{ "cells": [ { "cell_type": "markdown", "id": "ff8465b6", "metadata": {}, "source": [ "| [**Lattice QCD I**](https://homepages.uni-regensburg.de/~lec17310/teaching/wise2122/lqft.html) | - | [**Christoph Lehner**](https://go.ur.de/lehner) |\n", "|:-|--|-:|\n", "\n", "# Chapter 7: the static quark potential and spectrum of pure QCD\n", "\n", "In this chapter we study for the first time the physics of pure QCD.\n", "\n", "## Temporal Gauge\n", "\n", "Let us identify $\\mu=3$ with the time direction and consider a lattice with infinite time dimension.\n", "A gauge transformation allows us to select a $V(x) \\in$ SU(3) for every Euclidean lattice site $x$.\n", "By picking\n", "$$\n", "\\begin{align}\n", "V(\\vec{x},t=0)&= \\mathbb{1} \\,, \\\\\n", "V(\\vec{x},t=1)&= U_3(\\vec{x},t=0) \\,, \\\\\n", "V(\\vec{x},t=2)&= U_3(\\vec{x},t=0) U_3(\\vec{x},t=1) \\,, \\\\\n", "\\ldots \\\\\n", "V(\\vec{x},t=-1)&= U_3(\\vec{x},t=-1)^\\dagger \\,, \\\\\n", "V(\\vec{x},t=-2)&= U_3(\\vec{x},t=-1)^\\dagger U_3(\\vec{x},t=-2)^\\dagger \\,, \\\\\n", "\\ldots\n", "\\end{align}\n", "$$\n", "we can transform all temporal links to\n", "$$\n", "\\begin{align}\n", "U_3(x,t) = \\mathbb{1}\n", "\\end{align}\n", "$$\n", "which is the **temporal gauge** condition.\n", "This is a special version of a **tree gauge**, where one selects the $V(x)$ such that they\n", "set all links on a tree starting from a given origin site to the identity.\n", "The action and integration measure are invariant under this transformation, however, it\n", "is particularly useful in interpreting the system in a Hamiltonian sense in which\n", "the time direction is special as we will see below.\n", "\n", "## Static Quarks\n", "\n", "We remind ourselves that the Lagrangian of a free quark with mass $m$ in Minkowski space is given by\n", "$$\n", "\\begin{align}\n", "{\\cal L} = \\overline{\\psi} (i\\gamma^\\mu \\partial_\\mu - m) \\psi \\,.\n", "\\end{align}\n", "$$\n", "In a theory for sufficiently large mass $m$,\n", "the temporal derivatives $\\partial_0$ and therefore also $\\partial_0$\n", "must scale as\n", "$$\n", "\\begin{align}\n", "\\partial_0 \\psi = i(m + \\frac{p^2}{2m} + O(1/m^2)) \\psi\n", "\\end{align}\n", "$$\n", "with spatial momentum $p$. One finds that an appropriate action for the infinitely\n", "heavy quark ($m\\to\\infty$) is\n", "$$\n", "\\begin{align}\n", "{\\cal L} = \\overline{h} i \\gamma_0 \\partial_0 h + O(1/m) \\,,\n", "\\end{align}\n", "$$\n", "where the field $h$ has to be appropriately defined. Such a **static** quark\n", "no longer has a spatial derivative term, which means that it can no longer propagate\n", "in space. One can show that on a lattice, the propagator\n", "of such a static quark from $x$ to $x+\\hat{3}n$ is given\n", "by the Wilson line\n", "$$\n", "\\begin{align}\n", "U_3(x) U_3(x+\\hat{3}) \\cdots U_3(x+\\hat{3}(n-1)) \\,.\n", "\\end{align}\n", "$$\n", "\n", "## Static Quark Potential\n", "\n", "Since our gauge action is invariant under axis interchange, we can also\n", "consider static quarks that propagate in a given spatial direction.\n", "If we now considered a Wilson loop $W(r,t)$ of extend $r$ spatial sites and $t$\n", "temporal sites in temporal gauge, we could identify $W(r,t)$\n", "as two static quarks propagating the distance $r$ separated by $t$\n", "time steps. Another way to think about this is that we create a state\n", "of a static quark propagating distance $r$ and project to it by inserting\n", "the transition matrix $e^{-H t}$ in between. The energy of such a state\n", "$$\n", "\\begin{align}\n", "V(r) = \\lim_{t\\to\\infty} \\log \\frac{W(r,t)}{W(r,t+1)}\n", "\\end{align}\n", "$$\n", "is also called the static quark potential.