diff --git a/effort2/examples/Rates and Form Factors for B --> D** l nu.ipynb b/effort2/examples/Rates and Form Factors for B --> D** l nu.ipynb new file mode 100644 index 0000000..25a7529 --- /dev/null +++ b/effort2/examples/Rates and Form Factors for B --> D** l nu.ipynb @@ -0,0 +1,273 @@ +{ + "cells": [ + { + "cell_type": "markdown", + "id": "94a5cedf-b0c3-427a-8e05-88760121db96", + "metadata": {}, + "source": [ + "# How to Access Different Form Factors and Rates\n", + "\n", + "In this notebook we give an example for different form factor parameterizations and how to use them for $B$ to $D^{**}$ decays.\n", + "This will be a basic instructions and only concern itself with central values. " + ] + }, + { + "cell_type": "code", + "execution_count": 1, + "id": "e6880e6f-1638-4f3e-8422-ff149a4eb011", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Welcome to JupyROOT 6.24/06\n", + "For optimal usage set `plt.style.use('belle2')`\n" + ] + } + ], + "source": [ + "# from effort2.rates.BtoDStSt import BtoD0St\n", + "\n", + "import numpy as np\n", + "import matplotlib.pyplot as plt\n", + "import uncertainties.unumpy as unp\n", + "import pdg\n", + "import b2plot as bp\n", + "import effort2.rates.BtoDStSt" + ] + }, + { + "cell_type": "markdown", + "id": "638ad31e-22ba-403d-ae22-546c88d81d94", + "metadata": {}, + "source": [ + "## Setting Up \n", + "\n", + "* We will require the masses of the contributing $B$ and $D^{**}$ mesons. We work with zero lepton masses, which is the default for effort. Non-zero lepton masses will be explored in a different notebook.\n", + "\n", + "* We will look at the BLR form factor parametrisation. Please note that the chosen values for the form factors might be outdated, and only serve for an explanatory purpose." + ] + }, + { + "cell_type": "code", + "execution_count": 2, + "id": "f8158d15-5f71-4ae6-a7e0-2955ca2dd9d8", + "metadata": {}, + "outputs": [], + "source": [ + "m_Bzero = pdg.get(511).Mass()\n", + "m_Bplus = pdg.get(521).Mass()\n", + "m_tau = pdg.get(15).Mass()" + ] + }, + { + "cell_type": "markdown", + "id": "06599e5d-8f5e-48bd-ad2a-a05494d0a442", + "metadata": {}, + "source": [ + "## Plotting" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "id": "51b0c954-21a7-4e78-9435-e208cd029844", + "metadata": {}, + "outputs": [], + "source": [ + "def add_watermark(\n", + " ax,\n", + " t: str = None,\n", + " logo: str = \"Belle II\",\n", + " px: float = 0.033,\n", + " py: float = 1.022, #0.915,\n", + " fontsize: int = 10,\n", + " alpha_logo=1,\n", + " shift: float = 0.15,\n", + " bstyle: str = \"normal\",\n", + " *args,\n", + " **kwargs,\n", + "):\n", + " ax.text(px, py, logo, ha=\"left\", transform=ax.transAxes, fontsize=fontsize, style=bstyle, alpha=alpha_logo, weight=\"bold\", *args, **kwargs,)\n", + " ax.text(px + shift, py, t, ha=\"left\", transform=ax.transAxes, fontsize=fontsize, alpha=alpha_logo, *args, **kwargs,)" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "id": "a8de39bf", + "metadata": {}, + "outputs": [], + "source": [ + "dict_d = {\n", + " 'D0*': {\n", + " 'pdg': 10411,\n", + " 'rate': effort2.rates.BtoDStSt.BtoD0St,\n", + " 'str': r\"$B^0 \\to D^*_0 \\ell \\bar{\\nu}_\\ell$\",\n", + " },\n", + " 'D1*': {\n", + " 'pdg': 20413,\n", + " 'rate': effort2.rates.BtoDStSt.BtoD1St,\n", + " 'str': r\"$B^0 \\to D^*_1 \\ell \\bar{\\nu}_\\ell$\",\n", + " },\n", + " 'D1': {\n", + " 'pdg': 10413,\n", + " 'rate': effort2.rates.BtoDStSt.BtoD1,\n", + " 'str': r\"$B^0 \\to D_1 \\ell \\bar{\\nu}_\\ell$\",\n", + " },\n", + " 'D2*': {\n", + " 'pdg': 415,\n", + " 'rate': effort2.rates.BtoDStSt.BtoD2St,\n", + " 'str': r\"$B^0 \\to D^*_2 \\ell \\bar{\\nu}_\\ell$\",\n", + " },\n", + "}" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "id": "3ea235a8", + "metadata": { + "scrolled": false + }, + "outputs": [ + { + "data": { + "image/png": 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YjYyM8NGPfpSnnnqKxsZGPvOZzyx7jLe97W3U1dXxk5/8hFdffTX2+NTUFH/xF3+By+XiYx/7WMJzFREREREREZHUUoWdrBsLu7gCDA4O8vTTT9Pc3Ex1dTVf/vKXz3mPz+c7Z4+1qKKiIr75zW9e8rpf+MIXuPfee/nWt77FZz/7WXJycoD5ir7lLl194IEHeOKJJzDGMDExQUtLC88++yyzs7Ps37+fRx55hOzs7GWNGZ3HD37wA97xjnfw5je/mQ984APk5OTws5/9jFOnTvFf/st/iS2bFREREREREZG1S4GdrBtnd3FNS0ujtraWz3/+89x5550UFRWd855gMMiDDz543vG2bNmypMCuuLiYT3/603zzm9/k29/+dqwBw5EjR3A4HNx6663L+jqijTGcTider5eqqipuvfVWbrnlFt75znficMRf+PrWt