9Ve/LwDjvneDxDNM0TZsrJM0q9vYOszSNm2Yz3K/cYddR4wynXHWEdOuedqu6T3cTwZeBFweEZeWw/4aWAmQmScDG4EjgE3AL4CXlG3bI+IY4PPAMuCUzLyy0eilOdKGjfc4GzqNrulip03v85RjdRsrzahGC+7MvIDuPzVX+yTwih5tGylWFpLq58ZbahG3sdLsmtpVSiTNNjfekiRNhn/tLkmSJNXIgluSJEmqkQW3JEmSVCMLbkmSJKlGFtySJElSjSy4JUmSpBpZcEuSJEk1suCWJEmSamTBLUmSJNXIgluSJEmqkQW3JEmSVCMLbkmSJKlGFtySJElSjSy4JUmSpBpZcEuSJEk1suCWJEmSarS8yZlFxCnAM4Gtmblfl/bXAS+oxPZoYEVmbouIa4FbgbuB7Zm5upmoJUmafW5jpdnV9B7uDcCaXo2Z+fbMfFxmPg74n8CXM3NbpcshZbsrAqkBEXFKRGyNiCt6tL8uIi4tb1dExN0R8cCy7dqIuLxsu7jZyKW5tAG3sdJMarTgzszzgW2LdiwcBZxaYziSFrcBN+BSK7iNlWbXTB7DHRH3pdjIn14ZnMC5EXFJRKybTmTSfHEDLi09bmOl5s1kwQ08C/hqx56yJ2fm44HDgVdExO/2Gjki1kXExRFx8Q033FB3rNLcG2cDbr5KjRt5G2u+SqOZ1YL7SDr2lGXmlvJ+K3AGcECvkTNzfWauzszVK1asqDVQScAYG3DzVWrcyNtY81UazcwV3BGxM/A04MzKsPtFxAMWHgPPALqexCVpKsb6kiypGW5jpelo+rKApwIHA7tFxGbgTcAOAJl5ctnt2cC5mfnzyqgPAs6ICChi/mhmntNU3JJ6q2zAX1gZdj/gPpl5a2UD/uYphSjNBbex0uxqtODOzKMG6LOB4soI1WHXAPvXE5WkXtyAS+3hNlaaXY0W3JLaxQ24JEnjm7ljuCVJkqSlxIJbkiRJqpEFtyRJklQjC25JkiSpRhbckiRJUo0suCVJkqQaWXBLkiRJNbLgliRJkmpkwS1JkiTVyIJbkiRJqpEFtyRJklQjC25JkiSpRhbckiRJUo0suCVJkqQaWXBLkiRJNbLgliRJkmrUaMEdEadExNaIuKJH+8ERcUtEXFrejqu0rYmIqyNiU0Qc21zU0vwyZ6X2MF+l2dX0Hu4NwJpF+nwlMx9X3t4MEBHLgJOAw4F9gaMiYt9aI5UE5qzUJhswX6WZ1GjBnZnnA9tGGPUAYFNmXpOZdwKnAWsnGpykezFnpfYwX6XZNYvHcB8UEd+JiLMj4jHlsD2A6yp9NpfDJE2fOSu1h/kqTcHyaQfQ4VvAwzLztog4Avg0sA8QXfpmr4lExDpgHcDKlStrCFNSaeycNV+lxpiv0pTM1B7uzPxZZt5WPt4I7BARu1F8296r0nVPYEuf6azPzNWZuXrFihW1xizNs0nkrPkqNcN8laZnpgruiHhwRET5+ACK+G4CLgL2iYi9I2JH4EjgrOlFKgnMWalNzFdpeho9pCQiTgUOBnaLiM3Am4AdADLzZOCPgT+PiO3A7cCRmZnA9og4Bvg8sAw4JTOvbDJ2aR6Zs1J7mK/S7Gq04M7MoxZpPxE4sUfbRmBjHXFJ6s6cldrDfJVm10wdUiJJkiQtNRbckiRJUo0suCVJkqQaWXBLkiRJNbLgliRJkmpkwS1JkiTVyIJbkiRJqpEFtyRJklQjC25JkiSpRhbckiRJUo0suCVJkqQaWXBLkiRJNbLgliRJkmpkwS1JkiTVyIJbkiRJqpEFtyRJklQjC25JkiSpRgMX3BHx1IhYW3m+W0R8NCIujYi/j4gdBpjGKRGxNSKu6NH+goi4rLx9LSL2r7RdGxGXl/O7eNC4JY3OnJXaw3yVZtcwe7j/Dtiv8vzdwO8BFwIvBk4YYBobgDV92n8APC0zHwu8BVjf0X5IZj4uM1cPGLOk8WzAnJXaYgPmqzSThim4HwVcAhAR9wWeDfxlZh4NvB543mITyMzzgW192r+WmT8tn14I7DlEfJImzJyV2sN8lWbXMAX3jsC/l4+fDCwHPlc+/z7wkAnGBfBS4OzK8wTOjYhLImJdvxEjYl1EXBwRF99www0TDktSDyPnrKTGjZSvbl+l0Swfou9VFD9VnQe8APh6Zt5atj2UPt+qhxURh1CsDJ5SGfzkzNwSEbsDX4iIq8pv8/eSmespfypbvXp1TiouSd2Nk7Plxn0dwMqVKxuJV5pn4+Sr21dpNMPs4X4z8OqIuAF4PvC2Stsa4NuTCCgiHgt8AFibmTctDM/MLeX9VuAM4IBJzE/SeMbN2cxcn5mrM3P1ihUrmghZmltuY6XpGLjgzsyzgEcDRwP7ZWb1p6ivA38zbjARsRL4FPCizPx+Zfj9IuIBC4+BZwBdz8KW1BxzVmoP81WanoEPKYmIPwE+l5mnd2n+JPBM4BuLTONU4GBgt4jYDLwJ2AEgM08GjgN2Bd4bEQDby7OlHwScUQ5bDnw0M88ZNHZJozFnpfYwX6XZNcwx3B8EDgJu6tK2d9n+oX4TyMyjFml/GfCyLsOvAfa/9xiS6mTOSu1hvkqza5hjuKNP267Az8aMRZIkSVpy+u7hLv9Zcm1l0BvLkyarfg14KnDRhGOTJEmSWm+xQ0p2B36n8vwRwIM7+twJnMsETpqUJEmSlpq+BXdmvh94P0BEfAn488y8qonAJEmSpKVg4JMmM/OQOgORJEmSlqJhrlJCRDyU4vJ/e1Icu12Vmfk/JhWYJEmStBQMcx3uZwOnAsuArRTHblclYMEtSZIkVQyzh/utFCdHvjgzt9UUjyRJkrSkDFNw7wX8hcW2JEmSNLhh/vjma8Cj6gpEkiRJWoqG2cP9V8BHIuI24AvAzZ0dMvMXE4pLkiRJWhKGKbgvK+8/SHGCZDfLxgtHkiRJWlqGKbj/jN6FtiRJkqQuhvnjmw01xiFJkiQtScOcNClJkiRpSMP88c0NLHJISWbuPnZEkiRJ0hIyzB7uk7rcTgV+AtwOnLjYBCLilIjYGhFX9GiPiHhPRGyKiMsi4vGVtjURcXXZduwQcUuStOS5jZVm1zDHcB/fbXhEBPBxYPsAk9lAUZh/qEf74cA+5e1A4H3AgRGxjKLAPxTYDFwUEWdl5ncHjV/S8CLiFOCZwNbM3K9LewDvBo4AfkHxT7TfKtvWlG3LgA9k5tsaC1yaTxtwGyvNpLGP4c7MBD4AHDNA3/OBfv9UuRb4UBYuBHaJiIcABwCbMvOazLwTOK3sK6leG4A1fdqrG/B1FBtwKhvww4F9gaMiYt9aI5XmnNtYaXZN6qTJhwM7TmA6ewDXVZ5vLof1Gi6pRm7ApSXFbaw0JcOcNPnyLoN3BB4NvAD4xATiiS7Dss/w7hOJWEext42VK1dOICxJPQyzAT+w2wTMV6kxY29jzVdpNMP88U23kyLvoNiQvhc4YQLxbAb2qjzfE9hCUdh3G95VZq4H1gOsXr3aP+uR6jP2Btx8lRoz9jbWfJVGM8xJk01cs/ss4JiIOI1ib9gtmXl9eUnCfSJib+BHwJHA8xuIR1J/E/mSLKkRbmOlKRlmD/fYIuJU4GBgt4jYDLwJ2AEgM08GNlJc7WATxRUPXlK2bY+IY4DPU1zx4JTMvLLJ2CV15QZcmhFuY6XZNVTBHREPB14HPAV4IMXJVF8B3pGZ1yw2fmYetUh7Aq/o0baRYmUhqSFuwKX2cBsrza5hTpp8AvAl4N+Bz1L84c2DgP8KvCAiDlm4/q6kpcENuCRJ4xtmD/c7gG8Dh2fmLxYGRsR9KTaq7wCePtnwJEmSpHYb5kTIA4C/qxbbAOXzd9Djkl+SJEnSPBum4L4d2LVH2wMpDjWRJEmSVDFMwf054G0R8ZTqwPL53wKfmWRgkiRJ0lIwzDHcfwWcCXy5vOTXT4DdKU6c/CrwmsmHJ0mSJLXbMH98cxPwlIhYAzwReAhwPfCNzDy3pvgkSZKkVut7SElE7BoRp0fEYQvDMvOczHxLZr48M99SdIvTI2L32qOVJEmSWmaxY7hfBTwc6LcH+1xgbzykRJIkSbqXxQru5wInl39u0VXZ9o/A2kkGJkmSJC0FixXcDwO+O8B0vgesGjsaSZIkaYlZrOC+HfiNAaZz/7KvJEmSpIrFCu5vAX84wHTWln0lSZIkVSxWcJ8EvDQi/rRXh4j4E+AlwImTDEySJElaCvpehzszPxUR7wY+GBHHAOcAPwQSWAkcBqwG3pmZZ9QdrCRJktQ2i/7xTWa+JiLOo7hE4GuBncqmOyj+YXJtZn62rgAlSZKkNhvonyYz8zPAZyJiObBrOfimzNxeW2SSJEnSErDYMdz3kJnbM/Mn5W2kYjsi1kTE1RGxKSKO7dL+uoi4tLxdERF3R8QDy7ZrI+Lysu3iUeYvaXDmq9Qe5qs0uwbawz0pEbGM4kTMQ4HNwEURcVZm/vJa35n5duDtZf9nAa/OzG2VyRySmTc2GLY0l8xXqT3MV2m2DbWHewIOADZl5jWZeSdwGv3/ofIo4NRGIpPUyXyV2sN8lWZY0wX3HsB1leeby2H3EhH3BdYAp1cGJ3BuRFwSEetqi1ISmK9Sm5iv0gxr9JASILoMyx59nwV8tePnridn5paI2B34QkRclZnn32smxcpiHcDKlSvHjVmaV+ar1B7mqzTDmt7DvRnYq/J8T2BLj75H0vFzV2ZuKe+3AmdQ/IR2L5m5PjNXZ+bqFStWjB20NKfMV6k9zFdphjVdcF8E7BMRe0fEjhRJf1Znp4jYGXgacGZl2P0i4gELj4FnAFc0ErU0n8xXqT3MV2mGNXpISWZuL/+x8vPAMuCUzLwyIo4u208uuz4bODczf14Z/UHAGREBRdwfzcxzmotemi/mq9Qe5qs025o+hpvM3Ahs7Bh2csfzDcCGjmHXAPvXHJ6kCvNVag/zVZpdTR9SIkmSJM0VC25JkiSpRhbckiRJUo0suCVJkqQaWXBLkiRJNbLgliRJkmpkwS1JkiTVyIJbkiRJqpEFtyRJklQjC25JkiSpRhbckiRJUo0suCVJkqQaWXBLkiRJNbLgliRJkmpkwS1JkiTVyIJbkiRJqpEFtyRJklSjxgvuiFgTEVdHxKaIOLZL+8ERcUtEXFrejht0XEmTZb5K7WG+SrNreZMzi4hlwEnAocBm4KKIOCszv9vR9SuZ+cwRx5U0Aear1B7mqzTbmt7DfQCwKTOvycw7gdOAtQ2MK2l45qvUHuarNMOaLrj3AK6rPN9cDut0UER8JyLOjojHDDmupMkwX6X2MF+lGdboISVAdBmWHc+/BTwsM2+LiCOATwP7DDhuMZOIdcA6gJUrV44crDTnzFepPcxXaYY1vYd7M7BX5fmewJZqh8z8WWbeVj7eCOwQEbsNMm5lGuszc3Vmrl6xYsUk45fmifkqtYf5Ks2wpgvui4B9ImLviNgROBI4q9ohIh4cEVE+PqCM8aZBxpU0Uear1B7mqzTDGj2kJDO3R8QxwOeBZcApmXllRBxdtp8M/DHw5xGxHbgdODIzE+g6bpPxS/PEfJXaw3yVZlvTx3Av/Iy1sWPYyZXHJwInDjqupPqYr1J7mK/S7PKfJiVJkqQaWXBLkiRJNbLgliRJkmpkwS1JkiTVyIJbkiRJqpEFtyRJklQjC25JkiSpRhbckiRJUo0suCVJkqQaWXBLkiRJNbLgliRJkmpkwS1JkiTVyIJbkiRJqpEFtyRJklQjC25JkiSpRhbckiRJUo0suCVJkqQaNV5wR8SaiLg6IjZFxLFd2l8QEZeVt69FxP6Vtmsj4vKIuDQiLm42cmn+mK9Se5iv0uxa3uTMImIZcBJwKLAZuCgizsrM71a6/QB4Wmb+NCIOB9YDB1baD8nMGxsLWppT5qvUHuarNNua3sN9ALApM6/JzDuB04C11Q6Z+bXM/Gn59EJgz4ZjlFQwX6X2MF+lGdZ0wb0HcF3l+eZyWC8vBc6uPE/g3Ii4JCLW9RopItZFxMURcfENN9wwVsDSHGskXyVNhNtXaYY1ekgJEF2GZdeOEYdQrBCeUhn85MzcEhG7A1+IiKsy8/x7TTBzPcVPZaxevbrr9CUtqpF8LTfu6wBWrlw5ftTSfHL7Ks2wpvdwbwb2qjzfE9jS2SkiHgt8AFibmTctDM/MLeX9VuAMip/QJNWjkXzNzPWZuTozV69YsWKC4Utzxe2rNMOaLrgvAvaJiL0jYkfgSOCsaoeIWAl8CnhRZn6/Mvx+EfGAhcfAM4ArGotcmj/mq9Qe5qs0wxo9pCQzt0fEMcDngWXAKZl5ZUQcXbafDBwH7Aq8NyIAtmfmauBBwBnlsOXARzPznCbjl+aJ+Sq1h/kqzbamj+EmMzcCGzuGnVx5/DLgZV3GuwbYv3O4pPqYr1J7mK/S7PKfJiVJkqQaWXBLkiRJNbLgliRJkmpkwS1JkiTVyIJbkiRJqpEFtyRJklQjC25JkiSpRhbckiRJUo0suCVJkqQaWXBLkiRJNbLgliRJkmpkwS1JkiTVyIJbkiRJqpEFtyRJklQjC25JkiSpRhbckiRJUo0aL7gjYk1EXB0RmyLi2C7tERHvKdsvi4jHDzqupMkyX6X2MF+l2dVowR0Ry4CTgMOBfYGjImLfjm6HA/uUt3XA+4YYV9KEmK9Se5iv0mxreg/3AcCmzLwmM+8ETgPWdvRZC3woCxcCu0TEQwYcV9LkmK9Se5iv0gxruuDeA7iu8nxzOWyQPoOMK2lyzFepPcxXaYZFZjY3s4jnAIdl5svK5y8CDsjMv6j0+Rzwt5l5Qfn8X4DXAw9fbNzKNNZR/FwG8Cjg6gFD3A24cZTXNiVtirdNsUK74h021odl5orFOpmvE9emeNsUK7Qr3nnNV1ja79O0tSneNsUKw8XbM1+XTy6egWwG9qo83xPYMmCfHQcYF4DMXA+sHza4iLg4M1cPO960tCneNsUK7Yq3xljN1wlqU7xtihXaFe+85iv4PtWpTfG2KVaYXLxNH1JyEbBPROwdETsCRwJndfQ5C/iT8mzqJwG3ZOb1A44raXLMV6k9zFdphjW6hzszt0fEMcDngWXAKZl5ZUQcXbafDGwEjgA2Ab8AXtJv3Cbjl+aJ+Sq1h/kqzbamDykhMzdSJH112MmVxwm8YtBxJ2ykn8mmqE3xtilWaFe8tcVqvk5Um+JtU6zQrnjnNV/B96lObYq3TbHChOJt9KRJSZIkad741+6SJElSjeam4O73l7Yd/faOiG9ExL9GxMfKE0iIiN+OiK9HxB0R8doZj3Wg8ScUa6v+SnjMeE+JiK0RcYWx1st8rTXe1uRs23KgbfFOSpvydULxNpazbcrXCcS7tLexmTkXN4oTRc4GAngS8I0e/T4OHFk+Phn48/Lx7sATgf8NvHbGYx1o/AnEuQz4fxTXcN0R+A6w7yCvZZBxZynesu13gccDVzTweW1NrDW9fvN1xj5XTeds23KgbfFO+LW3Jl8nFK/b2AnHW7Yt6W3s3Ozhpvdf2v5SRATwdOCT5aB/Bv4IIDO3ZuZFwF2zHusg409I2/5KeJx4yczzgW01x9jGWOtgvtajTTnbthxoW7yT1KZ8HTveQcafkDbl67jxLvlt7DwV3IP8de2uwM2Zub1PnyaMG2tTf9Pbtr8SHifeprUp1jqYr/VoU862LQfaFu8ktSlfoT0526Z87RfLsH2a0His81RwR5dhnZdoGaRPE8aNtanXMU6c01jW8/QZaLs2vf625Oug85qVnG3TZwDaF+8kte21tyVn25Sv/WIZtk8TGo91SRfcEfGKiLg0Ii6l+Jvaxf669kaKnwyW9+lTiwnHOshf/E7COH8l3FSMg8QybJ8mtCnWiTBf+44/KW3K2bblQNviHUub8hVam7Ntytd+sQzbpwnNx5o1H5g+KzfgD7jnwe/f7NHvE9zzJImXd7QfT/0nYY0V66DjTyDO5cA1wN786qSDxwzyWgYZd5birbSvopkTOloTa02v33ydsc9V0znbthxoW7wTfu2tyddJxNtUzrYpX8eNt9LeSA5MI9ZaX9As3coFdhLFWamXA6srbRuBh5aPHw58k+Kvbz8B7FQOfzDFt52fATeXj39jRmPtOX4NsR4BfL+c1xvKYUcDRw/wWu41bgOfg3HiPRW4nuLEns3AS421ttduvs7m56rRnG1bDrQt3gm+7tbk64TidRu7BHKg6Vj9p0lJkiSpRkv6GG5JkiRp2iy4JUmSpBpZcEuSJEk1suCWJEmSamTBLUmSJNXIgluSJEmqkQW3JEmSVCMLbo0tIs6LiCxvr+po+6OIODciboqIOyPiRxFxWkQ8ech5fDYiLu/TfmJE/DQidoqI4yvxfHLElyUtSear1B798rVsN2dbwoJbk/Il4CDgtIUBEfFO4HTgR8DLgN8HjgUeAFwQEY8YYvqnAvtFxGM6GyJiGfDHwKcy8w7gA2Us3x7tpUhLnvkqtce98hXM2bZZPu0AtGRsy8wLF55ExFrgVcBLMnNDR98PR8SzgNuHmP6ZwC+AI4E3drQdAjyIYoVBZm4GNkfEz4Z5AdIcMV+l9rhHvoI520bu4Z5D5c9Cb46Ij5Q/Q22LiH+MiJ0mOJtXARd1WREAkJmfycwtHXE9JSK+HBG/KON6f0Q8oOx/G/BZ4HldJnck8BOKvQDSkmK+Su0yiznbL1/L/uZszSy450xEPAzYBfgrYBvwHOBdwDrgFROax3KKn5vOHWKcJwP/AvyY4qerVwFHAB+sdDsV2CcinlAZbwfg2cDHM/PusYOXZoj5KrXLLObsgPkK5mytPKRk/uxf3p+YmceWj78YEb8LrAH+YQLz2BXYCbiuOjAiAlhWGXR3Zmb5+G3A1zLzeZX+PwL+JSL2y8wrgLOBmym+bV9SdjsMeCDlT13SEmO+Su0yizk7SL6COVsr93DPn/0pjtN6e8fwTRRJNQlR3mfH8NcAd1VurwCIiPtSfFv/eEQsX7gBF5T9ngBQnqxxBvDccsUCxc9f/wbc4/g2aYkwX6V2mamcHTRfwZytmwX3/NkfuDgzb+oYvgrYcu/uI7kRuAPYs2P4h4Enlreq36T4Vv5e7rmyuAPYAdir0vdUYCVwUET8GrAWOLWy501aSsxXqV1mLWeHyVcwZ2vjISXzZ3/ga9UB5YkTTwLeVD4/EzgrM/8pIp5Jccby75UnVSwqM7dHxNeBZwDHVYb/hOLEC3715RkofsJK4HhgY5dJVldSXyyncSTwEIrLH/lTl5aqvvlaXvbr7Mx8ZKXtIuBpZb4tynyVJmrQbezDyuaVwCcy878POoMhc/ZmBs9XMGdrY8E9RyLifsAjKK7ZWfXK8v6fy/s3AJ+OiKuBtwKHDlpsV7yrnMaLMvPD/Tpm5s8j4kLgUZn55kX63h0Rn6A4EWUP4HuZedmQsUkzb5B8zcybI+IBEfHAzNxGsVFdP2ixXfEuzFdpLINuYzNzbdn/94C/5d6X4RvEuxggZ4fJ17K/OVsTC+758liKY78eERHHAV+h+Ib8GuCFmXkzQGZeERHfBD7OEHvKqjLzzIh4F7AhIg4BPkPxM9iuwKFlt2oR/3qKEzj+A/gkcCvFN/8/AN6Qmd+v9D0VOIbizOnjkJamgfKVYm/aARHxQ4o/vlg97IzMV2kiBs1ZIuL3KXZoPTMztw47oyFzdph8BXO2Fhbc82V/4GcUSfZBij3ZVwPPycwzFzpFxN7A44DtwPWjziwzXx0R5wMvB/6J4qepG4CvA0dk5tmVvheUZ3GfQHEc2jKKEzXOofyJrOLrwLUUx8SdhrQ0DZSvwFeBA4HXAa/NzLtGmZn5Ko1t0G3socD/Bv4gM28YdWaD5uyQ+QrmbC0suOfL/sDl5c9DT+jWISJ2Az5Ncc3Q5wCvBt4ywLSjPPO5eukwMvMMirOeF5WZ36C4bNJi/RLYu08g96E4ITh69ZFaYNF8LX0V+BxwfmZ+YcBpm6/S5A2yjT2MYps6TLHdNV9h8JwdNF/LvuZsDbxKyXzZH/hOr8by8kFnAm/OzAsoji17eUTsOsC0/wvFmc9/OYlAx3QcRSy/O+1ApDH0zdeKq4D7UvzRxqDMV2nyBsnZjwIrgC9ExKUR8Z4BpjtL+Qrm7EjCK73Mh/Kamj+j+Mn5Hyc87UdR/JQF8MNRjkebcDwPBR5aPt2WmddMMx5pWMPka0S8BbgzMwf5Jcp8lWpQ1zZ21vIVzNlRWXBLUguVG+IzgcuB54967LYkqX4W3JIkSVKNPIZbkiRJqpEFtyRJklQjC25JkiSpRhbckiRJUo0suCVJkqQaWXBLkiRJNbLgliRJkmpkwS1JkiTVyIJbkiRJqtH/BxBOLEvvMcBeAAAAAElFTkSuQmCC\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_momenta_hist(pxm,pym,pzm,r'$\\mu^+$ momentum components in the center of mass frame','orange')\n", + "plot_momenta_hist(pxam,pyam,pzam,r'$\\mu^-$ momentum components in the center of mass frame','blue')\n" + ] + }, + { + "cell_type": "code", + "execution_count": 19, + "metadata": {}, + "outputs": [], + "source": [ + "################################################" + ] + }, + { + "cell_type": "code", + "execution_count": 20, + "metadata": {}, + "outputs": [], + "source": [ + "#Boost the results to the laboratory frame\n", + "\n", + "vz = -np.sqrt(1-4*electron_mass**2/E**2) \n", + "gamma = 1/np.sqrt(1-vz**2)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 21, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Gamma 207.74676\n", + "Speed along z axis (vz) -0.99999\n" + ] + } + ], + "source": [ + "print('Gamma', '%.5f' % gamma)\n", + "print('Speed along z axis (vz)', '%.5f' % vz)" + ] + }, + { + "cell_type": "code", + "execution_count": 22, + "metadata": {}, + "outputs": [], + "source": [ + "# The boost is only performed for the Z direction (and the temporal component)\n", + "pxm_lb = pxm\n", + "pym_lb = pym\n", + "E_lb, pzm_lb = boost(vz,E/2,pzm)\n", + "\n", + "pxam_lb = pxam \n", + "pyam_lb = pyam\n", + "_, pzam_lb = boost(vz,E/2,pzam)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 23, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plot_momenta_hist(pxm_lb,pym_lb,pzm_lb,r'$\\mu^+$ momentum components in the laboratory frame','orange')\n", + "plot_momenta_hist(pxm_lb,pym_lb,pzm_lb,r'$\\mu^-$ momentum components in the laboratory frame','blue')\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the approximation of $v_\\mu =1$ (which is out case with $v_\\mu \\sim 0.99$) an expression for the maximum scattering angle can be obtained [LEMMA]:\n", + "\n", + "$$\\vartheta_\\mu^{max} = \\frac{4 m_e}{s}\\sqrt{\\frac{s}{4}-m_\\mu^2}$$\n", + "\n", + "It is also possible to obtain an expression for the difference between the maximum and the minimum energy of the produced muons:\n", + "\n", + "$$\\Delta E_\\mu = \\frac{\\sqrt{s}}{2m_e}\\sqrt{\\frac{s}{4}-m_\\mu^2}$$\n", + "\n", + "It is important to remember that those expression depend on $s$ and as a consequence only aplies to monochromatic positron beams." + ] + }, + { + "cell_type": "code", + "execution_count": 24, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Maximum theta according to the theory [LEMMA] 0.02674 deg\n", + "Maximum theta in the simulation 0.02686 deg\n" + ] + } + ], + "source": [ + "theta_lb = np.arccos(pzm_lb/np.sqrt(pxm_lb**2+pym_lb**2+pzm_lb**2))\n", + "phi_lb = np.arctan2(pym_lb,pxm_lb)+np.pi\n", + "\n", + "plot_angles_hist(theta_lb*deg, phi_lb*deg, 'coral','royalblue','Angles distribution in the lab frame')\n", + "\n", + "theta_max_t = 4 * electron_mass /E **2 * np.sqrt(E **2 /4. -muon_mass**2)\n", + "print('Maximum theta according to the theory [LEMMA]', \"{:.5f}\".format(theta_max_t*deg), \"deg\")\n", + "print('Maximum theta in the simulation ', \"{:.5f}\".format(np.max(theta_lb)*deg), \"deg\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 25, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Difference between max and min energy of the muons according to the theory [LEMMA] 2.13796 GeV\n", + "\n", + "Difference between max and min energy of the muons 4.27587 GeV\n" + ] + } + ], + "source": [ + "#Visualization of the energy spread\n", + "\n", + "fig, ax = plt.subplots(figsize=(12,4))\n", + "\n", + "n, bins, _ = ax.hist(E_lb, bins=50, color='orange', ec='black')\n", + "plt.title(r'$\\mu^+$ energy spread in the laboratory frame.', fontsize=20)\n", + "plt.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + "plt.xlabel(' Energy [GeV]', fontsize=20)\n", + "plt.ylabel('Counts', fontsize=20)\n", + "plt.show()\n", + "\n", + "de_max_t = E / (2*electron_mass) * np.sqrt(E **2 /4 - muon_mass**2)\n", + "print('Difference between max and min energy of the muons according to the theory [LEMMA]', \"{:.5f}\".format(de_max_t), \"GeV\")\n", + "print('')\n", + "print('Difference between max and min energy of the muons', \"{:.5f}\".format(np.max(E_lb)-np.min(E_lb)), \"GeV\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 26, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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ThetaPhiMuon pxMuon pyMuon pz
