DOC: add notebook for Lecture 11

docs/lecture11.ipynb

@@ -0,0 +1,394 @@
+{
+ "cells": [
+  {
+   "cell_type": "markdown",
+   "id": "087f68c1-f88d-43b6-9494-26da5bc621ca",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "# Lecture 11 Helicity Formalism\n",
+    "The example `Three-particles-3.dat` in lecture 11\n",
+    "based on [Lecture 11](https://indico.ific.uv.es/event/6803/contributions/21223) by Vincent Mathieu "
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "2b01c249-f183-4faf-9ccd-d6069f678467",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "hide-input",
+     "remove-output"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "%pip install -q gdown matplotlib numpy particle"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3e1d9835-1f27-4dcf-b359-3937ec89236b",
+   "metadata": {
+    "editable": true,
+    "jupyter": {
+     "source_hidden": true
+    },
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "hide-cell"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "from __future__ import annotations\n",
+    "\n",
+    "import warnings\n",
+    "\n",
+    "import gdown\n",
+    "import numpy as np\n",
+    "from IPython.display import display\n",
+    "\n",
+    "warnings.filterwarnings(\"ignore\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "62d3b045-8dab-4e5a-92d7-07d2d5af4c79",
+   "metadata": {
+    "editable": true,
+    "jupyter": {
+     "source_hidden": true
+    },
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "filename = gdown.cached_download(\n",
+    "    url=\"https://indico.ific.uv.es/event/6803/contributions/21223/attachments/11221/15563/Three-particles-3.dat\",\n",
+    "    path=\"data/Three-particles-3.dat\",\n",
+    "    md5=\"75fedf381f9b62d3210ff200fc63165f\",\n",
+    "    quiet=True,\n",
+    "    verify=False,\n",
+    ")\n",
+    "data = np.loadtxt(filename)\n",
+    "data.shape"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "166252ab-57a2-4628-88e1-32ab8f354f89",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "data"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "adfe5fbb-ab7b-41b2-8a8c-8f0bac0ce009",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "n_final_state = 3\n",
+    "pa, p1, p2, p3 = (data[i::4].T for i in range(n_final_state + 1))\n",
+    "p0 = p1 + p2 + p3\n",
+    "pb = p0 - pa"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "d10177c3-02c4-4248-8d0e-181a28453be5",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "def mass(p: np.ndarray) -> np.ndarray:\n",
+    "    return np.sqrt(mass_squared(p))\n",
+    "\n",
+    "\n",
+    "def mass_squared(p: np.ndarray) -> np.ndarray:\n",
+    "    return p[0] ** 2 - np.sum(p[1:] ** 2, axis=0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "adc55b5b-8490-4587-b468-848b32873eee",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "m0 = mass(p0)\n",
+    "print(f\"{m0.mean():.4g} +/- {m0.std():.4g}\")"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "59a10ead-6653-4344-ab55-f85f2f8fbbde",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from IPython.display import Math\n",
+    "\n",
+    "display(Math(Rf\"m_a = {mass(pa).mean():.3g}\\text{{ GeV}}\"))\n",
+    "display(Math(Rf\"m_b = {mass(pb).mean():.3g}\\text{{ GeV}}\"))\n",
+    "for i, p in enumerate([p0, p1, p2, p3]):\n",
+    "    display(Math(Rf\"m_{i} = {mass(p).mean():.3g}\\text{{ GeV}}\"))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "b63474a3-8445-49dc-97b8-20c3935853ce",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "from particle import Particle\n",
+    "\n",
+    "\n",
+    "def find_candidates(\n",
+    "    mass: float, delta: float = 0.001, charge: float | None = None\n",
+    ") -> list[Particle]:\n",
+    "    def identify(p) -> bool:\n",
+    "        if p.pdgid in {21}:\n",
+    "            return False\n",
+    "        if charge is not None and p.charge != charge:\n",
+    "            return False\n",
+    "        if (mass - delta) < 1e-3 * p.mass < (mass + delta):\n",
+    "            return True\n",
+    "        return False\n",
+    "\n",
+    "    return Particle.findall(identify)\n",
+    "\n",
+    "\n",
+    "ma = mass(pa).mean()\n",
+    "mb = mass(pb).mean()\n",
+    "m1 = mass(p1).mean()\n",
+    "m2 = mass(p2).mean()\n",
+    "m3 = mass(p3).mean()\n",
+    "initial_state = (\n",
+    "    find_candidates(ma.mean(), delta=1e-4)[0],\n",
+    "    find_candidates(mb.mean())[0],\n",
+    ")\n",
+    "final_state = tuple(find_candidates(m.mean())[0] for m in [m1, m2, m3])\n",
+    "display(\n",
+    "    Math(R\"\\text{Incoming: }\" + \", \".join(f\"{p.latex_name}\" for p in initial_state)),\n",
+    "    Math(R\"\\text{Outgoing: }\" + \", \".join(f\"{p.latex_name}\" for p in final_state)),\n",
+    ")"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "24fce750-e6d7-40f1-9e24-dec0d85fc7b8",
+   "metadata": {},
+   "source": [
+    "a photon&nbsp;$\\gamma$ hitting a proton&nbsp;$p$ and producing a meson&nbsp;$\\eta$, pion&nbsp;$\\pi^0$, and proton&nbsp;$p$."