76V5557jrvuuotHH30Uv9/Prl27+OpXv8qHPvShuMcVERERERERkZVjGWNWew6bkmVZVUAXQFdXF1VVVas8I1mu0tJSrr/+eh599NHVnoqIiIiIiIiIxKm7u5vq6uro3WpjTPdqzge0h51IXNra2hgYGODOO+9c7amIiIiIiIiIyAajJbEicWhoaEDVqSIiIiIiIiKSCgrsRNaw73znO4yNjV3ydXfccQd5eXkpn4+IiIiIiIiIpJ4CO5E17Dvf+Q6dnZ2XfN2BAwcU2ImIiIiIiIhsEArsRNawjo6O1Z6CiIiIiIiIiKwwNZ0QERERERERERFZQxTYiYiIiIiIiIiIrCEK7ERERERERERERNYQBXYiIiIiIiIiIiJriAI7ERERERERERGRNUSBnYiIiIiIiIiIyBqiwE5ERERERERERGQNUWAnIiIiIiIiIiKyhiiwExERERERERERWUMU2Mma19HRgWVZiw6Hw0FpaSnXXnstf/d3f0cgEDjnfbW1tWRnZ8c1vsfjoaamho985CO0trYm5es4cODAomu43W4KCgrYs2cPBw4c4IknniAUCp33vbW1tdxwww1xXffVV1/lS1/6Em9/+9spLCzEsize9a53JfCViIiIiIiIiEgquVZ7AiJLVV9fzwc/+EEAwuEwfX19PP7443zqU5/iySef5Kc//WnSxp+YmOD555/nxz/+MY899hiHDh2iqakp4a8B4BOf+AQVFRWEw2EmJiZobm7m0Ucf5cEHH2T//v088sgj1NbWJuVaAI899hj33HMPaWlpbN++nZGRkaSNLSIiIiIiIiLJp8BO1o2GhgYOHjy46LGxsTH27NnDz372M9rb26mrq0vq+Lfffjv33Xcf99xzDw899FDcYy/0yU9+kn379i16bHh4mDvuuIOHH36Ym266iRdffHFJ1YFL8d73vpc/+IM/YPfu3fT09LB169Zlj9HR0cHWrVu56667zvkzEhEREREREZHk0pJYWdfy8vLYv38/AENDQ0kf/8CBAwC89NJLSR97ocLCQh566CFuvPFGWltbuffee5M29q5du7jyyitxu91JG1NEREREREREUkcVdutZOAyz62R5Y0YBOJKfD4+Pj3P48GGysrJobGxM+vhRKxF2WZbFl770JZ566ikeffRRvvjFL6b8miIiIiIiIiKy9iiwW89mR+C/blvtWSzNfz4JWUUJDdHW1hZbjhkOhxkYGODxxx9ncnKSBx54gNzc3CRMdLEf/vCHAFx33XVJH/t83vSmN+FyuXjttdcIBoO4XPa3aEdHx4pcX0RERERERERW34oEdpZl/TlwvzFmYCWuJxvT8ePHufvuu895/MMf/jDXXnttwuMvDAQnJyf59a9/zaFDh6ivr+crX/lKwuMvRVpaGoWFhfT39zMyMkJJScmKXFdERERERERE1o6V2sPuINBpWdYPLcu6coWuKRvMzTffjDEmdvT39/OTn/yEn//851xzzTW0t7cnNH40ELz77rv567/+aw4dOsT27dt57rnnKCsrS9JXsfb96Ec/wrKsRUe0UcXdd999znPRff5EREREREREJDlWaknsOJALfAT4iGVZzwF/AzxmjAmv0BxkgykpKeEDH/gAMzMz3Hbbbdxzzz18//vfj3u8m2++mSeeeAKA/v5+7r//fg4ePMgtt9zCL3/5y9jy1FTy+XwMDw/jdDopKChI+fXO54orruCuu+5a9NjY2Bh/8zd/w/XXX88NN9xwzutFREREREREJHlWKrCrAD4EfAa4AngzcB3QZVnWvcAPjDFjKzSXjSOjwN4bbj3ISF34dM011wBw+PDhpI1ZWlrKXXfdRV9fH/fffz/f+973+NznPpe08S/k+eefJxgMsnfv3hUJCM/niiuuOCeE6+jo4G/+5m+44YYbYsuGRURERERERCQ1ViQRMMbMAj8AfmBZ1m8BfwL8e6AG+AZw0LKsh4DvGWOaV2JOG4LDkXAjh41gdHQUsBtRJNtXv/pVHn74Yb72ta9x22234fV6k36NKGMMX//61wF43/vel7LriIiIiIiIiMjatlJ72MUYY/7NGPMhoBr4f4BuIBP4Y+CIZVk/tyzr91Z6XrI+hcNhvvvd7wLwlre8JenjFxUVcfvttzM8PBy7TtTBgwexLCspFWcjIyN89