From 30cdc719d2e7c7ffa2908c3bfa6440d0964865ee Mon Sep 17 00:00:00 2001 From: Vitor Shen <17490173+shenvitor@users.noreply.github.com> Date: Fri, 28 Jun 2024 12:58:45 +0200 Subject: [PATCH] address to @redeboer comments until equation 3 and reduce events sample --- docs/report/999.ipynb | 53 +++++++++++++++++++++---------------------- 1 file changed, 26 insertions(+), 27 deletions(-) diff --git a/docs/report/999.ipynb b/docs/report/999.ipynb index 9fbe40ad..a2a5c7c9 100644 --- a/docs/report/999.ipynb +++ b/docs/report/999.ipynb @@ -25,7 +25,7 @@ ":::{card} PWA101: Amplitude Analysis with Python basics\n", "TR-999\n", "^^^\n", - "This document introduces Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model. Basic Python programming and libraries (e.g. `numpy`, `scipy`, etc.) are used to illustrate the general process and full workflow of PWA in hadron physics.\n", + "This document introduces Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model. Basic Python programming and libraries (e.g. `numpy`, `scipy`, etc.) are used to illustrate the more fundamental steps of PWA in hadron physics.\n", "+++\n", "✅ [ComPWA/RUB-EP1-AG#93](https://github.com/ComPWA/RUB-EP1-AG/issues/93), [compwa.github.io#217](https://github.com/ComPWA/compwa.github.io/pull/217)\n", ":::\n", @@ -38,7 +38,7 @@ "tags": [] }, "source": [ - "# Amplitude Analysis 101" + "# Amplitude Analysis 101 (PWA 101)" ] }, { @@ -60,10 +60,11 @@ "tags": [] }, "source": [ - "- This document introduces Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model.\n", - "- Only basic Python programming and libraries (e.g. `numpy`, `scipy`, etc.) are used to illustrate the general process in PWA.\n", - "- Before advancing to the complexities of symbolic expressions (computations) with e.g. `sympy` later, see [here](https://github.com/ComPWA/gluex-nstar/issues/1), and as a comparison .\n", - "- This tutorial aims to equip readers with a basic understanding of PWA methodologies and full workflow in hadron physics through a practical, hands-on example." + ":::{note}Summary\n", + "- This document introduces Amplitude Analysis / Partial Wave Analysis (PWA) by demonstrating its application to a specific reaction channel and amplitude model. It aims to equip readers with a basic understanding of the full workflow and methodologies of PWA in hadron physics through a practical, hands-on example.\n", + "- Only basic Python programming and libraries (e.g. `numpy`, `scipy`, etc.) are used to illustrate the more fundamental steps in a PWA.\n", + "- Before advancing to the complexities of symbolic expressions (computations) with tools such as `sympy` as illustrated in PWA101 v2.0 (see [here](https://compwa.github.io/gluex-nstar)), we will focus on Python basics. This will allow us to draw a comparison between basic Python programming and symbolic computations.\n", + ":::" ] }, { @@ -123,7 +124,7 @@ "\n", "This amplitude model is adapted from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/) by Vincent Mathieu.\n", "\n", - "The photo-production reaction is $ \\gamma p \\to \\eta \\pi^0 p$, which is one of the reaction channels in experiment such as [the GlueX experiment](http://www.gluex.org/). The decays are described by an amplitude model with three possible resonances: $a_2$, $\\Delta^+$, and $N^*$. " + "The photo-production reaction $ \\gamma p \\to \\eta \\pi^0 p$ is one of the reaction channels in experiment such as [the GlueX experiment](http://www.gluex.org/). For simplicity, the decays are described by an amplitude model with three possible resonances: $a_2$, $\\Delta^+$, and $N^*$. " ] }, { @@ -145,7 +146,7 @@ "tags": [] }, "source": [ - "The Amplitude $A$ has three parts in this case:" + "Given these three subsystems in this particle transition, we can identify three amplitudes $A^{12}$, $A^{23}$, and $A^{31}$:" ] }, { @@ -156,13 +157,13 @@ "source": [ "$$\n", "\\begin{eqnarray}\n", - "A^{12} &=& \\frac{\\sum a_m Y_2^m (\\Omega_1)}{s-m^2_{a_2}+im_{a_2} \\Gamma_{a_2}} \\times s^{0.5+0.9u_3} \\nonumber \\\\\n", - "A^{23} &=& \\frac{\\sum b_m Y_1^m (\\Omega_2)}{s-m^2_{\\Delta}+im_{\\Delta} \\Gamma_{\\Delta}} \\times s^{0.5+0.9t_1} \\nonumber \\\\\n", - "A^{31} &=& \\frac{c_0}{s-m^2_{N^*}+im_{N^*} \\Gamma_{N^*}} \\times s^{1.08+0.2t_2} \n", + "A^{12} &=& \\frac{\\sum a_m Y_2^m (\\Omega_1)}{s_{12}-m^2_{a_2}+im_{a_2} \\Gamma_{a_2}} \\times s_{12}^{0.5+0.9u_3} \\nonumber \\\\\n", + "A^{23} &=& \\frac{\\sum