From 55228be180953c4ed4fe8b0b3f54f21de38213ca Mon Sep 17 00:00:00 2001 From: Hans Dembinski Date: Tue, 4 Jun 2024 15:55:48 +0200 Subject: [PATCH] u --- posts/Cross-section.ipynb | 164 ---------- posts/cross_section_extrapolation_error.ipynb | 280 ++++++++++++++++++ posts/cross_section_pip_vs_pp.ipynb | 136 +++++++++ 3 files changed, 416 insertions(+), 164 deletions(-) delete mode 100644 posts/Cross-section.ipynb create mode 100644 posts/cross_section_extrapolation_error.ipynb create mode 100644 posts/cross_section_pip_vs_pp.ipynb diff --git a/posts/Cross-section.ipynb b/posts/Cross-section.ipynb deleted file mode 100644 index 0d162a1..0000000 --- a/posts/Cross-section.ipynb +++ /dev/null @@ -1,164 +0,0 @@ -{ - "cells": [ - { - "cell_type": "markdown", - "metadata": {}, - "source": [ - "# Inelastic cross-sections of proton-proton and pion-proton collisions\n", - "\n", - "According to a simple parton model, the cross-section for an inelastic proton-proton collision should be 3/2 of a pion-proton collision. In this picture, only the valence quarks matter. We know that at high energies most of the collisions involve sea quarks and gluons, so another theory says that the cross-sections might become equal at high energies.\n", - "\n", - "I check this here by downloading cross-section data from the Particle Data Group, interpolating the data points and then plot the ratio. We get indeed a ratio of about 3/2=1.5. In reality, it is a bit larger, about 1.6. There is no visible trend that it does down to 1 with energy." - ] - }, - { - "cell_type": "code", - "execution_count": 5, - "metadata": {}, - "outputs": [], - "source": [ - "import matplotlib.pyplot as plt\n", - "import numpy as np\n", - "import requests" - ] - }, - { - "cell_type": "code", - "execution_count": 74, - "metadata": {}, - "outputs": [], - "source": [ - "def read(url):\n", - " r = requests.get(url)\n", - " tab = r.text\n", - " xy = []\n", - " skip = 11\n", - " for line in tab.strip().split(\"\\n\"):\n", - " if skip:\n", - " skip -= 1\n", - " continue\n", - " items = line.split()\n", - " xi = float(items[3])\n", - " yi = float(items[4])\n", - " yei = (0.5 * sum(float(i) ** 2 for i in items[5:9])) ** 0.5\n", - " xy.append((xi, yi, yei))\n", - " xy.sort(key=lambda p: p[0])\n", - " return np.transpose(xy)" - ] - }, - { - "cell_type": "code", - "execution_count": 75, - "metadata": {}, - "outputs": [], - "source": [ - "pim_p = read(\"https://pdg.lbl.gov/2020/hadronic-xsections/rpp2020-pimp_total.dat\")\n", - "pip_p = read(\"https://pdg.lbl.gov/2020/hadronic-xsections/rpp2020-pipp_total.dat\")\n", - "p_p = read(\"https://pdg.lbl.gov/2020/hadronic-xsections/rpp2020-pp_total.dat\")" - ] - }, - { - "cell_type": "code", - "execution_count": 82, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "" - ] - }, - "execution_count": 82, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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", - "text/plain": [ - "
" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "plt.figure(figsize=(16, 6))\n", - "plt.errorbar(*pim_p, fmt=\"o\", label=\"pi- p\")\n", - "plt.errorbar(*pip_p, fmt=\"s\", label=\"pi+ p\")\n", - "plt.errorbar(*p_p, fmt=\"D\", label=\"p p\")\n", - "plt.loglog()\n", - "plt.legend()" - ] - }, - { - "cell_type": "code", - "execution_count": 61, - "metadata": {}, - "outputs": [ - { - "data": { - "text/plain": [ - "[]" - ] - }, - "execution_count": 61, - "metadata": {}, - "output_type": "execute_result" - }, - { - "data": { - "image/png": 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" - ] - }, - "metadata": { - "needs_background": "light" - }, - "output_type": "display_data" - } - ], - "source": [ - "from