KMf5amnnqKxsZHPfOYzCY8pIiIiIiIiIuvT6qy5A4wxg8DXLMu6B/h94Hbgd4C3A79rWdYJ4LvAj4wx06s1T1k7FnZxBRgcHOTpp5+mubmZ6upqvvzlL5/zHp/Pd8GmCEVFRXzzm9+85HW/8IUvcO+99/Ktb32Lz372s+Tk5ADzFX3LXbr6wAMP8MQTT2CMYWJigpaWFp599llmZ2fZv38/jzzyCNnZ2csa82JaWlr4y7/8SwCmpqYAeO2112J/Lkv9cxARERERERGRlbFqgV1UpOnEY8BjlmU1YO9z91GgHjuw+yqwOrvvy5oS7eIalZaWRm1tLZ///Oe58847KSo6d3lwMBjkwQcfPO94W7ZsWVJQVVxczKc//Wm++c1v8u1vfzvWkOHIkSM4HA5uvfXWZX0d0cYYTqcTr9dLVVUVt956K7fccgvvfOc7cTiSW/ja19d3zp9Bd3d37LGl/jmIiIiIiIiIyMqwjDGpv4hlZQJ5QP6C42L3K4FawAKMMcaZ8kmuMMuyqoAugK6uLqqqqlZ5RrJcpaWlXH/99Tz66KOrPRURERERERERiVN3dzfV1dXRu9XGmO7VnA+sXIXdFHCxZNBaoXmIJEVbWxsDAwPceeedqz0VEREREREREdlgVnpJbBhoBSaA8WWcRdaUhoYGVqI6VUREREREREQ2n5UK7EKAE7sr7QxwL/CIMSa0QtcX2TCeeeYZnnnmmUu+7oYbbuCGG25I+XxEREREREREJLlWKrCrBf4UuA3YB/wY+IZlWfcBf2eMGVmheYise88888yi5hsXo8BORERERERE5CLCYRhb9S3rzrEiTSdiF7ObTxzADu8asPe1mwMeBv7GGHNsxSazytR0QkRERERERERkhRgDE2dgsBkGWmCgGTPQTHighd6RSaq/PRV95aZqOgGAMWYGuA+4z7Ksm4E7gLcBnwBusyzrKeA7xpj/u5LzEhERERERERGRDcAYmB6EgWN2MDfYDAORkM63uE2Chb1/21q00k0nYowx/wj8o2VZu4DPAR8Efhe40bKs48DfAA9GQj4REREREREREZF5MyORMO4YDLZEbjfD7PrfeW3VArsoY8xR7Oq6LwKfjhwN2I0p/otlWT8wxvz/VnOOIiIiIiIiIiKySnxTdiDXf2Q+lBtohumB1Z5ZyqxKYBfZy8674MiOnNuArwH/AbgCyAf+E6DATkRERERERERkIwuHYOQUDByF/gXH6KmkXWLKpHPcVNEWrqLN2MdoRiHwx0m7RjKsSGBnWVYL86FcFvYy4UsxS3ydiIiIiIiIiIisJ9PDkYq5Y/a5/5hdNRecTcrws8bDcVMZC+daTRXHw1X0UARYVOZl8O7LK/ji5eXkhCao+XpSLps0K1Vh17DE180Bo8DYWWcREREREREREVlvgj4YbLUr5RZWzk31J2X4AG5OmHJaw3Ywd9xU0Wqq6TbFhHEsem1RdhoHLivn3ZdXsLcmD8uy68S6uyeTMpdkWqnA7u85fxC36GyM8a/QfEREREREREREJFmMgfHuSCAXrZw7CkPHwYQSH99yEC7YxkDGNl6cLePJgXyOBCvpNKWELtLrNTfDze/tLuPdl1dwbV0hTsf6WMy5IoGdMeYTK3EdERERERERERFJsaDfbgLR94YdzvW9YR9zY8kZP6sYSndByS5CJTt51V/JP3Rm8Y/No0zOBS/59kyPk9/dWcrvX17Bm+uL8bgcl3zPWrPqXWJFRERERERERGSNmhmZD+Si4dxgK4QDiY/tTIOSHVC6G0p22iFd6S5CmcW82DHC46+f4f/+Yx/D0zPAzEWH8rgcvLWxmN+/vJLf2VFChufCVXfrgQI7EREREREREZHNLhy2u7GeHc5N9CRn/LwaO5gr3RUJ53ZDQR047WgqFDa82DHCP/2il3868jqDk75LDul0WFy3vYh3X17B23eVkpPuTs5c14BNG9hZlrUPeCdwHbATKAYCwBng18DfG2OeW70ZSlRHRwdbt25d9JhlWRQXF7N161Y+9rGP8fGPfxy3e/E3Zm1tLUNDQ0xNTS17fLfbTVlZGTfccANf/vKXaWxsTPjrOHDgAA8++GDsvsvlwuv1UllZyVVXXcUtt9zC7/3e7+F0xv9bgIcffphf/epXvPTSSxw5cgS/388//MM/cMsttyQ8fxEREREREdkg/DN2R9a+1+fDuf6j4L/45+clScuF0vlqOUp2QUkTpOec89JQ2PBi+zD/9EYv/3Skb0khnWXB/toC3n15Bb+3u4zC7LTE57wGJTWwsyyrJpnjRRljTidzPMuyfgW8+TxPeYD6yHHAsqyHgE+oGcbaUF9fzwc/+EEAwuEwfX19PP7443zqU5/iySef5Kc//WnSxp+YmOD555/nxz/+MY899hiHDh2iqakp4a8B4BOf+AQVFRWEw2EmJiZobm7m0Ucf5cEHH2T//v088sgj1NbWxjX2V77yFTo7OykuLqa0tJSurq6kzFlERERERETWqZkR6H3NPqIB3fAJMOHEx87bAmV75o/S3XYlnXXhxg7RSrp/fKOX/7vEkA7g8qpc3n15BTdfVk55bkbic1/jkl1hdyrJ4wEYkj/Pisj5DPAPwL8CpwEn8FvAF4BK4COAG/hgkq8vcWhoaODgwYOLHhsbG2PPnj387Gc/o729nbq6uqSOf/vtt3Pfffdxzz338NBDD8U99kKf/OQn2bdv36LHhoeHueOOO3j44Ye56aabePHFF8nOzl722D/4wQ9oaGigpqaGgwcPcvfddy97jOj7Tp06FXdwKCIiIiIiIivMGJjsjYRzr88HdONJKORwptlVcmW7oeyySDi3C9Jzl/T2UNhwuGOEf1pmSLejzMvNe8p59+UV1BZlJfIVrDvJDsLWR29caAG+BPzUmHN6C//GsqwfYy+LbQA+YFnW/caYX630JOXS8vLy2L9/P93d3QwNDSUU2J3PgQMHuO+++3jppZeSOu7ZCgsLeeihh+jr6+Opp57i3nvv5Ytf/OKyx7nxxhtTMDsRERERERFZU6L7zUVDuWhINzOU+NiZRYur5sr2QGF9bK+5pUokpHvnnnLeuaec7SXLL2TZKJId2H3sEs9/Brgae6+4J4EXgP7Ic6WR596OXdX2InBfkucHgDHmXZd4fsiyrC8Aj0ceugVYc4Fd2IQZ842t9jSWJC8tD4eV/DbK4+PjHD58mKysrKTsM3chZ++PlwqWZfGlL32Jp556ikcffTSuwE5EREREREQ2mFAQhloXV831vg7+yQQHtqCo3l7GujCcyy696JLWi041EtL94+u9/Pzo8ivp3nlZOduKN29It1BSAztjzIMXes6yrL8H9mEHdf/BGHPeNiOWZVUC3wfeAbzZGHNbMue4DE8vuL1tleZwUWO+Ma5/5PrVnsaSPPu+ZylIL0hojLa2ttiS1XA4zMDAAI8//jiTk5M88MAD5OYurRR3OX74wx8CcN111yV97PN505vehMvl4rXXXiMYDOJybdq+MCIiIiIiIptPYA4Gji5e1jpwDIJziY3rSreXsJZdBuWX2eeSJvAkvsx0YUj3f4/0MTSlkC4ZViQNsCzrFuzqu8PAzedZhhpjjOmxLOvdwL8BH7Ms60ljzKMrMc+zLGwzcsH5yso5fvz4efdk+/CHP8y1116b8PgLA8HJyUl+/etfc+jQIerr6/nKV76S8PhLkZaWRmFhIf39/YyMjFBSUrIi1xUREREREZEVFpiFviPQ+yqcedU+DzTDhSOTpUnLmQ/myi+3bxc1LHtJ68WEwoYXTs0vd1VIl3wrVb7zx9jNI/76YmFdlDEmZFnWt4D/F/gksBqB3cLSteZVuL6c5eabb+aJJ56I3R8YGOAXv/gFf/qnf8rPf/5zDh06lNAeducLBLdv385zzz23YYOzG264gWefffa8z23duvWcx55++mluuOGGFM9KRERERERkgzk7nDvzCgy2JB7OZRVHwrnL5wO6vFpwJH9LqmAozKFTI/z8SJ9CuhWwUoHdZZFz2zLeE33tniTP5ZIsy3IACzcQW3ZgaFlW1SVeUrbcMWWxkpISPvCBDzAzM8Ntt93GPffcw/e///24x1sYCPb393P//fdz8OBBbrnlFn75y1+uyPJUn8/H8PAwTqeTgoLElhAvxYEDB84J4J555hmeffZZ/uN//I/k5eUtek5dY0VERERERC7BPwP9R+ar5s68mpxwLrdmcdVc+eXgLYt7v7mlmAuE+PWJIX5+pI9/ae5nbCawpPftKPPyrsvsxhF1CunislKBnTdyXk6ZUvS13ou+KjU+B+yP3P6ZMSaeFqFJ6Jt8cXlpeTz7vvNXR601eWl5KRv7mmuuAeDw4cNJG7O0tJS77rqLvr4+7r//fr73ve/xuc99LmnjX8jzzz9PMBhk7969KxIQHjhw4JzHDh48yLPPPssdd9yhgE5ERERERORi/DPQ98biZa2DLWDCCQwaaQaxsHKu7DLITH1RB8C0L8gzrYP83yO9PN0ywLR/aUFjU3kON+8pU0iXJCsV2HUCDcBHgH9e4ns+EjmfTsmMLsCyrOuBv4zcHQA+vZLXXw6H5Ui4kcNGMDo6CtiNKJLtq1/9Kg8//DBf+9rXuO222/B6U5cfG2P4+te/DsD73ve+lF1HRERERERE4hAN5868Mh/QDbUmFs5ZDnt/ufIroOIK+1y2B9JWNvAam/HzVPMAPz/Sx6+OD+IPLu1rUkiXOisV2P1v4M+A91uW9Zox5q8u9mLLsv4T8AHsfe/+1wrML3rdXZHruYA54L3GmIE4h6u+xPNl2E04JAHhcJjvfve7ALzlLW9J+vhFRUXcfvvtfOMb3+C73/0uX/7yl2PPHTx4kLvvvpu77ror1qwiXiMjI9xxxx089dRTNDY28pnPfCbBmYuIiIiIiEjcgv7IstZX4MzLdjiXaEOIs8O5iivtcC4JnVrjMTA5x5NH+/nno33828lhgmGzpPftqczlpt1l/N7uMoV0KbRSgd1fAn+EHVLdY1nWB4AHsQOrAexgrhS4OvK6KyLv6wO+sRITtCxrK/AkkI/dFfb9xphfxTueMab7EteLd+hNa2EXV4DBwUGefvppmpubqa6uXhSmRfl8vvMu+wQ7jPvmN795yet+4Qtf4N577+Vb3/oWn/3sZ8nJyQHmK/qWu3T1gQce4IknnsAYw8TEBC0tLTz77LPMzs6yf/9+HnnkEbKz4/tH7wc/+AHPPfccAK+++ioA/+2//bfY3nzvec97eM973hPX2CIiIiIiIhtSKGhXyp15BXpetgO6/qMQ8sc/puWAosb5qrmKK1Y1nIvqGpnhn4/28c9H+3ixcxSzhIzOsmDflnxu2l3OO3aVUpWfmfqJysoEdsaYMcuybsReDluF3YTiWxd5iwV0AzcZY8ZSPT/LsiqAp4AK7PDw48aY/53q68rynN3FNS0tjdraWj7/+c9z5513UlRUdM57gsEgDz744HnH27Jly5ICu+LiYj796U/zzW9+k29/+9vcddddABw5cgSHw8Gtt966rK8j2hjD6XTi9Xqpqqri1ltv5ZZbbuGd73wnjgS6+Tz33HPnfL3PPPNM7HZtba0COxERERER2bzCYRhpj1TNRQK6vtchMBP/mGs0nIs6MTDFPx/t4/8e6eVIz8SS3uNyWPzWtkJu2l3G7+4spcSbnuJZytkss5Q4NVkXsywv8OfAx7Er2c5nFPgh8BfGmKX9TUpsTkXAs8DOyEN/Yoz5bytw3SoijSm6urqoqrpUU1lZa0pLS7n++ut59NFlNxEWERERERGRVDMGxrsiVXPRpa2vgW88/jFj4dyVC/ac271mwjmw90c/emaCnx/p4+dH+zgxMLWk96W5HLyloZibdpVxY1MpuZnuFM907eju7qa6OrazWfWlVk2uhJVaEguAMWYS+M+WZX0JuArYA0S7JowCbwAvGWMSqDtdOsuycrGr/qJh3RdXIqyT9a+trY2BgQHuvPPO1Z6KiIiIiIiIAEwNQM9LCwK6V2BmKLExC7ZB5d5IQLd3VRpCLEUobHjl9GgspOsenV3S+7LTXPzOjhJu2l3G9Q3FZKWtaEwkF5H0/xKWZV1ujHntYq8xxgSA30SOVWFZVibwj8DeyENfM8asyH55sv41NDSwktWpIiIiIiIisoBv0m4E0fOSXTnX87JdTZeI3Bq7ai4a0JVfARl5ic81ReYCIX59Yognj/bzi5Z+hqaWVvuUn+nmd3eWctPuMt60rYh0tzPFM5V4pCI6fdmyrC7sMOxx4JcrVTG3VJZlebC7wf525KG/McZ8ZRWnJHJe3/nOdxgbG7vk6+644w7y8vJSPh8REREREZEVF/TDwNFI9dwr9nmwBXsL+jhll9oVcxVX2gFd+RWQXZysGafM6LSfX7YM8OSxPn7VNsRsYGlda0tz0njHrjJu2l3G/toCXM74906XlZH0PewsywpHbkYHnsFu6PA48I/GmP6kXjAOlmX9FPjDyN1fAndw8e90vzGmLclz