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" + ], + "text/plain": [ + " Theta Phi Muon px Muon py Muon pz\n", + "0 1.375098 0.146929 0.009986 0.001478 0.002001\n", + "1 1.386526 4.237571 -0.004625 -0.008998 0.001886\n", + "2 0.950013 2.624996 -0.007279 0.004135 0.005986\n", + "3 0.721060 0.254691 0.006575 0.001712 0.007730\n", + "4 1.239125 5.009806 0.002851 -0.009303 0.003351\n", + "... ... ... ... ... ...\n", + "9999995 0.234454 1.329902 0.000570 0.002322 0.010010\n", + "9999996 2.158597 6.008712 0.008243 -0.002321 -0.005707\n", + "9999997 1.796806 4.895994 0.001831 -0.009861 -0.002306\n", + "9999998 2.463999 3.944181 -0.004483 -0.004640 -0.008018\n", + "9999999 2.647336 1.451990 0.000579 0.004847 -0.009060\n", + "\n", + "[10000000 rows x 5 columns]" + ] + }, + "execution_count": 26, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#Write the results to a file\n", + "s1_muons_com = pd.DataFrame({'Theta' : theta_instances,'Phi' : phi_instances,'Muon px' : pxm, 'Muon py' : pym, 'Muon pz' : pzm})\n", + "#s1_muons_com.to_csv('s1_muons_momentum_com.csv', index=False)\n", + "\n", + "s1_muons_lab = pd.DataFrame({'Theta' : theta_lb,'Phi' : phi_lb,'Muon px' : pxm_lb, 'Muon py' : pym_lb, 'Muon pz' : pzm_lb})\n", + "#s1_muons_lab.to_csv('s1_muons_momentum_lab.csv', index=False)\n", + "\n", + "s1_muons_com\n" + ] + }, + { + "cell_type": "code", + "execution_count": 27, + "metadata": {}, + "outputs": [], + "source": [ + "##################################################################################\n", + "#Simulation parameters\n", + "E1 = 0.215\n", + "E2 = 0.225\n", + "N = 10**6\n", + "###################################################################################\n" + ] + }, + { + "cell_type": "code", + "execution_count": 28, + "metadata": {}, + "outputs": [], + "source": [ + "def simulation1(rs,N):\n", + " '''This function takes as inputs the CoM energy and the number of events \n", + " and outputs the muons energy in the Lab frame and the theta angle distribution '''\n", + " theta_instances = inv_cdf(rs,np.random.random(N))\n", + " #N_instances = len(theta_instances)\n", + " phi_instances = np.random.uniform(0., 2*np.pi, N)\n", + " #The resulting space-momentum magnitude for each muon is the square of half the com energy minus the square of the muon mass.\n", + " p = np.sqrt(rs**2/4-muon_mass**2)\n", + "\n", + " pxm, pym, pzm = sph_to_cart(p, theta_instances, phi_instances)\n", + "\n", + " vz = -np.sqrt(1-4*electron_mass**2/rs**2) \n", + " gamma = 1/np.sqrt(1-vz**2)\n", + "\n", + " pxm_lb = pxm\n", + " pym_lb = pym\n", + " E_lb, pzm_lb = boost(vz,rs/2,pzm)\n", + "\n", + " theta_lb = np.arccos(pzm_lb/np.sqrt(pxm_lb**2+pym_lb**2+pzm_lb**2))\n", + " \n", + " return E_lb,theta_lb" + ] + }, + { + "cell_type": "code", + "execution_count": 29, + "metadata": {}, + "outputs": [], + "source": [ + "E_lb1,theta_lb1 = simulation1(E1,N)\n", + "E_lb2,theta_lb2 = simulation1(E2,N)" + ] + }, + { + "cell_type": "code", + "execution_count": 30, + "metadata": {}, + "outputs": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax1= plt.subplots(figsize=(12, 4))\n", + "\n", + "en = [str(E1)+' Gev',str(E2)+' Gev']\n", + "\n", + "n, bins, _ = ax1.hist(theta_lb1*deg, bins=50, ec='black',label=en[0])\n", + "n, bins, _ = ax1.hist(theta_lb2*deg, bins=50, alpha=0.7, ec='black',label=en[1])\n", + "\n", + "plt.title(r'$\\mu^+$ $\\theta\\,$ spread in the laboratory frame.', fontsize=20)\n", + "ax1.set_xlabel(r'$\\theta$ [°]', fontsize=20)\n", + "ax1.set_ylabel('Counts', fontsize=20)\n", + "ax1.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + "\n", + "ax1.legend(prop={'size': 15})\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 31, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "fig, ax = plt.subplots(figsize=(12,4))\n", + "\n", + "en = [str(E1)+' Gev',str(E2)+' Gev']\n", + "\n", + "n, bins, _ = ax.hist(E_lb2, bins=50, ec='grey',color='C1', alpha=0.7,label=en[1])\n", + "n, bins, _ = ax.hist(E_lb1, bins=50, ec='grey',color='C0',label=en[0])\n", + "\n", + "\n", + "plt.title(r'$\\mu^+$ energy spread in the laboratory frame.', fontsize=20)\n", + "plt.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + "plt.xlabel(' Energy [GeV]', fontsize=20)\n", + "plt.ylabel('Counts', fontsize=20)\n", + "plt.ylim(0.,0.3e5)\n", + "\n", + "ax.legend(prop={'size': 15})\n", + "plt.show()" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Properties of the target \n", + "6. assume a $3$ cm thick Beryllium block is used as target and a rate of positron on target of $10^6$ Hz. Compute the rescaling factor (weight) you need to apply to the $N$ simulated events such that they represent the statistics that would be gathered in a week of countinuous operations;\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The number of $\\mu^+ \\mu^-$ pairs produced per positron on the target is given by:\n", + "\n", + "\n", + "$$n(\\mu^+ \\mu^-) = n^+ \\rho^- l \\sigma(\\mu^+ \\mu^-)$$\n", + "\n", + "\n", + "where $n^+$ is the number of positrons, $\\rho^-$ is the electron density in the medium, $l$ is the thickness of the target, and $\\sigma(\\mu^+ \\mu^-)$ is the muon pairs production cross section. [LEMMA]\n", + "\n", + "\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 32, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "text/html": [ + "
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1He24.002600.1450786.0
2Li36.941000.5120156.2
3Be49.012181.847735.2
4B510.811002.080022.2
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6Cu2963.546008.96001.4
