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  "name": ""
 },
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  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "    Solving and Plottings RGEs from PyR@TE"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Firts thing first we have to load pylab in order to be able to plot the results\n",
      "%pylab inline\n",
      "import numpy as np "
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Populating the interactive namespace from numpy and matplotlib\n"
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "1. Solving the RGEs"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#We asssume that we have a BetaFunction.py file as well as a SolveRGEs.py file both produced by PyR@TE during a previous run"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Make the RGEclass available\n",
      "import sys\n",
      "sys.path.append('./Source/Output/')\n",
      "#The RGEclass should be loaded\n",
      "import RGEclass as rge\n",
      "#The BetaFunction.py must be loaded (assumed in the current working directory, if not add the path to sys.path like above)\n",
      "from BetaFunction import beta_function_SM as bSM"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In order to create an object of the rgecls class and then solve the rges one needs to know how many equations are there and in which order they have be written in the BetaFunction.py file. First solution is to look directly into this file. Second solution is to look at the BetaFunction_SolveRGEs.py file where everything has been declared automatically and to copy the information here"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Now the first thing is to create an RGE object of the RGEclass for or result\n",
      "OurRGEs = rge.RGE(bSM,32,labels=['betaY_u[0,0]', 'betaY_u[0,1]', 'betaY_u[0,2]', 'betaY_u[1,0]', 'betaY_u[1,1]', 'betaY_u[1,2]', 'betaY_u[2,0]', 'betaY_u[2,1]', 'betaY_u[2,2]', 'betaY_e[0,0]', 'betaY_e[0,1]', 'betaY_e[0,2]', 'betaY_e[1,0]', 'betaY_e[1,1]', 'betaY_e[1,2]', 'betaY_e[2,0]', 'betaY_e[2,1]', 'betaY_e[2,2]', 'betaY_d[0,0]', 'betaY_d[0,1]', 'betaY_d[0,2]', 'betaY_d[1,0]', 'betaY_d[1,1]', 'betaY_d[1,2]', 'betaY_d[2,0]', 'betaY_d[2,1]', 'betaY_d[2,2]', 'bg_SU2L', 'bg1', 'bg_SU3c', 'bLambda_1', 'bmu_1'])\n",
      "#note that the labels have to correspond to the ordering of the beta functions in BetaFunction.py"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, we set all the initial values and pass them to the RGE object using the Y0 attribute of the instance. Note that there are pre-defined values for the SM initial values at the Z mass inside the RGEclass object. To have an exaustive list one can print the instance itself"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#list of all pre-defined values\n",
      "OurRGEs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "Instance of the RGE class. Physical parameters predefined calculated at the Z boson mass : \n",
        "\t Pi 3.14159265359\n",
        "\t alpha 0.00775735008921\n",
        "\t alphaS 0.1184\n",
        "\t sinthetasq 0.2316 \n",
        "\t ZbosonMass 91.1876\n",
        "\t Gf 1.16637e-05\n",
        "\t Higgs vev 246.22\n",
        "\t Top pole mass 173.3\n",
        "\t Up matrix [0.0024, 1.27, 165.3308]\n",
        "\t Down matrix [0.00475, 0.104, 4.19]\n",
        "\t Lepton matrix [0.000511, 0.10566, 1.777]\n",
        "."
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Set the initial values, here we use the SM values predefine in the RGE class\n",
      "lbd0 = 0.07\n",
      "mu0 = -lbd0*OurRGEs.vev**2\n",
      "#Initial all the values to zero and modify the one we want to be different\n",
      "Y0 = [0]*32\n",
      "#Up diagonal Yukawas\n",
      "Y0[0],Y0[4],Y0[8]=OurRGEs.yU[0],OurRGEs.yU[1],OurRGEs.yU[2]\n",
      "#Down diagonal Yukawas\n",
      "Y0[9],Y0[13],Y0[17]=OurRGEs.yD[0],OurRGEs.yD[1],OurRGEs.yD[2]\n",
      "#Gauge Couplings\n",
      "Y0[-4],Y0[-5],Y0[-3]=OurRGEs.g10,OurRGEs.g20,OurRGEs.g30\n",
      "#lambda and mu1\n",
      "Y0[-2],Y0[-1] = lbd0,mu0\n",
      "OurRGEs.Y0 = Y0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Set initial and final values for the scale directly e.g. Mz to 10**16 (same as initial values)\n",
      "tmin,tmax,tstep = np.log(OurRGEs.Mz),19,0.5\n",
      "#By default the assumptions is set to 'two-loop': True,'diag':True which means that the two loop equations are used if provided and Yukawas are diagonal\n",
      "#Note that the user is free to modify the betaFunction.py file to introduce new assumptions and then add them to the dictionnary.\n",