b_m Y_1^m (\\Omega_2)}{s_{23}-m^2_{\\Delta}+im_{\\Delta} \\Gamma_{\\Delta}} \\times s_{23}^{0.5+0.9t_1} \\nonumber \\\\\n", + "A^{31} &=& \\frac{c_0}{s_{31}-m^2_{N^*}+im_{N^*} \\Gamma_{N^*}} \\times s_{31}^{1.08+0.2t_2} \n", "\\end{eqnarray}\n", "$$ (full_model_label)\n", "\n", - "where $s, t, u$ are the Mandelstam variables $s_{ij}=(p_i+p_j)^2$, $t_i=(p_a-p_i)^2$, and $u_i=(p_b-p_i)^2$, m is the mass, $\\Gamma$ is the width, $Y^m_l$ is the spherical harmonics, $\\Omega_i$ is the decay angles (a pair of Euler angles), and $a_i$, $b_i$, and $c_i$ are coefficients" + "where $s, t, u$ are the Mandelstam variables $s_{ij}=(p_i+p_j)^2$, $t_i=(p_a-p_i)^2$, and $u_i=(p_b-p_i)^2$, m is the mass, $\\Gamma$ is the width, $Y^m_l$ is the spherical harmonics, $\\Omega_i$ is the decay angles which is a pair of Euler angles (polar angle $\\theta$ and azimuthal angle $\\phi$), and $a_i$, $b_i$, and $c_i$ are coefficients" ] }, { @@ -171,9 +172,8 @@ "tags": [] }, "source": [ - "The original full amplitude model from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/) is shown in equation {eq}`full_model_label`.\n", - "\n", - "*In this report, only the Breit-Wigner and Spherical harmonics terms are kept for doing PWA eventually (The exponential mandelstam variable term is abandoned), as shown in equation {eq}`BW_SH_label`." + "The original full amplitude model from the [Lecture 11 in STRONG2020 HaSP School](https://indico.ific.uv.es/event/6803/contributions/21223/) is shown in Equation {eq}`full_model_label`.\n", + "*In this report, only the Breit-Wigner and Spherical harmonics terms are kept for doing PWA eventually (The exponential mandelstam variable term is abandoned), as shown in Equation {eq}`BW_SH_label`.*" ] }, { @@ -184,10 +184,10 @@ "source": [ "$$\n", "\\begin{eqnarray}\n", - "A^{12} &=& \\frac{\\sum a_m Y_2^m (\\Omega_1)}{s-m^2_{a_2}+im_{a_2} \\Gamma_{a_2}} \\\\\n", - "A^{23} &=& \\frac{\\sum b_m Y_1^m (\\Omega_2)}{s-m^2_{\\Delta}+im_{\\Delta} \\Gamma_{\\Delta}} \\\\\n", + "A^{12} &=& \\frac{\\sum a_m Y_2^m (\\Omega_1)}{s_{12}-m^2_{a_2}+im_{a_2} \\Gamma_{a_2}} \\\\\n", + "A^{23} &=& \\frac{\\sum b_m Y_1^m (\\Omega_2)}{s_{23}-m^2_{\\Delta}+im_{\\Delta} \\Gamma_{\\Delta}} \\\\\n", "\\\n", - "A^{31} &=& \\frac{c_0}{s-m^2_{N^*}+im_{N^*} \\Gamma_{N^*}} \n", + "A^{31} &=& \\frac{c_0}{s_{31}-m^2_{N^*}+im_{N^*} \\Gamma_{N^*}} \n", "\\end{eqnarray}\n", "$$ (BW_SH_label)" ] @@ -198,7 +198,7 @@ "tags": [] }, "source": [ - "with intensity $I$ and amplitude $A$:\n", + "The intensity $I$ that describes our measured distributions is then expressed as a coherent sum of the amplitudes $A^{ij}$:\n", "\n", "$$\n", "\\begin{eqnarray}\n", @@ -207,7 +207,7 @@ "\\end{eqnarray}\n", "$$ (123_label)\n", "\n", - "where $\\quad 1 \\equiv \\eta ; \\quad 2 \\equiv \\pi^0 ; \\quad 3 \\equiv p$" + "where $\\quad 1 \\equiv \\eta , \\quad 2 \\equiv \\pi^0 , \\quad 3 \\equiv p$." ] }, { @@ -217,7 +217,7 @@ }, "source": [ ":::{note}\n", - "The ultimate choice of the amplitude model (equations (2) and (3)) for PWA in this tutorial consists of three resonances, and each of them are formed by two terms: Breit-Wigner with Spherical harmonics ($l = 2, 1, 0$).\n", + "The ultimate choice of the amplitude model (Equations {eq}`BW_SH_label` and {eq}`123_label`) for PWA in this tutorial consists of three resonances, and each of them are formed by two terms: Breit-Wigner with spherical harmonics ($l = 2, 1, 0$).\n", ":::" ] }, @@ -228,10 +228,9 @@ }, "source": [ ":::{important}\n", - "The spin of the $\\eta$ meson and the $\\pi^0$ meson are all 0. But the spin of the proton is not 0, it is spin-$\\frac{1}{2}$.\n", - "\n", - "In this amplitude model the **spin** of baryon (proton in this example reaction) is simplified, treated as spin-0 particle, and thus not realistic.\n", - "Additionally, the mesons $\\eta$ and $\\pi^0$ are originally spin-0 particles.\n", + "The spin of the $\\eta$ meson and the $\\pi^0$ meson are all 0, but the spin of the proton is not 0, it is spin-$\\frac{1}{2}$.\n", + "In this amplitude model the **spin** of baryon (proton in this example reaction) is simplified, \n", + "by treating it as a spin-0 particle.\n", "Overall,\n", "the $\\eta$, $\\pi^0$ and $p$ are all treated as spin-0 particles.\n", "\n", @@ -278,8 +277,8 @@ }, "outputs": [], "source": [ - "phsp_events = 1_000_000\n", - "data_events = 500_000" + "phsp_events = 800_000\n", + "data_events = 400_000" ] }, {