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" + ], + "text/plain": [ + " Material Z A Density X0\n", + "0 H 1 1.00794 0.0763 900.6\n", + "1 He 2 4.00260 0.1450 786.0\n", + "2 Li 3 6.94100 0.5120 156.2\n", + "3 Be 4 9.01218 1.8477 35.2\n", + "4 B 5 10.81100 2.0800 22.2\n", + "5 C 6 12.01070 2.8000 21.4\n", + "6 Cu 29 63.54600 8.9600 1.4\n", + "7 W 74 183.84000 19.3000 0.4\n", + "8 Pb 82 207.20000 11.3400 0.6" + ] + }, + "execution_count": 32, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#We build a dataframe with some material properties to be analysed\n", + "\n", + "Material = ['H', 'He', 'Li', 'Be', 'B', 'C', 'Cu', 'W', 'Pb']\n", + "Z = [ 1 , 2, 3, 4, 5, 6, 29, 74, 82]\n", + "A = [1.00794, 4.0026, 6.941, 9.01218, 10.811, 12.0107, 63.546, 183.84, 207.2]\n", + "density = [0.0763, 0.145, 0.512, 1.8477 , 2.08, 2.8, 8.96, 19.3 , 11.34]\n", + "X0 = [900.6, 786, 156.2, 35.2, 22.2, 21.4, 1.4, 0.4, 0.6]\n", + "\n", + "properties_dic = {'Material': Material, 'Z': Z, 'A': A,'Density': density, 'X0': X0}\n", + "properties = pd.DataFrame(data=properties_dic)\n", + "properties\n" + ] + }, + { + "cell_type": "code", + "execution_count": 33, + "metadata": {}, + "outputs": [], + "source": [ + "######\n", + "#Realistic target\n", + "positron_frequency = 1.e6 #[Hz]\n", + "target_length = 3 #[cm]\n", + "cs = cross_section(E)*10.e-31 #[uBarn]--> [cm^2]\n", + "time = 60 * 60 *24 *7 #[secconds]\n", + "\n", + "\n", + "properties['L'] = target_length\n", + "properties['Cross section'] = cs\n", + "\n", + "\n", + "#Number of positrons \n", + "N_positrons = positron_frequency * time \n", + "\n", + "#Number of muons\n", + "properties['N_muons'] = N_positrons * (properties['Z']*properties['Density']*Avogadro_number/properties['A']) * properties['Cross section'] * properties['L']\n", + "\n", + "#Weight\n", + "rf = properties.at[3,'N_muons']/N_positrons\n" + ] + }, + { + "cell_type": "code", + "execution_count": 34, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "
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8Pb82207.2000011.34000.632.792678e-311.369437e+06
\n", + "
" + ], + "text/plain": [ + " Material Z A Density X0 L Cross section N_muons\n", + "0 H 1 1.00794 0.0763 900.6 3 2.792678e-31 2.309908e+04\n", + "1 He 2 4.00260 0.1450 786.0 3 2.792678e-31 2.210857e+04\n", + "2 Li 3 6.94100 0.5120 156.2 3 2.792678e-31 6.752646e+04\n", + "3 Be 4 9.01218 1.8477 35.2 3 2.792678e-31 2.502456e+05\n", + "4 B 5 10.81100 2.0800 22.2 3 2.792678e-31 2.935434e+05\n", + "5 C 6 12.01070 2.8000 21.4 3 2.792678e-31 4.268210e+05\n", + "6 Cu 29 63.54600 8.9600 1.4 3 2.792678e-31 1.247736e+06\n", + "7 W 74 183.84000 19.3000 0.4 3 2.792678e-31 2.370576e+06\n", + "8 Pb 82 207.20000 11.3400 0.6 3 2.792678e-31 1.369437e+06" + ] + }, + "execution_count": 34, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "properties" + ] + }, + { + "cell_type": "code", + "execution_count": 35, + "metadata": {}, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of positrons produced in a week 6.05e+11\n", + "\n", + "Number of muons produced after a week using Be as a target 2.50e+05\n", + "\n", + "Rescaling factor if using Be as a target 4.14e-07\n" + ] + } + ], + "source": [ + "print('Number of positrons produced in a week '\"{:.2e}\".format( N_positrons))\n", + "print('')\n", + "print('Number of muons produced after a week using Be as a target '\"{:.2e}\".format( properties.at[3,'N_muons']))\n", + "print('')\n", + "print('Rescaling factor if using Be as a target '\"{:.2e}\".format( rf))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Properties of the beam\n", + "7. repeat what done so far simulating now the actual transverse shape and energy spread of the beam: for the former assume a flat distribution in a circle of radius $r=1$ cm and for the latter a gaussian distribution centered at the nominal beam energy and a width of $0.5$ GeV;" + ] + }, + { + "cell_type": "code", + "execution_count": 36, + "metadata": {}, + "outputs": [], + "source": [ + "##################################################################################\n", + "#Simulation parameters\n", + "\n", + "N = 10**7 #Number of positrons\n", + "E_lab = 45 #GeV\n", + "sigma = 0.5 # mean and standard deviation\n", + "\n", + "###################################################################################" + ] + }, + { + "cell_type": "code", + "execution_count": 37, + "metadata": {}, + "outputs": [], + "source": [ + "#Realistic beam\n", + "#Up to this point we have been assuming that the energy of the incident \n", + "#beam had a constant value, now we want to make a model where the energy\n", + "#of the beam has a gaussian distribution.\n", + "\n", + "E_lab_instances = np.random.normal(E_lab, sigma, N)\n", + "\n", + "#Now we need to boost them to the CoM frame\n", + "vz = np.sqrt((E_lab-electron_mass)/(E_lab+electron_mass))\n", + "gamma = 1/np.sqrt(1-vz**2)\n", + "\n", + "E_cm_instances = 2 *gamma*(E_lab_instances-vz*np.sqrt(E_lab_instances**2-electron_mass**2))\n" + ] + }, + { + "cell_type": "code", + "execution_count": 38, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Plot scaled histogram\n", + "fig, (ax1,ax2) = plt.subplots(nrows=2, ncols=1, figsize=(12, 10))\n", + "\n", + "n, bins, _ = ax1.hist(E_lab_instances, bins=90,color='orange', ec='black')\n", + "\n", + "d = (bins[1]-bins[0])\n", + "scaling = d * n.sum()\n", + "\n", + "ax1.plot(bins, scaling/(sigma * np.sqrt(2 * np.pi)) *np.exp( - (bins - E_lab)**2 / (2 * sigma**2) ),color='blue', label='Gaussian distribution media=45 GeV sigma= 0.5 GeV')\n", + "\n", + "ax1.set_title('Positron beam energy distribution in the Lab frame', fontsize=15)\n", + "ax1.set_xlabel(' Energy [GeV]', fontsize=15)\n", + "ax1.set_ylabel('Counts', fontsize=15)\n", + "ax1.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + "ax1.legend()\n", + "\n", + "n, bins, _ = ax2.hist(E_cm_instances, bins=90,color='orange', ec='black')\n", + "\n", + "d = (bins[1]-bins[0])\n", + "scaling = d * n.sum()\n", + "\n", + "ax2.axvline(x=2*muon_mass, label='Threshold energy')\n", + "ax2.set_title('Positron beam energy distribution in the CoM frame', fontsize=15)\n", + "ax2.set_xlabel(' Energy [GeV]', fontsize=15)\n", + "ax2.set_ylabel('Counts', fontsize=15)\n", + "ax2.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + "ax2.legend()\n", + "\n", + "plt.subplots_adjust(top=0.8, wspace=0.4, hspace=0.4)\n", + "\n", + "plt.show()\n" + ] + }, + { + "cell_type": "code", + "execution_count": 39, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Once we have the energy distribution plot a heatmap of the beam\n", + "\n", + "\n", + "pixels=300\n", + "size =(-1.5,1.5,-1.5,1.5)\n", + "\n", + "# We randomly pick (pixel x pixels) elements of the energy distribution to plot the beam cross section\n", + "\n", + "z = np.random.choice(E_lab_instances, size=(pixels,pixels), replace=True, p=None) \n", + "\n", + "\n", + "plt.rcParams[\"figure.figsize\"] = (8,8)\n", + "plt.imshow(circular_section(z),cmap='plasma', extent=(size),origin='lower')\n", + "plt.title('Positron beam cross section',fontsize=17)\n", + "plt.ylabel(r'${y}$ [cm]',fontsize=17) \n", + "plt.xlabel(r'${x}$ [cm]',fontsize=17)\n", + "plt.colorbar()\n", + "plt.clim(np.min(E_lab_instances),np.max(E_lab_instances))\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## SIMULATION 2" + ] + }, + { + "cell_type": "code", + "execution_count": 40, + "metadata": {}, + "outputs": [], + "source": [ + "##################################################################################\n", + "#Simulation parameters\n", + "\n", + "N = 10**6 #Number of positrons \n", + "E_lab = 45 #GeV\n", + "sigma = 0.5 # mean and standard deviation\n", + "\n", + "###################################################################################" + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [], + "source": [ + "##Now that we have the energy distributions and also an idea of the shape\n", + "##we can repeat the previous part\n", + "\n", + "#Obtain the positron energy samples in the laboratory frame\n", + "E_lab_samples = np.random.normal(E_lab, sigma, N)\n", + "\n", + "#Boost of the positrons energy to the Center of Mass Frame\n", + "vz = np.sqrt((E_lab-electron_mass)/(E_lab+electron_mass))\n", + "gamma = 1/np.sqrt(1-vz**2)\n", + "\n", + "E_cm_samples = 2 *gamma*(E_lab_samples-vz*np.sqrt(E_lab_samples**2-electron_mass**2))\n", + "\n", + "#Filter the values below the threshold\n", + "E_cm_samples = E_cm_samples[E_cm_samples> 2* muon_mass]\n", + "\n", + "N_instances = len(E_cm_samples)\n", + "\n", + "theta_cm_instances = inv_cdf(E_cm_samples,np.random.random(N_instances))\n", + "\n", + "phi_cm_instances = np.random.uniform(0., 2*np.pi, N_instances)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [], + "source": [ + "#Calculate the total momentum p CM\n", + "#Calculate the momentum components in CM\n", + "p_cm_instances = np.sqrt(E_cm_samples**2/4-muon_mass**2)\n", + "\n", + "pxm_cm, pym_cm, pzm_cm = sph_to_cart(p_cm_instances,theta_cm_instances,phi_cm_instances) \n", + "#Calculate the momentum components in LAB\n", + "vz = -np.sqrt(1-4*electron_mass**2/E_cm_samples**2) \n", + "gamma = 1/np.sqrt(1-vz**2)\n", + "\n", + "pxm_lb = pxm_cm\n", + "pym_lb = pym_cm\n", + "pzm_lb = gamma * pzm_cm - vz * gamma *E_cm_samples/2\n", + "\n", + "#Calculate the total momentum p LAB\n", + "#Obtain the angles thet and phi LAB\n", + "p_lb_instances = np.sqrt(pxm_lb**2 + pym_lb**2 + pzm_lb**2)\n", + "\n", + "theta_lb_instances = np.arccos(pzm_lb/p_lb_instances)\n", + "phi_lb_instances = np.arctan2(pym_lb,pxm_lb) + np.pi\n" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Maximum theta according to the theory [LEMMA] 0.09271 deg\n", + "Maximum theta in the simulation 0.09832 deg\n", + "The media for the theta angle 0.03715 deg\n" + ] + } + ], + "source": [ + "plot_angles_hist(theta_cm_instances*deg,phi_cm_instances*deg,'coral','royalblue','Muon angle distribution in the CoM frame')\n", + "plot_angles_hist(theta_lb_instances*deg,phi_lb_instances*deg,'coral','royalblue','Muon angle distribution in the Lab frame')\n", + "\n", + "theta_max_t = 4 * electron_mass /np.max(E_cm_samples) **2 * np.sqrt(np.max(E_cm_samples) **2 /4. -muon_mass**2)\n", + "print('Maximum theta according to the theory [LEMMA]', \"{:.5f}\".format(theta_max_t*deg), \"deg\")\n", + "print('Maximum theta in the simulation ', \"{:.5f}\".format(np.max(theta_lb_instances)*deg), \"deg\")\n", + "print('The media for the theta angle ', \"{:.5f}\".format(np.average(theta_lb_instances)*deg), \"deg\")\n" + ] + }, + { + "cell_type": "code", + "execution_count": 44, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", 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ThetaPhiMuon pxMuon pyMuon pz
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" + ], + "text/plain": [ + " Theta Phi Muon px Muon py Muon pz\n", + "0 0.000646 4.056046 0.009198 0.011942 23.341541\n", + "1 0.000322 0.064698 -0.007016 -0.000455 21.816152\n", + "2 0.000268 3.813472 0.004168 0.003315 19.856162\n", + "3 0.000929 2.852193 0.019475 -0.005799 21.881739\n", + "4 0.000641 6.124583 -0.013487 0.002157 21.310167\n", + "... ... ... ... ... ...\n", + "905960 0.000938 4.935098 -0.005120 0.022609 24.715916\n", + "905961 0.000490 1.520282 -0.000582 -0.011520 23.529080\n", + "905962 0.000731 1.867105 0.005163 -0.016910 24.178993\n", + "905963 0.001188 6.211744 -0.028318 0.002027 23.896666\n", + "905964 0.001155 4.111988 0.013236 0.019330 20.281724\n", + "\n", + "[905965 rows x 5 columns]" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#Write the results to a file \n", + "\n", + "s2_muons_com = pd.DataFrame({'Theta' : theta_cm_instances,'Phi' : phi_cm_instances,'Muon px' : pxm_cm, 'Muon py' : pym_cm, 'Muon pz' : pzm_cm})\n", + "#s2_muons_com.to_csv('s2_muons_momentum_com.csv', index=False)\n", + "\n", + "s2_muons_lab = pd.DataFrame({'Theta' : theta_lb_instances,'Phi' : phi_lb_instances,'Muon px' : pxm_lb, 'Muon py' : pym_lb, 'Muon pz' : pzm_lb})\n", + "#s2_muons_lab.to_csv('s2_muons_momentum_lab.csv', index=False)\n", + "\n", + "s2_muons_lab\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Aditional considerations\n", + "\n", + "8. given that the electrons traversing the target lose energy as $E(z)=E_0 \\exp{-z/X_0}$ (with z the longitudinal coordinate of the target, the one parallel to the beam direction and $X_0$ is the Beryllium radiation length), compute the nominal beam energy $E_0$ such that muon pairs can be generated along the whole length of the target;\n", + "9. (optional) take the former point into account when generating the events (i.e. the proccess $\\sqrt{s}$ depend on the position along the target where the $e^+ - e^-$ scattering occurrs.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The threshold energy in the center of mass frame is $E_{t CoM} = 2 m_\\mu$. As the law for the energy decay is given in the laboratory frame where the Beryllium target has a length of 3 cm we boost $E_{threshold CoM}$ to the laboratory frame where the electron is at rest and the positron has all the kinetic energy.\n", + "\n", + "$$E_{tLab} = m_e \\gamma ^2 + \\gamma v p$$\n", + "\n", + "Where $$\\gamma =\\frac{1}{\\sqrt{1-v^2}}$$ and $$v = \\sqrt{\\frac{E_{t CoM}^2-4m_e^2}{E_{t CoM}^2}}$$\n", + "\n", + "Using the identity $m\\gamma^2v =\\gamma p$ to write all in term of the masses $m_\\mu$ and $m_e$ obtaining as a result:\n", + "$$E_{tLab} = 2\\frac{m_\\mu^2}{m_e}-m_e$$\n", + "\n", + "$$E_{tLab} \\sim 43.6931 \\,\\,\\,GeV$$\n", + "\n", + "Now the nominal beam energy can be obtained solving the equation for the energy decay in the target:\n", + "\n", + "$$E_{0 lab} = E_{tLab} e^{l/X_0}$$\n", + "\n", + "Taking a target length of $l=3$cm and the Beryllium radiation length as $X_0 = 35.2$ cm we obtain the nominal beam energy: \n", + "\n", + "$$E_{0 lab} \\sim 47.58 \\,\\,\\,GeV$$ " + ] + }, + { + "cell_type": "code", + "execution_count": 46, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Plots of energy decay for different materials\n", + "x = np.linspace(0,3,num=100)\n", + "for i in range(0,8):\n", + " plt.plot(x, 45 * np.exp(-x/properties.at[i,'X0']),label = properties.at[i,'Material'])\n", + " \n", + "plt.axhline(y=43.6931, color='r', linestyle=':',label =r'$E_{tLab}$')\n", + "plt.axhline(y=47.58, color='b', linestyle=':',label =r'$E_{0 lab}$')\n", + "plt.title('Energy decay for different materials', fontsize=15)\n", + "plt.xlabel('Distance [cm]', fontsize=15)\n", + "plt.xlim(0.,3.)\n", + "plt.ylabel('Energy [Gev]', fontsize=15)\n", + "plt.ylim(0.,48.)