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "376674d5-3bd0-458b-b5d8-3cc356c42f31",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "outputs": [],
+   "source": [
+    "s12 = mass_squared(p1 + p2)\n",
+    "s23 = mass_squared(p2 + p3)\n",
+    "s31 = mass_squared(p3 + p1)\n",
+    "\n",
+    "m12 = mass(p1 + p2)\n",
+    "m23 = mass(p2 + p3)\n",
+    "m31 = mass(p3 + p1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "dcef09fd-7994-4302-9e08-70b9950f9b84",
+   "metadata": {
+    "editable": true,
+    "jupyter": {
+     "source_hidden": true
+    },
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "import matplotlib.pyplot as plt\n",
+    "\n",
+    "fig, ax = plt.subplots()\n",
+    "fig.suptitle(\"Dalitz plot – 2D histogram\")\n",
+    "ax.hist2d(s12, s23, bins=100, cmin=1)\n",
+    "ax.set_xlabel(R\"$s_{12}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "ax.set_ylabel(R\"$s_{23}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "# fig.tight_layout()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "3da3dd63-d9e1-4603-8167-2298619062e6",
+   "metadata": {},
+   "outputs": [],
+   "source": [
+    "R12 = 1.74\n",
+    "R23 = 1.53\n",
+    "R31 = 2.45"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "9f8606f4-c64f-4f68-b88f-80f8de58b707",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "fig, (ax1, ax2) = plt.subplots(figsize=(10, 4), ncols=2)\n",
+    "fig.suptitle(\"Dalitz plot – scatter plot\")\n",
+    "ax1.scatter(s12, s23, c=\"black\", s=1e-3)\n",
+    "ax1.set_xlabel(R\"$s_{12}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "ax1.set_ylabel(R\"$s_{23}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "ax1.axvline(R12, c=\"C0\", ls=\"dashed\", label=\"$R_{12}$\")\n",
+    "ax1.axhline(R23, c=\"C1\", ls=\"dashed\", label=\"$R_{23}$\")\n",
+    "ax1.legend()\n",
+    "ax2.scatter(s31, s12, c=\"black\", s=1e-3)\n",
+    "ax2.set_xlabel(R\"$s_{31}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "ax2.set_ylabel(R\"$s_{12}\\;\\left[\\mathrm{GeV}^2\\right]$\")\n",
+    "ax2.axvline(R31, c=\"C2\", ls=\"dashed\", label=\"$R_{31}$\")\n",
+    "ax2.axhline(R12, c=\"C0\", ls=\"dashed\", label=\"$R_{12}$\")\n",
+    "ax2.legend()\n",
+    "fig.tight_layout()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": null,
+   "id": "95aa6945-6427-42ee-8105-9e600b193d03",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": [
+     "full-width",
+     "hide-input"
+    ]
+   },
+   "outputs": [],
+   "source": [
+    "fig, (ax1, ax2, ax3) = plt.subplots(figsize=(12, 4), ncols=3)\n",
+    "fig.suptitle(\"1D histogram of $s_{12}, s_{23}$, and $s_{31}$\")\n",
+    "ax1.hist(s12, bins=100, color=\"black\", histtype=\"step\")\n",
+    "ax1.set_xlabel(R\"$s_{12}$\")\n",
+    "ax1.set_ylabel(\"counts\")\n",
+    "ax1.axvline(R12, c=\"C0\", ls=\"dashed\", label=\"$R_{12}$\")\n",
+    "ax1.legend()\n",
+    "\n",
+    "ax2.hist(s23, bins=100, color=\"black\", histtype=\"step\")\n",
+    "ax2.set_xlabel(R\"$s_{23}$\")\n",
+    "ax2.set_ylabel(\"counts\")\n",
+    "ax2.axvline(R23, c=\"C1\", ls=\"dashed\", label=\"$R_{23}$\")\n",
+    "ax2.legend()\n",
+    "\n",
+    "ax3.hist(s31, bins=100, color=\"black\", histtype=\"step\")\n",
+    "ax3.set_xlabel(R\"$s_{31}$\")\n",
+    "ax3.set_ylabel(\"counts\")\n",
+    "ax3.axvline(R31, c=\"C2\", ls=\"dashed\", label=\"$R_{31}$\")\n",
+    "ax3.legend()\n",
+    "\n",
+    "fig.tight_layout()\n",
+    "plt.show()"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "id": "360f674e-801c-4fda-aa3a-e57595e0da44",
+   "metadata": {
+    "editable": true,
+    "slideshow": {
+     "slide_type": ""
+    },
+    "tags": []
+   },
+   "source": [
+    "The intensity of band seems stronger Compare to `Three-particles-1.dat` and `Three-particles-2.dat` in {doc}`lecture02`, but needded further analysis for the modulations."
+   ]
+  }
+ ],
+ "metadata": {
+  "colab": {
+   "toc_visible": true
+  },
+  "kernelspec": {
+   "display_name": "Python 3 (ipykernel)",
+   "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": "3.10.13"
+  }
+ },
+ "nbformat": 4,
+ "nbformat_minor": 5
+}