scipy.interpolate import interp1d\n", - "l_pip_p = interp1d(*pip_p)\n", - "l_p_p = interp1d(*p_p)\n", - "x = np.geomspace(1, 1e4)\n", - "plt.plot(x, l_p_p(x) / l_pip_p(x))\n", - "plt.axhline(3/2, ls=\"--\", color=\"0.5\")\n", - "plt.semilogx()" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": {}, - "outputs": [], - "source": [] - } - ], - "metadata": { - "kernelspec": { - "display_name": "py38", - "language": "python", - "name": "py38" - }, - "language_info": { - "codemirror_mode": { - "name": "ipython", - "version": 3 - }, - "file_extension": ".py", - "mimetype": "text/x-python", - "name": "python", - "nbconvert_exporter": "python", - "pygments_lexer": "ipython3", - "version": "3.8.6" - } - }, - "nbformat": 4, - "nbformat_minor": 4 -} diff --git a/posts/cross_section_extrapolation_error.ipynb b/posts/cross_section_extrapolation_error.ipynb new file mode 100644 index 0000000..31352eb --- /dev/null +++ b/posts/cross_section_extrapolation_error.ipynb @@ -0,0 +1,280 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# pp cross-section extrapolation uncertainty\n", + "\n", + "Here we estimate the extrapolated uncertainty of the pp inelastic cross-section at 100 TeV before and after the LHC era." + ] + }, + { + "cell_type": "code", + "execution_count": 41, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import requests\n", + "from iminuit import Minuit\n", + "from iminuit.cost import LeastSquares\n", + "from chromo.kinematics import FixedTarget, GeV, Momentum\n", + "from chromo.constants import nucleon_mass\n", + "from jacobi import propagate\n", + "from numpy.polynomial import Chebyshev\n", + "from IPython.display import display" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We grab the raw data from the PDG website. Statistical and systematic uncertainties are added in quadrature." + ] + }, + { + "cell_type": "code", + "execution_count": 42, + "metadata": {}, + "outputs": [], + "source": [ + "def read(url):\n", + " r = requests.get(url)\n", + " tab = r.text\n", + " xy = []\n", + " skip = 11\n", + " for line in tab.strip().split(\"\\n\"):\n", + " if skip:\n", + " skip -= 1\n", + " continue\n", + " items = line.split()\n", + " xi = float(items[3])\n", + " yi = float(items[4])\n", + " yei = (0.5 * sum(float(i) ** 2 for i in items[5:9])) ** 0.5\n", + " xy.append((xi, yi, yei))\n", + " xy.sort(key=lambda p: p[0])\n", + " return np.transpose(xy)\n", + "\n", + "p_p = read(\"https://pdg.lbl.gov/2020/hadronic-xsections/rpp2020-pp_total.dat\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "To estimate the extrapolation uncertainty, we fit a COMPETE-like model to the data (Patrignani C., et al., Particle Data Group\n", + "Chin. Phys. C, 40 (2016), Article 100001). The covariance matrix of the fit is propagated into an uncertainty on the cross-section at $\\sqrt{s} = 100$ GeV. \n", + "\n", + "The original data is given in the lab frame and provides the proton momentum. We compute $\\sqrt{s}$ from the momentum with the kinematic tools in Chromo for convenience.\n", + "\n", + "To simulate the effect of the pre LHC era, we cut away all data points with $\\sqrt s > 3$ TeV. This also removes cross-sections inferred from air shower data, but these do not affect our study anyway because of their relatively large uncertainties." + ] + }, + { + "cell_type": "code", + "execution_count": 68, + "metadata": {}, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
Migrad
FCN = 95.12 (χ²/ndof = 0.7) Nfcn = 1626
EDM = 0.000169 (Goal: 0.0002)
Valid Minimum Below EDM threshold (goal x 10)
SOME parameters at limit Below call limit
Hesse ok Covariance accurate