\n", + "plt.legend(fontsize=15)\n", + "plt.show()\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## SIMULATION 3" + ] + }, + { + "cell_type": "code", + "execution_count": 47, + "metadata": {}, + "outputs": [], + "source": [ + "##################################################################################\n", + "#Simulation parameters\n", + "\n", + "N = 10**6 #Number of positrons\n", + "E_lab = 47.58 #[GeV]\n", + "sigma = 0.5 # mean and standard deviation\n", + "\n", + "###################################################################################" + ] + }, + { + "cell_type": "code", + "execution_count": 48, + "metadata": {}, + "outputs": [], + "source": [ + "#Obtain the positron energy samples in the laboratory frame\n", + "E_lab_samples = np.random.normal(E_lab, sigma, N)\n", + "\n", + "#We keep the distribution for ploting purposes\n", + "E_lab_plot = E_lab_samples \n", + "\n", + "#Now we distribute the energies according the position in the Beryllium plate\n", + "##########################################################################\n", + "x = np.random.uniform(low=0., high=target_length, size=(len(E_lab_samples),))\n", + "E_lab_samples = E_lab_samples*np.exp(-x/properties.at[3,'X0'])\n", + "##########################################################################\n", + "\n", + "#Boost of the positrons energy to the Center of Mass Frame\n", + "vz = np.sqrt((E_lab_samples-electron_mass)/(E_lab_samples+electron_mass)) \n", + "gamma = 1/np.sqrt(1-vz**2)\n", + "\n", + "E_cm_samples = 2 *gamma*(E_lab_samples-vz*np.sqrt(E_lab_samples**2-electron_mass**2))\n", + "\n", + "#Filter the values below the threshold\n", + "b = E_cm_samples[E_cm_samples> 2* muon_mass]\n", + "\n", + "N_instances = len(b)\n", + "\n", + "theta_cm_instances = inv_cdf(b,np.random.random(N_instances))\n", + "\n", + "phi_cm_instances = np.random.uniform(0., 2*np.pi, N_instances)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 49, + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "#Energy distributions\n", + "fig, (ax1,ax2) = plt.subplots(nrows=1, ncols=2, figsize=(12, 4))\n", + "\n", + "n, bins, _ = ax1.hist(E_lab_plot, bins=50,color='orange', ec='grey')\n", + "ax1.axvline(x=43.6931, color='r', label=r'$E_{tLab}$')\n", + "ax1.axvline(x=47.58, label=r'$E_{0 lab}$')\n", + "ax1.set_title('Beam energy', fontsize=15)\n", + "ax1.set_xlabel(r'$Energy$ [GeV]', fontsize=15)\n", + "ax1.set_ylabel('Counts', fontsize=15)\n", + "ax1.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + "ax1.xaxis.set_major_formatter(FormatStrFormatter('%.2f'))\n", + "ax1.legend()\n", + "\n", + "\n", + "n, bins, _ = ax2.hist(E_lab_samples, bins=50,color='orange', ec='grey')\n", + "ax2.axvline(x=43.6931, color='r', label=r'$E_{tLab}$')\n", + "ax2.axvline(x=47.58, label=r'$E_{0 lab}$')\n", + "ax2.set_title('Beam energy atenuation (material)', fontsize=15)\n", + "ax2.set_xlabel(r'$Energy$ [GeV]', fontsize=15)\n", + "ax2.ticklabel_format(axis=\"y\", style=\"sci\", scilimits=(5,5))\n", + "ax2.xaxis.set_major_formatter(FormatStrFormatter('%.2f'))\n", + "ax2.legend()\n", + "\n", + "plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 50, + "metadata": {}, + "outputs": [], + "source": [ + "#Calculate the total momentum p CM\n", + "#Calculate the momentum components in CM\n", + "p_cm_instances = np.sqrt(b**2/4-muon_mass**2)\n", + "\n", + "pxm_cm, pym_cm, pzm_cm = sph_to_cart(p_cm_instances, theta_cm_instances, phi_cm_instances)\n", + "\n", + "#Calculate the momentum components in LAB\n", + "vz = -np.sqrt(1-4*electron_mass**2/b**2) \n", + "gamma = 1/np.sqrt(1-vz**2)\n", + "\n", + "pxm_lb = pxm_cm\n", + "pym_lb = pym_cm\n", + "pzm_lb = gamma * pzm_cm - vz * gamma *b/2\n", + "\n", + "#Calculate the total momentum p LAB\n", + "#Obtain the angles thet and phi LAB\n", + "p_lb_instances = np.sqrt(pxm_lb**2 + pym_lb**2 + pzm_lb**2)\n", + "\n", + "theta_lb_instances = np.arccos(pzm_lb/p_lb_instances)\n", + "phi_lb_instances = np.arctan2(pym_lb,pxm_lb) + np.pi" + ] + }, + { + "cell_type": "code", + "execution_count": 51, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Maximum theta according to the theory [LEMMA] 0.09214 deg\n", + "Maximum theta in the simulation 0.09508 deg\n", + "The media for the theta angle 0.04276 deg\n" + ] + } + ], + "source": [ + "plot_angles_hist(theta_cm_instances*deg,phi_cm_instances*deg,'coral','royalblue','Muon angle distribution in the CoM frame')\n", + "plot_angles_hist(theta_lb_instances*deg,phi_lb_instances*deg,'coral','royalblue','Muon angle distribution in the Lab frame')\n", + "\n", + "theta_max_t = 4 * electron_mass /np.max(b) **2 * np.sqrt(np.max(b) **2 /4. -muon_mass**2)\n", + "print('Maximum theta according to the theory [LEMMA]', \"{:.5f}\".format(theta_max_t*deg), \"deg\")\n", + "print('Maximum theta in the simulation ', \"{:.5f}\".format(np.max(theta_lb_instances)*deg), \"deg\")\n", + "print('The media for the theta angle ', \"{:.5f}\".format(np.average(theta_lb_instances)*deg), \"deg\")" + ] + }, + { + "cell_type": "code", + "execution_count": 52, + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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\n", 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" + ], + "text/plain": [ + " Theta Phi Muon px Muon py Muon pz\n", + "0 0.000475 5.588164 -0.007795 0.006499 21.346439\n", + "1 0.000492 5.825823 -0.008819 0.004341 19.991146\n", + "2 0.001341 3.617090 0.027505 0.014162 23.075905\n", + "3 0.000247 2.399713 0.004441 -0.004070 24.354779\n", + "4 0.001132 3.325873 0.020908 0.003897 18.789982\n", + "... ... ... ... ... ...\n", + "950154 0.000108 3.904517 0.001996 0.001908 25.562654\n", + "950155 0.000929 1.028358 -0.011230 -0.018631 23.415400\n", + "950156 0.001045 3.210778 0.019456 0.001348 18.665914\n", + "950157 0.000896 1.463935 -0.002008 -0.018718 21.003176\n", + "950158 0.000935 0.724451 -0.014750 -0.013053 21.061306\n", + "\n", + "[950159 rows x 5 columns]" + ] + }, + "execution_count": 53, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "#Write the results to a file \n", + "\n", + "s3_muons_com = pd.DataFrame({'Theta' : theta_cm_instances,'Phi' : phi_cm_instances,'Muon px' : pxm_cm, 'Muon py' : pym_cm, 'Muon pz' : pzm_cm})\n", + "#s3_muons_com.to_csv('s3_muons_momentum_com.csv', index=False)\n", + "\n", + "s3_muons_lab = pd.DataFrame({'Theta' : theta_lb_instances,'Phi' : phi_lb_instances,'Muon px' : pxm_lb, 'Muon py' : pym_lb, 'Muon pz' : pzm_lb})\n", + "#s3_muons_lab.to_csv('s3_muons_momentum_lab.csv', index=False)\n", + "\n", + "s3_muons_lab\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "### References\n", + "\n", + "* [LEMMA](https://doi.org/10.1016/j.nima.2015.10.097) Antonelli, M., Boscolo, M., Di Nardo, R., & Raimondi, P. (2016). Novel proposal for a low emittance muon beam using positron beam on target. Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, 807, 101–107.\n", + "* [Babayaga](https://www2.pv.infn.it/~hepcomplex/babayaga.html) event generator.\n", + "* [2018 Experiment](https://doi.org/10.1088/1748-0221/15/01/p01036): Amapane, N., Antonelli, M., Anulli, F., Ballerini, G., Bandiera, L., Bartosik, N., Bauce, M., Bertolin, A., Biino, C., Blanco-Garcia, O. R., Boscolo, M., Brizzolari, C., Cappati, A., Casarsa, M., Cavoto, G., Collamati, F., Cotto, G., Curatolo, C., Nardo, R. D., … Zanetti, M. (2020). Study of muon pair production from positron annihilation at threshold energy. Journal of Instrumentation, 15(01), P01036–P01036.