\n", "\n", "From perturbative QCD, we know that the effective coupling constant $g$ at short\n", "distances vanishes in QCD, i.e., at short distances the QCD action's field\n", "strength tensor\n", "$$\n", "\\begin{align}\n", "F_{\\mu\\nu} = \\partial_\\mu A_\\nu - \\partial_\\nu A_\\mu + i g [A_\\mu,A_\\nu]\n", "\\end{align}\n", "$$\n", "goes over to 8 separate contributions (number of SU(3) generators) that look like\n", "the electromagnetic field strength tensor\n", "$$\n", "\\begin{align}\n", "F^{\\rm em}_{\\mu\\nu} = \\partial_\\mu A_\\nu - \\partial_\\nu A_\\mu \\,.\n", "\\end{align}\n", "$$\n", "\n", "We should therefore expect QCD to behave similarly to electrodynamics at very\n", "short distances, i.e., we would expect a Coulomb potential $V(r)\\propto 1/r$\n", "at short distances.\n", "\n", "In the next chapter, we will systematically study the strong coupling expansion\n", "of QCD and will find that in this limit, we will expect a linear\n", "rise in the potential which we can identify with the long-distance\n", "behavior $V(r) \\propto r$.\n", "\n", "In total, a reasonable ansatz for $V(r)$ is\n", "$$\n", "\\begin{align}\n", "V(r) = A + \\frac{B}{r} + \\sigma r \\,.\n", "\\end{align}\n", "$$\n", "\n", "We will confirm this behavior below by explicit numerical study. The long distance\n", "behavior also tells us that the force\n", "$$\n", "\\begin{align}\n", "F(r) = V'(r)\n", "\\end{align}\n", "$$\n", "between to static quarks, will be constant for sufficiently large $r$.\n", "This constant force is captured by the **string tension** $\\sigma$\n", "and signals quark **confinement**, i.e., no matter how far we\n", "separate the static quarks, they will always have a restoring force\n", "that binds them together. The unusual sign definition used here allows\n", "for a more convenient sign definition in the next subsection.\n", "\n", "By introducing dynamical quarks to the theory, the energy stored in this\n", "potential may be sufficient to create a quark-antiquark pair that can\n", "then break the string, more on this at the appropriate chapter.\n", "\n", "## Sommer scale\n", "\n", "By also studying the spectra of bottom and charm quark states and comparing them\n", "to experimentally measured results one can determine that the force between\n", "static quarks at **Sommer scale**\n", "$$\n", "\\begin{align}\n", "r_0 \\approx 0.5 \\textrm{fm}\n", "\\end{align}\n", "$$\n", "satisfies\n", "$$\n", "\\begin{align}\n", "r_0^2 F(r_0) = 1.65 \\,.\n", "\\end{align}\n", "$$\n", "\n", "This was one of the first means to determine the physical lattice spacing given\n", "a set of ensemble parameters. We will illustrate its use below. We will\n", "also discuss more modern techniques in later chapters.\n", "\n", "## Glueball spectrum\n", "\n", "The spectrum of pure QCD contains bound states of gluons or **glueballs**.\n", "This is possible due to the self-interaction of SU(3) gauge theory, see comparison\n", "of the field-strength tensor with the U(1) field strength tensor above.\n", "\n", "The spectrum of such states can be categorized using good quantum numbers obtained\n", "by studying the irreducible representations of the spacetime symmetry group\n", "of the lattice and the continuum. We shall discuss this also in later chapters\n", "more systematically. For now, we learn that the trivial scalar representation\n", "that is also invariant under parity and flipping the charge $g\\to-g$,\n", "called $A_1^{++}$ representation, contains the lightest glueball state.\n", "\n", "Any operator transforming in this irreducible representation will excited such a particle.\n", "The simplest such operator is the sum over all spatial plaquettes $P_{ij}$ with\n", "$i,j<3$. Note that since the vacuum expectation value of the plaquette does not vanish,\n", "we need to subtract the expectation value of the plaquette when constructing \n", "a correlator to measure its mass. This is identical to the case of the $\\phi^2$ operator\n", "in the real scalar theory studied in chapter 4.\n", "\n", "## Reduction of excited state contributions by gauge smearing\n", "\n", "In the operators constructed below, we replace the original gauge fields by\n", "gauge fields that are smeared out over a finite spatial distance, while still\n", "satisfying the gauge transformation property\n", "$$\n", "\\begin{align}\n", "U_\\mu(x) \\to V(x) U_\\mu(x) V(x + \\hat{\\mu})^\\dagger \\,.