      "OurRGEs.solve_rges(tmin,tmax,tstep,assumptions={'two-loop': False,'diag':True})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Now we can acces all the results via rge.Sol\n",
      "OurRGEs.Sol['bLambda_1'][:10]#ten first points of lambda(t)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "array([ 0.04357418,  0.01944982, -0.00264243, -0.02292316, -0.04157585,\n",
        "       -0.05875525, -0.07459352, -0.08920489, -0.1026891 , -0.11513409])"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#There is also an interpolated object accessible by,Can be called in any point\n",
      "OurRGEs.Solint['bLambda_1'],OurRGEs.Solint['bLambda_1'](6)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "(<scipy.interpolate.interpolate.interp1d at 0x10544ac90>,\n",
        " array(-0.07219024007593562))"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "2. Plotting the results "
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Let's first plot the quartic coupling. To do so we use the plot function of the pylab library\n",
      "plot(OurRGEs.Sol['t'],OurRGEs.Solint['bLambda_1'](OurRGEs.Sol['t']),label=r'$\\Lambda_1$')\n",
      "#add a grid\n",
      "grid(True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
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       "text": [
        "<matplotlib.figure.Figure at 0x10544a350>"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Let's now look at the gauge couplings \n",
      "plot(OurRGEs.Sol['t'],OurRGEs.Sol['bg1']**-2*np.sqrt(3/5.)**2,'k',label=r'$\\alpha_1^{-1}$')\n",
      "plot(OurRGEs.Sol['t'],OurRGEs.Sol['bg_SU2L']**-2,'b',label=r'$\\alpha_2^{-1}$')\n",
      "plot(OurRGEs.Sol['t'],OurRGEs.Sol['bg_SU3c']**-2,'r',label=r'$\\alpha_3^{-1}$')\n",
      "grid(True)\n",
      "#titles\n",
      "xlabel('$t=\\log_{10}(Q\\ \\mathrm{GeV})$')\n",
      "ylabel('Running in the SM')\n",
      "title('Running of the gauge couplings in the SM obtained from PyR@TE')\n",
      "#number of column of location of the legend, collects all the label entries above\n",
      "legend(loc=4,ncol=3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 11,
       "text": [
        "<matplotlib.legend.Legend at 0x10574b5d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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Ftq8nPT0dgwYNgpeXFzw9PWFgYKBqiRQKRQ5csp30VVWB8CWOWxWdTZo0gaen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\nJjpubBhjjImOGxvGGGOi48aGMcaY6P4PsVNh5NlZs0QAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10572a190>"
       ]
      }
     ],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#To illustrate the difference between one loop and two loop we can create a new object with the same RGEs but soolve it for two loop.\n",
      "#Note that we could use the same instance we have already created but we won't be able to compare the results then.\n",
      "rge2L = rge.RGE(bSM,32,labels=['betaY_u[0,0]', 'betaY_u[0,1]', 'betaY_u[0,2]', 'betaY_u[1,0]', 'betaY_u[1,1]', 'betaY_u[1,2]', 'betaY_u[2,0]', 'betaY_u[2,1]', 'betaY_u[2,2]', 'betaY_e[0,0]', 'betaY_e[0,1]', 'betaY_e[0,2]', 'betaY_e[1,0]', 'betaY_e[1,1]', 'betaY_e[1,2]', 'betaY_e[2,0]', 'betaY_e[2,1]', 'betaY_e[2,2]', 'betaY_d[0,0]', 'betaY_d[0,1]', 'betaY_d[0,2]', 'betaY_d[1,0]', 'betaY_d[1,1]', 'betaY_d[1,2]', 'betaY_d[2,0]', 'betaY_d[2,1]', 'betaY_d[2,2]', 'bg_SU2L', 'bg1', 'bg_SU3c', 'bLambda_1', 'bmu_1'])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rge2L.Y0 = Y0"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "rge2L.solve_rges(tmin,tmax,tstep,assumptions={'two-loop': True,'diag':True})"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#Now we can compare the top yukawa at one and two loop\n",
      "plot(rge2L.Sol['t'],rge2L.Solint['betaY_u[2,2]'](rge2L.Sol['t']),label=r'Two loop $Y_t$')\n",
      "plot(OurRGEs.Sol['t'],OurRGEs.Solint['betaY_u[2,2]'](OurRGEs.Sol['t']),label=r'One loop $Y_t$')\n",
      "grid(True)\n",
      "xlabel('$t=\\log_{10}(Q\\ \\mathrm{GeV})$')\n",
      "ylabel(r'$Y_t$')\n",
      "title('Comparison 1L vs 2L of $Y_t$')\n",
      "#number of column of location of the legend, collects all the label entries above\n",
      "legend(loc=4,ncol=3)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 15,
       "text": [
        "<matplotlib.legend.Legend at 0x1056f23d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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rw5S9U0jRy/8DIV40Ty0SH374YaYiEBERwWeffcbcuXOJi4sjIiIi3wJqmVba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\ntagWE3dN5MiVIxb3+6eFz10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       "text": [
        "<matplotlib.figure.Figure at 0x10570bc90>"
       ]
      }
     ],
     "prompt_number": 15
    }
   ],
   "metadata": {}
  }
 ]
}