\n", + "* [2021 proposal](https://cds.cern.ch/record/2712394?ln=en): the proposal for the experiment in 2021\n", + "* [MANDL] Mandl, F., & Shaw, G. (2013). _Quantum Field theory_. John Wiley & Sons.\n", + "* [CARDANO](http://encyclopediaofmath.org/index.php?title=Cardano_formula&oldid=29227) Cardano formula. _Encyclopedia of Mathematics_.\n", + "* [DEVROYE](https://doi.org/10.1007/978-1-4612-0711-5) Devroye, L., Györfi, L., & Lugosi, G. (1996). A Probabilistic Theory of Pattern Recognition. In Stochastic Modelling and Applied Probability. Springer New York." + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 2 +} \ No newline at end of file diff --git a/NEW_FILE.plt b/NEW_FILE.plt new file mode 100644 index 0000000..e69de29 diff --git a/Project.ipynb b/Project.ipynb index ea9396b..d9e85ad 100644 --- a/Project.ipynb +++ b/Project.ipynb @@ -80,7 +80,7 @@ "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", - "version": "3.5.4" + "version": "3.8.5" } }, "nbformat": 4, diff --git a/img/.~lock.boost.odg# b/img/.~lock.boost.odg# 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Differential cross section in the center of mass frame $\\sigma(\\vartheta,\\sqrt{s})$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Mandelstam variable s\n", + "The [Mandelstam variable](https://en.wikipedia.org/wiki/Mandelstam_variables) represents the squared of the 4-momenta for the in-going particles (and for the out-going particles too since the conservation of the 4 momentum)\n", + "\n", + "$$s=(p_1+p_2)^2=(p_3+p_4)^4$$\n", + "\n", + "Notice that $s$ represents the squared energy in the center of mass frame:\n", + "$$s=(E_{CM})^2$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "This means that the function we are searching $\\sigma(\\vartheta,\\sqrt{s})\\equiv\\sigma(\\vartheta,E_{CM})$, after we find that we can apply a boost to the laboratory frame where the electron on the target are at rest (point 3)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Deriving the differential cross section" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Remember that we are in the center of mass frame, this means that the electron and positron will have opposite momentum in this frame" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The scattering equation can be found computing the scattering amplitude $\\mathcal{M}$ that can be seen as a sort of wave function sice its modulus squared is linked to the probability of the event to happend (for a given $\\vartheta$ and $\\sqrt{s}$).\n", + "$\\mathcal{M}$ depends on the spin interactions of the particles, we will just compute\n", + "$$X=\\frac{1}{4}\\sum M$$ that represent the mean $\\mathcal{M}$ between all types of spin interactions (unpolarized cross section approximation)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "There are 3 possible versions of the differential cross section depending on the approximation you can make:\n", + "* $\\textbf{No approximations}$: this formula is pretty ugly and not necessary as the second one is way easier to implement and still be a good approximation\n", + "* $\\textbf{Neglecting $m_e$ in the energy term}$ this can make sense since the rest mass energy is $2 m_\\mu $: the contribution of the energy of the rest mass of electrons is way smaller\n", + "$$\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{CM}=\\frac{\\alpha^2}{16\\, s^2}\\frac{|p'|}{\\sqrt{s}}\\left(s+p'^2\\cos^2\\vartheta+m_\\mu^2\\right)$$\n", + "* In $\\textbf{ultrarelativistic limit}$, the muons are so energetic that we can neglet their rest mass energy, this means:\n", + "$E>>m_\\mu\\rightarrow s>>m_\\mu^2\\\\\n", + "|p|\\approx E$\n", + "\n", + " The formula from before becomes: $$\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{CM}=\\frac{\\alpha^2}{16 s}(1+\\cos^2\\vartheta)$$\n", + " However in the assignment it is clearly stated that the energy we are dealing with are in the order of $m_\\mu$ $(\\sqrt{s}\\sim m_\\mu)$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The differential cross section we choosed is then $$\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{CM}=\\frac{\\alpha^2}{16\\, s^2}\\frac{|p'|}{\\sqrt{s}}\\left(s+p'^2\\cos^2\\vartheta+m_\\mu^2\\right)$$\n", + "The relativistic total energy is $$E_{CM}^2=2p'^2c^2+4m_\\mu^2c^4\\rightarrow p'^2=\\frac{E_{CM}^2}{2c^2}-2m_\\mu^2c^2\\rightarrow p'^2=\\frac{s}{2c^2}-2m_\\mu^2c^2$$\n", + "Then our differential cross section becomes:\n", + "$$\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{CM}=\\frac{\\alpha^2}{16\\, s^2}\\sqrt{\\frac{{\\frac{s}{2c^2}-2m_\\mu^2c^2}}{{s}}}\\left(s+\\left(\\frac{s}{2c^2}-2m_\\mu^2c^2\\right)\\cos^2\\vartheta+m_\\mu^2\\right)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 2) The energy and angle distributions $\\sigma\\left(\\sqrt{s}\\right)$ and $\\sigma(\\vartheta)$\n", + "\n", + "We can see $\\left(\\frac{d\\sigma}{d\\Omega}\\right)_{CM}\\equiv \\sigma(\\vartheta,\\sqrt{s})$ as a [joint probability distribution](https://en.wikipedia.org/wiki/Joint_probability_distribution) i.e the probability of the event to happend with a specific $\\vartheta$ AND $\\sqrt{s}$.\n", + "If we integrate $\\sigma(\\vartheta,\\sqrt{s})$ in one of the two variable, we get the [marginal distribution](https://en.wikipedia.org/wiki/Marginal_distribution) for the other variable: for example if we integrate $\\sigma(\\vartheta,\\sqrt{s})$ in $\\sqrt{s}$ we obtain a certain function (distribution) for the other variable:\n", + "\n", + "$$\\int\\sigma(\\vartheta,\\sqrt{s})\\,d(\\sqrt{s})\\equiv \\sigma(\\vartheta)$$\n", + "\n", + "$\\sigma(\\vartheta)$ represents the probability for the event to happend according to a certain $\\vartheta$ independing of the energy $\\sqrt{s}$\n", + "\n", + "(and $\\sigma(\\sqrt{s})$ is obtained integrating in $\\vartheta$ and represents the probabiliy for the event to happend at a certain energy ($\\sqrt{s}$) for any given $\\vartheta$)\n", + "\n", + "Let's obtain those two distributions:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Deriving $\\sigma(\\vartheta)$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Oh God" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Deriving $\\sigma\\left(\\sqrt{s}\\right)$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "By integrating in $\\vartheta\\in[0,2\\pi]$ we get\n", + "$$\\sigma(\\sqrt{s})=\\frac{\\pi\\alpha^2}{8}\\frac{1}{(\\sqrt{s})^5}\\left[\\sqrt{\\frac{1}{2c^2}(\\sqrt{s})^2-2m_\\mu^2c^2}\\left((\\sqrt{s})^2\\left(1+\\frac{1}{4c^2}\\right)-m_\\mu^2\\left(1+c^2\\right)\\right)\\right]$$\n", + "Note that the argument in the $\\sqrt{\\quad}$ must be positive, this means:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$\\sqrt{\\frac{1}{2c^2}(\\sqrt{s})^2-2m_\\mu^2c^2}\\geq0$$\n", + "\n", + "$$\\sqrt{\\frac{1}{2c^2}(E)^2-2m_\\mu^2c^2}\\geq0$$\n", + "\n", + "$$\\sqrt{(E)^2-4m_\\mu^2c^4}\\geq0$$\n", + "\n", + "$$ \\sqrt{s}=E_{CM}\\geq 2m_\\mu c^2$$" + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import math\n", + "import numpy as np" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def sigma_of_sqrts(e):\n", + " alpha = 1\n", + " m_mu = 1\n", + " c = 1\n", + "\n", + " return ((math.pi*alpha*alpha)/8)/(math.pow(e,5))*math.sqrt( ((e*e)/(2*c*c)) - 2*m_mu*m_mu*c*c )*( e*e*(1+1/(4*c*c)) - m_mu*m_mu*(1+c*c) )" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "m_mu = 1\n", + "c = 1\n", + "energies = np.arange(20)\n", + "energies = energies+ 2*m_mu*c*c\n", + "\n", + "ss = []\n", + "for i in range(np.size(energies)):\n", + " ss.append(sigma_of_sqrts(energies[i]))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(1.5, 0.02, 'threshold energy')" + ] + }, + "execution_count": 4, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "import matplotlib.pyplot as plt\n", + "plt.figure(figsize=(10, 3))\n", + "plt.plot(energies, ss, '-o')\n", + "plt.xlim(0,)\n", + "plt.plot([2, 2], [0, .025], color='r', linestyle='-', linewidth=1, alpha = 0.5)\n", + "plt.xlabel(\"centre of mass energy\")\n", + "plt.ylabel(\"cross section\")\n", + "plt.text(1.5, .02, 'threshold energy', fontsize=10, color='r')" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# 3) Bosting to the laboratory frame" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have to apply a boost for the resulting momenta to get the result in the laboratory frame, that is the frame where the electron are at rest (in a target).\n", + "To get the boost application we have to find the electrons momentum in the centre of mass frame, not a problem since we know its energy and mass." + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Deriving the Lorentz matrix $\\Lambda$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We have to boost in a frame where the electron $e^-$ is at rest, this means that we have to find the velocity of the electron in the COM frame and since the velocity is negative we will find a Lorentz matrix of the following form:\n", + "$$\\left(\\begin{array}\n", + " &\\gamma &-v\\gamma & 0 & 0 \\\\\n", + " -v\\gamma & \\gamma & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " 0 & 0 & 0 & 1 \\\\ \n", + "\\end{array}\\right)\\Rightarrow\\left(\\begin{array}\n", + " &\\gamma &v\\gamma & 0 & 0 \\\\\n", + " v\\gamma & \\gamma & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " 0 & 0 & 0 & 1 \\\\ \n", + "\\end{array}\\right)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Since the particle $e^-$ is moving in the direction $\\hat{x}$, we can easily find the velocity using the definition of the relativistic momentum:\n", + "$$p=m_e\\gamma v\\to v\\gamma = \\frac{p}{m_e}\\to \\frac{v}{\\sqrt{1-v^2}}=\\frac{p}{m_e}\\to v= \\frac{p}{m_e\\sqrt{1+\\frac{p^2}{m_e^2}}}=\\frac{p}{\\sqrt{m_e^2 + p^2}}$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Notice that the energy of the particle in the COM is $E_p=\\sqrt{m_e^2+p^2}$ (the denominator)\n", + "\n", + "$$\\begin{cases}E_p^2=m_e^2+p^2\\\\ E^2_{CM}=4m_e^2+4p^2\\end{cases}$$\n", + "\n", + "v then becomes:" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$v=\\sqrt{ \\frac{E^2_{CM}-4m_e^2}{E^2_{CM}} }$$" + ] + }, + { + "cell_type": "code", + "execution_count": 7, + "metadata": {}, + "outputs": [], + "source": [ + "def velocity(ecm):\n", + " me = 1\n", + " k = 0.05 # just for plotting purposes\n", + " return k*math.sqrt(ecm*ecm - 4*me*me)/ecm\n", + "\n", + "ecm = np.arange(2,3,0.1)\n", + "v = []\n", + "for i in range(np.size(ecm)):\n", + " v.append(velocity(ecm[i]))\n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 8, + "metadata": {}, + "outputs": [ + { + "data": { + "text/plain": [ + "Text(0, 0.5, 'cross section')" + ] + }, + "execution_count": 8, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 3))\n", + "plt.plot(energies, ss, '-o',color = 'g')\n", + "plt.plot(ecm, v, '-o',color='b')\n", + "plt.plot([2, 2], [0, .02], color='r', linestyle='-', linewidth=1, alpha = 0.5)\n", + "plt.xlabel(\"centre of mass energy\")\n", + "plt.ylabel(\"cross section\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## The Lorentz transformation" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "The Lorentz matrix is then:\n", + "$$\\left(\\begin{array}\n", + " &\\gamma &v\\gamma & 0 & 0 \\\\\n", + " v\\gamma & \\gamma & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " 0 & 0 & 0 & 1 \\\\ \n", + "\\end{array}\\right),\\qquad\\qquad v=\\sqrt{ \\frac{E^2_{CM}-4m_e^2}{E^2_{CM}} }$$\n", + "Let's see how a boost work:\n", + "$$\\Lambda^\\mu_\\nu P^\\nu = P'^\\mu$$\n", + "Where $P^\\nu$ is the 4 momentum before the boosting (in the COM frame) and $P'^\\nu$ is the 4 momentum after the boosting (in the LAB frame)\n", + "\n", + "$$P^\\mu=\\left(\\begin{array}{c}m\\gamma \\\\ p\\cos\\vartheta \\\\ p\\sin\\vartheta\\\\ 0 \\end{array}\\right)$$\n", + "\n", + "$m\\gamma$ is the total energy of the particle $E_p$ (you can write $E_p$ either as $m\\gamma$ or the formula with the squared root, that is the same)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "$$P'=\\left(\\begin{array}\n", + " &\\gamma &v\\gamma & 0 & 0 \\\\\n", + " v\\gamma & \\gamma & 0 & 0 \\\\\n", + " 0 & 0 & 1 & 0 \\\\\n", + " 0 & 0 & 0 & 1 \\\\ \n", + "\\end{array}\\right)\\left(\\begin{array}{c}m\\gamma \\\\ p\\cos\\vartheta \\\\ p\\sin\\vartheta\\\\ 0 \\end{array}\\right)=\\left(\\begin{array}{c}m\\gamma^2 + \\gamma vp\\cos\\vartheta \\\\ m\\gamma^2 v + \\gamma p\\cos\\vartheta \\\\ p\\sin\\vartheta\\\\ 0 \\end{array}\\right)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "You can check that $P^2=P'^2=-m^2$ since it is a scalar it is invariant under lorentz boost, it is just to check if the boost is done correctly (I already checked)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "From here we can get the relationship $\\vartheta\\leftrightarrow\\vartheta'$ the angle of the scattered particle before and after the boosts (yes it changes using special relativity!)\n", + "\n", + "$$\\begin{cases}\n", + " m\\gamma^2v+\\gamma p\\cos\\vartheta = p'\\cos\\vartheta' \\\\\n", + " p\\sin\\vartheta = p\\sin\\vartheta'\n", + "\\end{cases}$$\n", + "\n", + "Writing $m\\gamma^2 v$ as $\\gamma p$ we have\n", + "\n", + "$$\\begin{cases}\n", + " \\gamma p +\\gamma p\\cos\\vartheta = p'\\cos\\vartheta' \\\\\n", + " p\\sin\\vartheta = p\\sin\\vartheta'\n", + "\\end{cases}$$\n", + "\n", + "Dividing the first to the second we get:\n", + " $$\\tan\\vartheta'=\\frac{1}{\\gamma}\\left(\\frac{\\sin\\vartheta}{1+\\cos\\vartheta}\\right)$$\n", + " \n", + "Here you can play with an [interactive desmos graph](https://www.desmos.com/calculator/n1ldtauxer), g is the $gamma$ factor, for $g=1$ we have no boost and the transformation $\\vartheta\\leftrightarrow\\vartheta'$ is indeed identical" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.5" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}