\n", "\\end{align}\n", "$$\n", "This merely creates a different operator in the same irreducible representation\n", "but has the effect of suppressing overlap with the more short-distance excited states.\n", "\n", "Note: in this chapter, we will use the relation between units $0.1973\\: \\textrm{GeV}\\: \\textrm{fm} = 1$." ] }, { "cell_type": "code", "execution_count": 2, "id": "e57ac072", "metadata": {}, "outputs": [], "source": [ "import gpt as g;\n", "import numpy as np;\n", "from matplotlib import pyplot as plt;\n", "\n", "def generate_ensemble(Ls, Lt, beta, Nthermalize, Nmax, Nskip):\n", " L = [Ls, Ls, Ls, Lt]\n", "\n", " grid = g.grid(L, g.double)\n", " grid_eo = g.grid(L, g.double, g.redblack)\n", "\n", " rng = g.random(\"test\", \"vectorized_ranlux24_24_64\")\n", " U = g.qcd.gauge.unit(grid)\n", " Nd = len(U)\n", "\n", " mask_rb = g.complex(grid_eo)\n", " mask_rb[:] = 1\n", "\n", " # full mask\n", " mask = g.complex(grid)\n", "\n", " def staple(U, mu):\n", " st = g.lattice(U[0])\n", " st[:] = 0\n", " Nd = len(U)\n", " for nu in range(Nd):\n", " if mu != nu:\n", " st += g.qcd.gauge.staple(U, mu, nu) / U[0].otype.Nc\n", " return st\n", "\n", " g.default.set_verbose(\"su2_heat_bath\", False)\n", " markov = g.algorithms.markov.su2_heat_bath(rng)\n", " plaquette_heatbath = []\n", " for it in range(Nmax):\n", " plaq = g.qcd.gauge.plaquette(U)\n", " plaquette_heatbath.append(plaq)\n", " if it % (Nmax//20) == 0:\n", " g.message(f\"SU(2)-subgroup heatbath {it} has P = {plaq}\")\n", " for cb in [g.even, g.odd]:\n", " mask[:] = 0\n", " mask_rb.checkerboard(cb)\n", " g.set_checkerboard(mask, mask_rb)\n", "\n", " for mu in range(Nd):\n", " st = g.eval(beta * staple(U, mu))\n", " markov(U[mu], st, mask)\n", " if it > Nthermalize and it % Nskip == 0:\n", " g.default.push_verbose(\"io\", False)\n", " g.save(f\"{Ls}c{Lt}_{beta}/su3.{it}\",U)\n", " g.default.pop_verbose()\n", " \n", " \n", " fig, ax = plt.subplots()\n", " ax.plot(range(len(plaquette_heatbath)), plaquette_heatbath, marker='+', ls='', c='red', label=\"Heatbath\")\n", " plt.legend()\n", " plt.show()\n", " \n", "#generate_ensemble(8, 32, 5.5, 100, 10000, 5)\n", "#generate_ensemble(8, 8, 5.9, 50, 300, 5)\n", "#generate_ensemble(8, 8, 5.5, 100, 300, 5)\n", "#for beta in [5.6,5.7,5.8]:\n", "# generate_ensemble(8, 8, beta, 100, 300, 5)\n" ] }, { "cell_type": "code", "execution_count": 3, "id": "3098d43c", "metadata": {}, "outputs": [], "source": [ "from scipy.optimize import curve_fit\n", "\n", "g.default.set_verbose(\"io\", False)\n", "\n", "def jackknife_covariance_estimator(f, x):\n", " N = len(x)\n", " X = sum(x) / N\n", " mean = f(X)\n", " def outer_sqr(a):\n", " return np.outer(a,a)\n", " return sum([outer_sqr(f((N*X - x[j])/(N-1)) - mean) for j in range(N)])*(N-1)/N\n", "\n", "def V(t0, configurations):\n", " U = g.load(configurations[0])\n", "\n", " Wt = [{},{}]\n", " \n", " for t in [t0,t0+1]:\n", " for r in range(1,5):\n", " Wt[t-t0][r] = g.qcd.gauge.transport(U,[g.qcd.gauge.path().f(3,t).f(nu,r).b(3,t).b(nu,r)\n", " for nu in range(3)])\n", " for r in [1,2]:\n", " Wt[t-t0][np.sqrt(2.)*r] = g.qcd.gauge.transport(U, \n", " [g.qcd.gauge.path().f(3,t).f(nu,r).f(rho,r).b(3,t).b(rho,r).b(nu,r)\n", " for nu in range(3) for rho in range(3) if nu != rho])\n", "\n", " Wlc = []\n", " for conf in configurations:\n", " U = g.load(conf)\n", " \n", " for i in range(4):\n", " U = g.qcd.gauge.smear.stout(U, rho=1.0/12.0,orthogonal_dimension=3)\n", " \n", " print(conf, end=\"\\r\")\n", " Wlc.append([[sum([g.sum(g.trace(l)).real for l in wti[r](U)]) for wti in Wt] for r in Wt[0]])\n", " \n", " Wlc = np.array(Wlc)\n", " Wl_mean = np.mean(Wlc,axis=0)\n", " V_mean = [np.log(Wl_mean[i,0]/Wl_mean[i,1]) for i in range(len(Wl_mean))]\n", " rs = [r for r in Wt[0]]\n", " V_cov = jackknife_covariance_estimator(lambda x: np.array([np.log(x[i,0]/x[i,1]) for i in range(len(Wl_mean))]),\n", " Wlc)\n", " V_err = [V_cov[i,i]**0.5 for i in range(len(V_mean))]\n", " print()\n", " return rs, V_mean, V_err, V_cov\n", "\n", "def lattice_spacing(configurations):\n", " def model(r,*p):\n", " return p[0] + p[1]/r + p[2]*r\n", "\n", " def model_gradient(r,*p):\n", " return np.array([r**0,r**-1,r]).T\n", " \n", " rs1, Vm1, Ve1, Vc1 = V(1, configurations)\n", " rs2, Vm2, Ve2, Vc2 = V(2, configurations)\n", "\n", " par_mean, par_cov = curve_fit(model, rs2, Vm2, p0=[0.5,0.5,0.5], sigma=Vc2, absolute_sigma=True, jac=model_gradient)\n", " a_in_fm = ((par_mean[1] + 1.65)/par_mean[2])**-0.5 * 0.5\n", "\n", " a_in_fm_dpar1 = -0.5 * ((par_mean[1] + 1.65)/par_mean[2])**-1.5 * 0.5 * 1.0 / par_mean[2]\n", " a_in_fm_dpar2 = 0.5 * ((par_mean[1] + 1.65)/par_mean[2])**-1.5 * 0.5 * 1.0 * (par_mean[1] + 1.65) / par_mean[2]**2\n", " a_in_fm_dpar = np.array([0,a_in_fm_dpar1,a_in_fm_dpar2])\n", "\n", " a_in_fm_err = np.dot(a_in_fm_dpar,np.dot(par_cov,a_in_fm_dpar))**0.5\n", " print(a_in_fm, a_in_fm_err)\n", "\n", " def err_f(r,p,cov_p):\n", " return np.dot(model_gradient(r,*p), np.dot(cov_p, model_gradient(r,*p)))**0.5\n", "\n", " rrange = np.arange(0.1, 5.0, 0.01)\n", " fy = np.array([model(r,*par_mean) for r in rrange])\n", " fyerr = np.array([err_f(r,par_mean,par_cov) for r in rrange])\n", "\n", " fig, ax = plt.subplots()\n", "\n", " plt.ylim(0,2.5)\n", " plt.xlim(0,5)\n", "\n", " plt.xlabel(\"r/a\")\n", " plt.ylabel(\"aV(r)\")\n", " ax.fill_between(rrange,fy-fyerr,fy+fyerr,alpha=0.1,color=\"blue\")\n", " ax.plot(rrange,fy,c=\"blue\")\n", " \n", " ax.errorbar(rs2, Vm2, Ve2, fmt=\"o\", label=\"V(r) with t=2\")\n", " ax.errorbar(rs1, Vm1, Ve1, fmt=\"o\", label=\"V(r) with t=1\")\n", "\n", " plt.legend()\n", " plt.show()\n", "\n", " return (a_in_fm, a_in_fm_err, rs2, Vm2, Ve2, par_mean, par_cov)" ] }, { "cell_type": "code", "execution_count": 4, "id": "e5587154", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "8c8_5.5/su3.295\n", "8c8_5.5/su3.295\n", "0.24683174310693679 0.01064766513162157\n" ] }, { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "betas = [5.5,5.6,5.7,5.8,5.9]\n", "a_mean_err = []\n", "for beta in betas:\n", " a_mean_err.append(lattice_spacing([f\"8c8_{beta}/su3.{it}\" for it in range(105,300,5)]))\n" ] }, { "cell_type": "code", "execution_count": 11, "id": "65157f7e", "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "\n", "plt.xlabel(\"beta\")\n", "plt.ylabel(\"a/fm\")\n", " \n", "ax.errorbar(betas, [a[0] for a in a_mean_err], [a[1] for a in a_mean_err], fmt=\"o\", label=\"a(beta)/fm\")\n", "\n", "plt.legend()\n", "plt.show()\n", "\n", "fig, ax = plt.subplots()\n", "\n", "plt.xlabel(\"a/fm\")\n", "plt.ylabel(\"g(a)\")\n", " \n", "ax.plot([a[0] for a in a_mean_err], [(6/b)**0.5 for b in betas], marker=\"+\", label=\"g(a)\")\n", "\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 13, "id": "eb6d4704", "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()\n", "plt.xlabel(\"r/fm\")\n", "plt.ylabel(\"V(r)/GeV\")\n", "\n", "# merge all\n", "\n", "for i in range(2,len(betas)):\n", " r_in_fm = []\n", " V_in_GeV = []\n", " V_in_GeV_err = []\n", " for j in range(len(a_mean_err[i][2])):\n", " r_in_fm.append(a_mean_err[i][0]*a_mean_err[i][2][j])\n", " V_in_GeV.append((a_mean_err[i][3][j]-a_mean_err[i][5][0])/a_mean_err[i][0]*0.1973)\n", " V_in_GeV_err.append(a_mean_err[i][4][j]/a_mean_err[i][0]*0.1973)\n", " ax.errorbar(r_in_fm, V_in_GeV, V_in_GeV_err, fmt=\"o\", label=f\"beta={betas[i]}\")\n", "\n", "plt.legend()\n", "plt.show()\n", "\n", "# Show also coarser" ] }, { "cell_type": "code", "execution_count": 61, "id": "38bcdddf", "metadata": { "collapsed": true }, "outputs": [ { "data": { "image/png": "iVBORw0KGgoAAAANSUhEUgAAAYIAAAEGCAYAAABo25JHAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjQuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8rg+JYAAAACXBIWXMAAAsTAAALEwEAmpwYAAAVaElEQVR4nO3df7TcdX3n8eerIZSsFgNLjkIAoVtEY48SN6VSqoLoBqkF3LULdLHi2g271lprxQOrR1tPrRzRdvXoaqhYiq6Iy2YjPfJLCq6tG5FolIhsNMYt5IJLbIxKjRCS9/4xE5xc7o+5yf3OzL3f5+OcOZn5fL8z93Und+7rfn+nqpAktdfPDTuAJGm4LAJJajmLQJJaziKQpJazCCSp5Q4adoCZOuKII+q4444bdgxJmlO+8pWvfL+qlkw0bc4VwXHHHcf69euHHUOS5pQk/zDZNFcNSVLLWQSS1HIWgSS1nEUgSS1nEUhSy1kEktRyFoEktZxFIEkt15oiOG/1Os5bvW7YMSRp5LSmCCRJE7MIJKnlLAJJajmLQJJaziKQpJazCCSp5SwCSWo5i0CSWs4ikKSWa6wIknwsyUNJvjHJ9GcmWZfkkSRvbiqHJGlqTS4RXA2cOcX07cAbgPc2mEGSNI3GiqCqvkDnl/1k0x+qqruAXU1lkCRNb05sI0iyKsn6JOu3bds27DiSNK/MiSKoqiurakVVrViyZMmw40jSvDInikCS1ByLQJJa7qCmXjjJtcBpwBFJtgLvABYCVNVHkjwNWA8cCuxJ8kZgWVX9qKlMkqQnaqwIquqCaaZ/Dzi6qa8vSeqPq4YkqeUsAklqOYtgnjtv9TrOW71u2DEkjTCLQPOWJSj1xyKQpJazCCSp5SwCSWo5i0CSWs4ikKSWswgkqeVaUQRrN4yx4b4d3Pnd7Zx6+e2s3TA27EiSNDLmfRGs3TDGZWs28ujuPQCM7djJZWs2WgaS1DXvi+CKWzaxc9fufcZ27trNFbdsGlIiSRot874IHtixc0bjktQ2874Ijlq8aEbjktQ2874ILll5IosWLthnbNHCBVyy8sQhJZKk0dLYhWlGxbnLlwLwluvv5tHde1i6eBGXrDzx8XFJart5XwTQKYNrv3wfANddfMqQ00jSaJn3q4YkSVOzCCSp5SwCzUseTS71zyLQvOPR5NLMWASadzyaXJoZi2Aea+vqEY8ml2bGIpin2rx6xKPJpZmxCOapNq8e8WhyaWZacUBZG7V59YhHk0szYxHMU0ctXsTYBL/027J6xKPJpf65amiecvWIpH65RDBPuXpE/Thv9TrApaa2swjmMVePSOqHq4YkqeUsAklqOYtAklrOIpCklrMIJKnlLAJJarnGiiDJx5I8lOQbk0xPkg8k2Zzk7iTPayqLJGlyTS4RXA2cOcX0lwEndG+rgA83mEWSNInGiqCqvgBsn2KWc4BrquNLwOIkRzaVR5I0sWFuI1gK3N/zeGt37AmSrEqyPsn6bdu2DSScJLXFnNhYXFVXVtWKqlqxZMmSYceRpHllmEUwBhzT8/jo7pgkaYCGWQQ3AL/T3Xvo+cAPq+rBIeaRpFaa9uyjSU4BLgReABwJ7AS+AXwW+ERV/XCS510LnAYckWQr8A5gIUBVfQS4ETgL2Az8BHjNAX4v0j4846rUnymLIMlNwAPAZ4B3AQ8BhwDPAE4HPpPkz6vqhvHPraoLpnrtqirg9/Yz94z5S0GSJjbdEsGrqur748YeBr7avb0vyRGNJJMkDcSURTC+BJIc2vucqto+QVFIkuaQvq5QluRi4E+AnwLVHS7gFxvKJUkakH4vVflm4Jf961+S5p9+i+A7dPbs0RzjRnJJ0+m3CC4D/neSO4FH9g5W1RsaSSVJGph+i2A1cDuwEdjTXBxJ0qD1WwQLq+pNjSaRJA1Fv6eYuKl7BtAjkxy+99ZoMknSQPS7RLD3KOHLesbcfVSS5oHpTjHxW1X134EzqmrLgDJJkgZoulVDe5cArm86iCRpOKZbNbQ9ya3A8UkmOrHc2c3EkiQNynRFcBbwPODjwPuajyNJGrTpiuCPgJuBX6sqLxYsSfPQdEWwBfgD4LlJvg7cBNxaVT9oPJkkaSCmOw31dcB1AEmWA2cCa5IsAG4Dbq6qLzeeUpLUmCn3GkqycO/9qtpQVe+uqtOBlwP3AL/bcD5JDVm7YYwN9+3gzu9u59TLb2fthrFhR9KQTLf76FiSjyY5I0n2DlbVj6rqf1TVqobzSWrA2g1jXLZmI4/u7pw6bGzHTi5bs9EyaKnpiuBZwF3A24D7k7w/yfObjyWpSVfcsomdu3bvM7Zz126uuGXTkBJpmKYsgqr6x6pa3V0ddDKdjcd/keQ7Sd41kISSZt0DO3bOaFzzW78nnaOqHgCuAj4M/Bi3D0hz1lGLF81oXPPbtEWQ5JAkv5VkDbAZeDFwKXBU0+EkNeOSlSeyaOGCfcYWLVzAJStPHFIiDdN0J537JPAS4H8B/w347ar66SCCSWrOucuXAvCW6+/m0d17WLp4EZesPPHxcbXLdAeU3QxcXFU/HkQYSYNz7vKlXPvl+wCvbd12020svqaqfpzkqUmuSnIzQJJlSV47mIiSpCb1u7H4auAW4Mju428Bb2wgjyRpwPotgiOq6tN0L1xfVY8Bu6d+iiRptpy3eh3nrV7XyGv3WwT/lOSf07k8Jd2Dyn7YSCJJ0kD1e83iNwE3AP8iyReBJcArG0slSRqYvoqgqr6a5EXAiUCATVW1q9FkkqSBmO7so4cmOQEe3y6wjM4Vyy5I8tQB5JMkNWy6bQTvBU7tefxuYAXwQuBPmgolSRqc6VYN/Qpwcc/jH1fVGwCS/H1jqSRJAzPdEsFBVVU9j1/Vc3/x7MeRJA3adEWwJ8nT9j6oqm8AJFlK95gCSdLcNl0RXAH8TZIXJvmF7u1FwNruNEnSHDfdxes/keT7wJ8Cz6ZzQNk9wNur6qYB5JMkNWza4wiq6mY6ZyGdsSRnAu8HFgAfrarLx01/OvAxOgeobQcurKqt+/O1JEn7Z7rjCN6W5PAppr84ycsnmbYA+BDwMjrHH1yQZNm42d4LXFNVzwHeSWf3VEnSAE23RLCRzjaCnwJfBbYBhwAnACcBtwF/NslzTwY2V9UWgCSfAs4BvtkzzzI6p68AuIPOtgdJ0gBNdz2Cz1TVqcB/pLNtYAHwI+ATwMlV9YdVtW2Spy8F7u95vLU71uvrwL/u3n8F8Avdk9vtI8mqJOuTrN+2bbIvJ0naH9NdqvIy4Oaq2gB8u4Gv/2bgg0kuAr4AjDHB6a2r6krgSoAVK1bU+OmSpP033aqhLcAfJHkunb/ebwJuraof9PHaY8AxPY+P7o49rqoeoLtEkOTJwL+pqh39RZckzYbpdh+9DrgOIMly4ExgTXdD8G10lha+PMnT7wJOSHI8nQI4H/jt3hmSHAFsr6o9wGV09iCSJA1Qvxemoao2VNW7q+p04OV0thn87hTzPwa8ns4lLu8FPl1V9yR5Z5Kzu7OdBmxK8i3gqcC79u/bkCTtr34vTEOSX6azl88he8eqatVUz6mqG4Ebx429vef+9cD1/WaQJM2+voogyTvo/PW+jM4v9pcBfw9c01gySdJA9Ltq6JXAGcD3quo1wHOBpzSWSpI0MP0Wwc7uBt3HkhwKPMS+ewRJkuaofrcRrE+yGPhL4CvAw8C6pkJJkgan34vXv6579yNJbgYOraq7m4slSRqUmew19BzguL3PSfJLVbWmoVySpAHpd6+hjwHPoXPswN4rkxVgEUjSHNfvEsHzq2r8KaQlSfNAv3sNrZvgWgKSpHmg3yWCa+iUwfeAR4AA1b2gjKQ56rqLTxl2BI2AfovgKuBVdC5Us2eaeSVJc0i/RbCtqm5oNIkkaSj6LYINST4J/A2dVUMAuPuoJM19/RbBIjoF8K96xtx9VJLmgX6PLH5N00EkScPR7wFlH5hg+IfA+qr6zOxGkiQNUr/HERwCnETnAvbfpnOU8dHAa5P8l0aSSZIGot9tBM8BTq2q3QBJPgz8HfDrdHYplSTNUf0uERwGPLnn8ZOAw7vF8MjET5EkzQX9LhG8B/haks/TOar4hcCfJXkScFtD2SRJA9DvXkNXJbkROLk79J+r6oHu/UsaSSZJGogpVw0leWb33+cBRwL3d29P645Jkua46ZYI3gSsAt7XM1Y9918864kkSQM15RJBVa3q3v0wcE5VnQ7cQecYgjc3nE2SNAD97jX0tqr6UZJfp7MU8FE65SBJmuP6LYLd3X9/A/jLqvoscHAzkSRJg9RvEYwlWQ2cB9yY5Odn8FxJ0gjr95f5vwVuAVZW1Q7gcNxtVJLmhX6PI/gJPaecrqoHgQebCiVJGhxX70hSy1kEkjTi1m4YY8N9O7jzu9s59fLbWbthbFZf3yKQpBG2dsMYl63ZyKO79wAwtmMnl63ZOKtlYBFI0gi74pZN7Ny1e5+xnbt2c8Utm2bta1gEkjTCHtixc0bj+8MikKQRdtTiRTMa3x8WgSSNsEtWnsiihQv2GVu0cAGXrDxx1r5GvxemkSQNwbnLlwLwluvv5tHde1i6eBGXrDzx8fHZ0OgSQZIzk2xKsjnJpRNMPzbJHUk2JLk7yVlN5pGkuejc5UtZfuxifvX4w/nipS+e1RKABosgyQLgQ8DLgGXABUmWjZvtbcCnq2o5cD7wX5vKI0maWJNLBCcDm6tqS1U9CnwKOGfcPAUc2r3/FOABJEkD1WQRLKVzWcu9tnbHev0xcGGSrcCNwO9P9EJJViVZn2T9tm3bmsgqSa017L2GLgCurqqjgbOAjyd5QqaqurKqVlTViiVLlgw8pCTNZ00WwRhwTM/jo7tjvV4LfBqgqtYBhwBHNJhJkjROk0VwF3BCkuOTHExnY/AN4+a5DzgDIMmz6BSB634kaYAaK4Kqegx4PZ0L2txLZ++ge5K8M8nZ3dn+CPgPSb4OXAtcVFXVVCZJ0hM1ekBZVd1IZyNw79jbe+5/Ezi1yQySpKkNe2OxJGnILAJJajmLQJJaziKQpJazCCSp5SwCSWo5i0CSWs4ikKSWswgkqeUsAklqOYtAklrOIpCklrMIJKnlLAJJajmLQJJaziKQpJazCCSp5SwCSWo5i0CSWs4ikKSWswgkqeUsAklqOYtAklrOIpCklrMIJKnlLAJJajmLQJJaziKQpJazCCSp5SwCSWo5i0CSWs4ikKSWswgkqeUsAklqOYtAklrOIpCklrMIJKnlGi2CJGcm2ZRkc5JLJ5j+F0m+1r19K8mOJvNIkp7ooKZeOMkC4EPAS4GtwF1Jbqiqb+6dp6r+sGf+3weWN5VHkjSxJpcITgY2V9WWqnoU+BRwzhTzXwBc22AeSdIEGlsiAJYC9/c83gr86kQzJnk6cDxw+yTTVwGrAI499tjZTSlJc8B1F5/S2GuPysbi84Hrq2r3RBOr6sqqWlFVK5YsWTLgaJI0vzVZBGPAMT2Pj+6OTeR8XC0kSUPRZBHcBZyQ5PgkB9P5ZX/D+JmSPBM4DFjXYBZJ0iQaK4Kqegx4PXALcC/w6aq6J8k7k5zdM+v5wKeqqprKIkmaXJMbi6mqG4Ebx429fdzjP24ygyRpaqOysViSNCQWgSS1nEUgSS1nEUhSy2Wu7ayTZBvwD0OOcQTw/SFnmKm5mBnmZm4zD4aZZ+bpVTXhEblzrghGQZL1VbVi2DlmYi5mhrmZ28yDYebZ46ohSWo5i0CSWs4i2D9XDjvAfpiLmWFu5jbzYJh5lriNQJJaziUCSWo5i0CSWs4iGCfJmUk2Jdmc5NIJpr8wyVeTPJbklT3jJyVZl+SeJHcnOW/UM/dMPzTJ1iQfHEziA8uc5Ngktya5N8k3kxw3BzK/p/uzcW+SDyTJIDL3mftN3ffx7iR/271i4N5pr07y7e7t1aOeecQ/h5O+z93pA/8cPq6qvHVvwALgO8AvAgcDXweWjZvnOOA5wDXAK3vGnwGc0L1/FPAgsHiUM/dMfz/wSeCDo/4+d6d9Hnhp9/6TgX82ypmBXwO+2H2NBXSuvXHaCL3Xp+99D4H/BFzXvX84sKX772Hd+4eNeOZR/hxOmLln+kA/h703lwj2dTKwuaq2VNWjwKeAc3pnqKr/W1V3A3vGjX+rqr7dvf8A8BAwiOtq7ndmgCT/EngqcOsAsu6135mTLAMOqqrPded7uKp+MsqZgQIOofML4ueBhcD/az4y0F/uO3rewy/RuZogwErgc1W1vap+AHwOOHOUM4/453Cy93lYn8PHWQT7Wgrc3/N4a3dsRpKcTOdD/51ZyjWV/c6c5OeA9wFvbiDXVA7kfX4GsCPJmiQbklyRZMGsJ3yi/c5cVeuAO+j8dfogcEtV3TvrCSc209yvBW7az+fOlgPJ/LgR/xw+nnmIn8PHNXphmjZKciTwceDVVfWEv8BHzOuAG6tq6wBXWR+og4AXAMuB+4DrgIuAq4aYaUpJfgl4Fj/7C/BzSV5QVX83xFhPkORCYAXwomFn6ddkmUf5czhB5qF/Di2CfY0Bx/Q8Pro71pckhwKfBd5aVV+a5WyTOZDMpwAvSPI6OuvaD07ycFU9YUPXLDuQzFuBr1XVFoAka4Hn03wRHEjmVwBfqqqHAZLcROe9H0QR9JU7yUuAtwIvqqpHep572rjnfr6RlPs6kMwj/TmcJPOwPoc/M+iNEqN8o1OMW4Dj+dkGn2dPMu/V7LtB8GDgb4E3zpXM46ZdxOA2Fh/I+7ygO/+S7uO/An5vxDOfB9zWfY2F3Z+T3xyV95rO0tV36G5k7Rk/HPgunQ3Fh3XvHz7imUf2czhZ5nHzDOxzuM/XHfQXHPUbcBbwre5/2Fu7Y+8Ezu7e/xU6f5X+E/CPwD3d8QuBXcDXem4njXLmca8x0B/AA8kMvBS4G9jY/aV78ChnplNeq4F7gW8Cfz5iP9O30dl4vffn9oae5/57YHP39ppRzzzin8NJ3+ee1xjo53DvzVNMSFLLudeQJLWcRSBJLWcRSFLLWQSS1HIWgSS1nEUgHYAklyb5d0mWJLmze9qLFww7lzQTFoF0YFbSOVHYGcDGqlpeI3bqCGk6FoHUhyRrk3yle577Vd2xQ+kcRboUeA9wTpKvJVmU5OHuCfHuSXJbkpOTfD7JliRnD/N7kcbzgDKpD0kOr6rtSRYBd9E5YdiL6By1+vYkFwErqur13fkLOKuqbkryP4EnAb8BLAP+uqpOGsb3IU3Ek85J/XlDkld07x8DnEDn3Px/Ncn8jwI3d+9vBB6pql1JNtK5gI00Mlw1JE0jyWnAS4BTquq5wAY6F5o5GfjyJE/bVT9b3N4DPAJQnVMi+weYRopFIE3vKcAPquonSZ5J57TXzwb+T1XtHm406cBZBNL0bgYOSnIvcDmdywwu4merfqQ5zY3F0n5I8jngd6rqwWFnkQ6URSBJLeeqIUlqOYtAklrOIpCklrMIJKnlLAJJajmLQJJa7v8Dr1oryWSkYqkAAAAASUVORK5CYII=\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots()\n", "plt.xlabel(\"a/fm\")\n", "plt.ylabel(\"sigma/(GeV/fm)\")\n", "\n", "# merge all\n", "a_in_fm = []\n", "sigma_in_GeV = []\n", "sigma_in_GeV_err = []\n", "for i in range(len(betas)):\n", " a_in_fm.append(a_mean_err[i][0])\n", " sigma_in_GeV.append(a_mean_err[i][5][2]/a_mean_err[i][0]**2.*0.1973)\n", " sigma_in_GeV_err.append(a_mean_err[i][6][2,2]**0.5/a_mean_err[i][0]**2.