" + ], + "text/plain": [ + "┌─────────────────────────────────────────────────────────────────────────┐\n", + "│ Migrad │\n", + "├──────────────────────────────────┬──────────────────────────────────────┤\n", + "│ FCN = 95.12 (χ²/ndof = 0.7) │ Nfcn = 1626 │\n", + "│ EDM = 0.000169 (Goal: 0.0002) │ │\n", + "├──────────────────────────────────┼──────────────────────────────────────┤\n", + "│ Valid Minimum │ Below EDM threshold (goal x 10) │\n", + "├──────────────────────────────────┼──────────────────────────────────────┤\n", + "│ SOME parameters at limit │ Below call limit │\n", + "├──────────────────────────────────┼──────────────────────────────────────┤\n", + "│ Hesse ok │ Covariance accurate │\n", + "└──────────────────────────────────┴──────────────────────────────────────┘" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "text/html": [ + "\n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + " \n", + "
Migrad
FCN = 75.18 (χ²/ndof = 0.6) Nfcn = 3310
EDM = 0.000153 (Goal: 0.0002)
Valid Minimum Below EDM threshold (goal x 10)
SOME parameters at limit Below call limit
Hesse ok Covariance accurate
" + ], + "text/plain": [ + "┌─────────────────────────────────────────────────────────────────────────┐\n", + "│ Migrad │\n", + "├──────────────────────────────────┬──────────────────────────────────────┤\n", + "│ FCN = 75.18 (χ²/ndof = 0.6) │ Nfcn = 3310 │\n", + "│ EDM = 0.000153 (Goal: 0.0002) │ │\n", + "├──────────────────────────────────┼──────────────────────────────────────┤\n", + "│ Valid Minimum │ Below EDM threshold (goal x 10) │\n", + "├──────────────────────────────────┼──────────────────────────────────────┤\n", + "│ SOME parameters at limit │ Below call limit │\n", + "├──────────────────────────────────┼──────────────────────────────────────┤\n", + "│ Hesse ok │ Covariance accurate │\n", + "└──────────────────────────────────┴──────────────────────────────────────┘" + ] + }, + "metadata": {}, + "output_type": "display_data" + }, + { + "data": { + "image/png": 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", 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "def model(sqrts, par):\n", + " x = np.log(sqrts)\n", + " return Chebyshev(par)(x)\n", + "\n", + "\n", + "def compete(sqrts, h, m, pab, rab1, rab2, eta1, eta2):\n", + " s = sqrts**2\n", + " sabm = 2 * nucleon_mass + m\n", + " x = s / sabm\n", + " return h * np.log(x) ** 2 + pab + rab1 * x**-eta1 + rab2 * x**-eta2\n", + "\n", + "\n", + "sqrts = []\n", + "sig = []\n", + "sige = []\n", + "\n", + "for plab, s, se in zip(*p_p):\n", + " if plab < 5:\n", + " continue\n", + " sqrts.append(FixedTarget(Momentum(plab * GeV), \"p\", \"p\").ecm)\n", + " sig.append(s)\n", + " sige.append(se)\n", + "\n", + "sqrts = np.array(sqrts)\n", + "sig = np.array(sig)\n", + "sige = np.array(sige)\n", + "\n", + "cost = LeastSquares(sqrts, sig, sige, compete)\n", + "m = Minuit(cost, h=0.27, m=2.1, pab=34, rab1=13, rab2=7.4, eta1=0.451, eta2=0.549)\n", + "m.limits[:] = (0, None)\n", + "# some parameters need to be fixed, because they are not constrained by this data set\n", + "m.fixed[\"eta1\", \"eta2\"] = True\n", + "\n", + "for emax in (1e6, 3e3):\n", + " cost.mask = sqrts < emax\n", + " display(m.migrad(ncall=int(1e5)).fmin)\n", + " val = m.values\n", + " cov = m.covariance\n", + " plt.figure()\n", + " plt.errorbar(sqrts[cost.mask], sig[cost.mask], sige[cost.mask], fmt=\"o\", label=\"PDG 2020\")\n", + " msqrts = np.geomspace(10, 1e5, 1000)\n", + " msig, cov_msig = propagate(lambda v: compete(msqrts, *v), val, cov)\n", + " msige = np.diag(cov_msig) ** 0.5\n", + " plt.plot(msqrts, msig, color=\"C1\", label=\"COMPETE-like model\")\n", + " plt.fill_between(msqrts, msig - msige, msig + msige, color=\"C1\", alpha=0.5)\n", + " plt.semilogx()\n", + " plt.xlabel(r\"$\\sqrt{s}$ / GeV\")\n", + " plt.ylabel(\"inelastic cross-section / mb\")\n", + " plt.title(\n", + " rf\"uncertainty at 100 TeV = {msige[-1]:.0f} mb ({msige[-1]/msig[-1] * 100:.1f} %)\"\n", + " )\n", + " plt.legend(frameon=False, title=\"pp\", loc=\"upper left\");\n", + " plt.savefig(f\"cross_section_extrapolation_uncertainty_{emax}.pdf\")" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "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": "3.12.3" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +} diff --git a/posts/cross_section_pip_vs_pp.ipynb b/posts/cross_section_pip_vs_pp.ipynb new file mode 100644 index 0000000..8583352 --- /dev/null +++ b/posts/cross_section_pip_vs_pp.ipynb @@ -0,0 +1,136 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "# Inelastic cross-sections of proton-proton and pion-proton collisions\n", + "\n", + "According to a simple parton model, the cross-section for an inelastic proton-proton collision should be 3/2 of a pion-proton collision. In this picture, only the valence quarks matter. We know that at high energies most of the collisions involve sea quarks and gluons, so another theory says that the cross-sections might become equal at high energies.\n", + "\n", + "I check this here by downloading cross-section data from the Particle Data Group, interpolating the data points and then plot the ratio. We get indeed a ratio of about 3/2=1.5. In reality, it is a bit larger, about 1.6. There is no visible trend that it does down to 1 with energy." + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "metadata": {}, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "import requests\n", + "from scipy.interpolate import interp1d" + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "metadata": {}, + "outputs": [], + "source": [ + "def read(url):\n", + " r = requests.get(url)\n", + " tab = r.text\n", + " xy = []\n", + " skip = 11\n", + " for line in tab.strip().split(\"\\n\"):\n", + " if skip:\n", + " skip -= 1\n", + " continue\n", + " items = line.split()\n", + " xi = float(items[3])\n", + " yi = float(items[4])\n", + " yei = (0.5 * sum(float(i) ** 2 for i in items[5:9])) ** 0.5\n", + " xy.append((xi, yi, yei))\n", + " xy.sort(key=lambda p: p[0])\n", + " return np.transpose(xy)" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": {}, + "outputs": [], + "source": [ + "pim_p = read(\"https://pdg.lbl.gov/2020/hadronic-xsections/rpp2020-pimp_total.dat\")\n", + "pip_p = read(\"https://pdg.lbl.gov/2020/hadronic-xsections/rpp2020-pipp_total.dat\")\n", + "p_p = read(\"https://pdg.lbl.gov/2020/hadronic-xsections/rpp2020-pp_total.dat\")" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "plt.figure(figsize=(10, 6))\n", + "plt.errorbar(*pim_p, fmt=\"o\", label=\"pi- p\")\n", + "plt.errorbar(*pip_p, fmt=\"s\", label=\"pi+ p\")\n", + "plt.errorbar(*p_p, fmt=\"D\", label=\"p p\")\n", + "plt.xlabel(r\"$p_\\mathrm{lab}$ / GeVc$^{-1}$\")\n", + "plt.ylabel(r\"inelastic cross-section / mb\")\n", + "plt.loglog()\n", + "plt.legend();" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [ + { + "data": { + "image/png": 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", + "text/plain": [ + "
" + ] + }, + "metadata": {}, + "output_type": "display_data" + } + ], + "source": [ + "l_pip_p = interp1d(*pip_p[:2])\n", + "l_p_p = interp1d(*p_p[:2])\n", + "x = np.geomspace(1, 1e4)\n", + "plt.figure()\n", + "plt.plot(x, l_p_p(x) / l_pip_p(x))\n", + "plt.axhline(3/2, ls=\"--\", color=\"0.5\")\n", + "plt.semilogx();" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": ".venv", + "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": "3.12.3" + } + }, + "nbformat": 4, + "nbformat_minor": 4 +}