*0.1973)\n", " \n", " #sigma_in_GeV.append(a_mean_err[i][5][1]*0.1973)\n", " #sigma_in_GeV_err.append(a_mean_err[i][6][1,1]**0.5*0.1973)\n", "\n", "ax.errorbar(a_in_fm, sigma_in_GeV, sigma_in_GeV_err, fmt=\"o\")\n", "\n", "#plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4c2d9acb", "metadata": {}, "source": [ "***Homework***: Compute the Coulomb coefficient $B$ in units of GeV fm with $V(r)=A + B/r + \\sigma r$ for the same lattice spacings and make a similar plot to the one for $\\sigma$." ] }, { "cell_type": "code", "execution_count": 103, "id": "9e2983d2", "metadata": {}, "outputs": [], "source": [ "def glueball_A1_correlator(U0, nsmear):\n", " Usmear = g.copy(U0)\n", " L = U0[0].grid.gdimensions\n", " for i in range(nsmear):\n", " Usmear = g.qcd.gauge.smear.stout(Usmear, rho=0.15,orthogonal_dimension=3)\n", " Pfield1, Pfield2 = g.qcd.gauge.loops.rectangle(Usmear, \n", " [[ (mu,1,nu,1) for mu in range(3) for nu in range(mu)], \n", " [ (mu,3,nu,1) for mu in range(3) for nu in range(3) if mu != nu]],\n", " field=True)\n", " return (\n", " [x/(L[0]*L[1]*L[2]) for x in g.slice(Pfield1,3)], \n", " g.sum(Pfield1) / Pfield1.grid.gsites,\n", " [x/(L[0]*L[1]*L[2]) for x in g.slice(Pfield2,3)], \n", " g.sum(Pfield2) / Pfield2.grid.gsites\n", " )" ] }, { "cell_type": "code", "execution_count": 81, "id": "6daadea1", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "GPT : 23458.421117 s : Initializing gpt.random(test,vectorized_ranlux24_24_64) took 3.69549e-05 s\n", "GPT : 23458.458663 s : SU(2)-subgroup heatbath 0 has P = 1.0\n", "GPT : 23792.066852 s : SU(2)-subgroup heatbath 250 has P = 0.5823681093358043\n", "GPT : 24085.247532 s : SU(2)-subgroup heatbath 500 has P = 0.5820270769700736\n", "GPT : 24375.536335 s : SU(2)-subgroup heatbath 750 has P = 0.5827176520994317\n", "GPT : 24667.319774 s : SU(2)-subgroup heatbath 1000 has P = 0.5821944491517359\n", "GPT : 24956.718762 s : SU(2)-subgroup heatbath 1250 has P = 0.5823229107943341\n", "GPT : 25246.901014 s : SU(2)-subgroup heatbath 1500 has P = 0.5830595553523381\n", "GPT : 25535.126178 s : SU(2)-subgroup heatbath 1750 has P = 0.5831393794879535\n", "GPT : 25824.375946 s : SU(2)-subgroup heatbath 2000 has P = 0.5831170585874009\n", "GPT : 26116.473709 s : SU(2)-subgroup heatbath 2250 has P = 0.5807010396911295\n", "GPT : 26403.073038 s : SU(2)-subgroup heatbath 2500 has P = 0.5815773381540428\n", "GPT : 26691.175756 s : SU(2)-subgroup heatbath 2750 has P = 0.5829950881588777\n", "GPT : 26980.989076 s : SU(2)-subgroup heatbath 3000 has P = 0.5817829587379455\n", "GPT : 27274.689568 s : SU(2)-subgroup heatbath 3250 has P = 0.5814936616603346\n", "GPT : 27566.837664 s : SU(2)-subgroup heatbath 3500 has P = 0.5805751461356455\n", "GPT : 27855.261779 s : SU(2)-subgroup heatbath 3750 has P = 0.5800671857797849\n", "GPT : 28138.893678 s : SU(2)-subgroup heatbath 4000 has P = 0.5804503576728808\n", "GPT : 28421.909804 s : SU(2)-subgroup heatbath 4250 has P = 0.5816100159724532\n", "GPT : 28706.761141 s : SU(2)-subgroup heatbath 4500 has P = 0.5817419634089783\n", "GPT : 28989.230684 s : SU(2)-subgroup heatbath 4750 has P = 0.5819070143898305\n" ] }, { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "#generate_ensemble(8, 32, 5.7, 100, 10000, 5)\n", "generate_ensemble(8, 32, 5.9, 100, 5000, 5)" ] }, { "cell_type": "code", "execution_count": 108, "id": "feea5535", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "9995\r" ] } ], "source": [ "operators_5p7 = []\n", "for it in range(105,10000,5):\n", " operators_5p7.append(glueball_A1_correlator(g.load(f\"8c32_5.7/su3.{it}\"), 6))\n", " print(it,end=\"\\r\")" ] }, { "cell_type": "code", "execution_count": 105, "id": "12b78611", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "4995\r" ] } ], "source": [ "operators_5p9 = []\n", "for it in range(105,5000,5):\n", " operators_5p9.append(glueball_A1_correlator(g.load(f\"8c32_5.9/su3.{it}\"), 8))\n", " print(it,end=\"\\r\")" ] }, { "cell_type": "code", "execution_count": 111, "id": "2d75e269", "metadata": {}, "outputs": [], "source": [ "def bin_data(res, bin_size):\n", " assert len(res) % bin_size == 0\n", " n = len(res) // bin_size\n", " return [ sum(res[bin_size*i:bin_size*(i+1)])/bin_size for i in range(n) ]\n", "\n", "def jackknife_variance_estimator(f, x):\n", " N = len(x)\n", " X = sum(x) / N\n", " mean = f(X)\n", " return sum([(f((N*X - x[j])/(N-1)) - mean)**2 for j in range(N)])*(N-1)/N\n", "\n", "def correlate(X, P):\n", " pdelta = [x - P for x in X]\n", " Lt = len(pdelta)\n", " return np.array([ sum([ pdelta[t]*pdelta[(t+dt) % Lt] for t in range(Lt)]) for dt in range(Lt)],dtype=np.complex128)\n", "\n", "def glueball_spectrum(operators, a_in_fm):\n", " plaquette1 = np.mean([op[1] for op in operators])\n", " plaquette2 = np.mean([op[3] for op in operators])\n", " \n", " correlators1=[correlate(op[0],plaquette1) for op in operators]\n", " correlators2=[correlate(op[2],plaquette2) for op in operators]\n", " \n", " ldiv8 = len(correlators1)-(len(correlators1)%8)\n", " \n", " err1=[y**0.5 for y in jackknife_variance_estimator(lambda x:x, correlators1)]\n", " err2=[y**0.5 for y in jackknife_variance_estimator(lambda x:x, bin_data(correlators1[0:ldiv8],4))]\n", " err4=[y**0.5 for y in jackknife_variance_estimator(lambda x:x, bin_data(correlators1[0:ldiv8],8))]\n", " print(\"Binning study of correlator (nbin=1,4,8):\",err1[0], err2[0], err4[0])\n", " \n", " corr1=np.mean(correlators1,axis=0)\n", " emp_mean_1 = [ np.log(corr1[t]/corr1[t+1]) for t in range(4)]\n", " err_emp_1=[y**0.5 for y in jackknife_variance_estimator(lambda x: np.array([np.log(x[t]/x[t+1]) for t in range(4)]), bin_data(correlators1[0:ldiv8],4))]\n", " \n", " corr2=np.mean(correlators2,axis=0)\n", " emp_mean_2 = [ np.log(corr2[t]/corr2[t+1]) for t in range(4)]\n", " err_emp_2=[y**0.5 for y in jackknife_variance_estimator(lambda x: np.array([np.log(x[t]/x[t+1]) for t in range(4)]), bin_data(correlators2[0:ldiv8],4))]\n", " \n", " fig, ax = plt.subplots()\n", "\n", " plt.ylim(0,2)\n", " ax.errorbar(range(len(emp_mean_1)), emp_mean_1, err_emp_1, marker=\"+\")\n", " ax.errorbar(range(len(emp_mean_2)), emp_mean_2, err_emp_2, marker=\"+\")\n", "\n", " #plt.legend()\n", " plt.show()\n", "\n", " print(\"t=1\",emp_mean_1[1]*0.1973/a_in_fm,err_emp_1[1]*0.1973/a_in_fm,\"GeV\")\n", " print(\"t=2\",emp_mean_1[2]*0.1973/a_in_fm,err_emp_1[2]*0.1973/a_in_fm,\"GeV\")" ] }, { "cell_type": "code", "execution_count": 118, "id": "b0499a85", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", " beta = 5.7, a = 0.17 fm\n", "\n", "Binning study of correlator (nbin=1,4,8): (9.195666010766062e-07+0j) (1.1338207652267015e-06+0j) (1.235564926411823e-06+0j)\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "t=1 (1.1395837688526864+0j) (0.041178362087299636+0j) GeV\n", "t=2 (0.9971292560027318+0j) (0.09740385965874282+0j) GeV\n", "\n", " beta = 5.9, a = 0.11 fm\n", "\n", "Binning study of correlator (nbin=1,4,8): (2.5400932771942773e-07+0j) (3.226258039722407e-07+0j) (3.490387661363861e-07+0j)\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ "t=1 (1.5290449848516772+0j) (0.06852290270749113+0j) GeV\n", "t=2 (1.5391866165060522+0j) (0.1773080551731805+0j) GeV\n" ] } ], "source": [ "print(f\"\\n beta = {betas[2]}, a = {a_mean_err[2][0]:.2f} fm\\n\")\n", "glueball_spectrum(operators_5p7, a_mean_err[2][0])\n", "\n", "print(f\"\\n beta = {betas[4]}, a = {a_mean_err[4][0]:.2f} fm\\n\")\n", "glueball_spectrum(operators_5p9, a_mean_err[4][0])" ] }, { "cell_type": "markdown", "id": "9876f761", "metadata": {}, "source": [ "***Homework (optional)***: Generate an even finer ensemble with same physical volume as the $\\beta=5.9$ ensemble, determine the lattice spacing and measure the $A_1^{++}$ glueball mass. You should find that once the lattice spacing is sufficiently small, that the glueball state remains at constant energy in GeV (see, e.g., https://doi.org/10.1016/0370-2693(88)91510-9). The $A_1^{++}$ glueball state in quenched QCD is at $1.6(1)$ GeV." ] } ], "metadata": { "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": "3.9.6" } }, "nbformat": 4, "nbformat_minor": 5 }