0B52ckm1tbV0dnZe8nWnTp2itrY29RMSERERERFJpYVNIXpeso/e1yHki3/MjPz5Ja3RgM5bbrc/XQe6RmZ48lg/T0Y6u4bCS8txagoy+b3dZbxjdxlXVOXhcKyPr3c1bJY97KqAdwHvBt4GZAF/APw+YCzLegk7vHv8UktnU+gPF9z+HeD1S7y+E6hN2WxELqCjo2O1pyAiIiIiIpI6k332ctZoOHfmZZhLoCmEJ9uulqu8cj6ky69dN+Ec2E0jjvRM8C/H+njyWD8tfZNLfm9DaTY37S7npl1lNJV7sdbR1y2LJT2wM8acAR4AHrAsKwO4ETvAexdQDlwN7APutiyrm/mls79Ya0tnRURERERERCRJfJN2I4hoONfzMkz0xD+ewwWlu+2Kucqr7KOoARzrb082fzDMoVPD/Muxfv7lWD+943NLep/Dgn21Bbx9Zym/u7OULYVrp1utJCal7T+MMbNEqukALMu6Crvy7l3YzR6qgT+OHDOWZa3I0lljjCJmERERERERkVQJBWGwGbpfhJ4XoTsJ+84VbJsP5iqvsju2utOTNuWVNjkX4JnWQf7lWD9Ptw4wORdc0vvS3Q7eUl/M7+4s5W1NpRRkeVI8U1kNK9qv1xjzEvAScNCyrArml87+Dmtz6ayIiIiIiIiIXMp4TySYezGytPUVCMzEP15WCVTtm6+eq7jS3otunesbn+Nfmu0qun87OUQgtLQAsyDLw41NJfzuzjKu215Ehmf9VRHK8iS96URck7CsdOyls9Hqu/LIU9HJ9WCHd/cbY95Y+Rkmn5pOiIiIiIiIyLrkm4osbV0Q0E32xj+eJ3u+GUS0ei6ncl3tO3chxhja+qdi+9G93r30/flqCzN5+64yfndnKXtr8nGqaUTKbJamE8tmjJkDnogc0aWz0eq7vdiNLD4F9AMbIrATERERERERWfPCIXsp66Klrc1gwvGN53BB6S6o3Ldg37n6dbnv3IVE96P7RfMAv2jpp2tkdsnvvaI6j9/dWcrbd5ayvSRbTSM2saQHdpZl/X7k5i+MMdPxjLFg6ezdkaWz7wZuBhKopxURERERERGRi5roPXdpq38q/vHyttihXNU+O6QrvwzcGcmb7xoxPOXj6dZBftHcz78eH2LKt7T96DxOB2/aXsjv7izlxqZSSnPW7558klypqLB7DAgDlwHHEh0s0nX27yKHiIiIiIiIiCRDYBZ6X4fuw5HjRZhIYCVgWq69rDUazlVeBdnFyZvvGmKMobV/0q6ia+7nla4xlrrjmDfdxdt22PvRXd9YTHbamlj8KGtMqv5WqGZTREREREREZK0wBkZP2aFcNKDrewPCS6sEO8fCpa3RgK5wOzgcyZ33GjIXCPGb9mF+2TLAL5oH6Blb+lLXitz02H50+7cW4HZu3D+n1WaMwczOEp6eJjw9TShyto+ZBbfnj96+vtWe9jkU44qIiIiIiIhsNHMTcObl+cq57sMwMxz/eHk1C8K5q6D88g25tPVsg5M+nm4Z4Knmfp47McSMP7Sk91kWXF6Vx41NJfzOjlKayr3aj+4Swn4/4akpwlNThCYnCU9NE56eIjw5SWhqivDkFOHpKfv2RcK38MwMhJe3x+JUIJCiryp+Cuxkzevo6GDr1q2LHrMsi+LiYrZu3crHPvYxPv7xj+N2uxe9pra2lqGhIaamLr7fwvnGd7vdlJWVccMNN/DlL3+ZxsbGhL+OAwcO8OCDD8buu1wuvF4vlZWVXHXVVdxyyy383u/9Hk5nfJut9vT08A//8A/80z/9Ey0tLfT19VFQUMBv//Zv82d/9mdcc801F51bbW0tBw8ejOvaIiIiIiKyisIhGGxdvLR1sAVY4hrNs6XlRDq2LgjoskuSOuW1yhjDsd4Jftk8wFMtA7zWNbbk92Z5nLy5vpjfaSrhrY0lFHvTUjfRNcSEw4RnZghPTNhB2+TkfOA2FQnbpqYJT07agdvk1HwwNzV/2/j9q/2lrCkK7GTdqK+v54Mf/CAA4XCYvr4+Hn/8cT71qU/x5JNP8tOf/jRp409MTPD888/z4x//mMcee4xDhw7R1NSU8NcA8IlPfIKKigrC4TATExM0Nzfz6KOP8uCDD7J//34eeeQRamtrlz3u9773Pb7xjW+wbds23v72t1NcXMzx48d57LHHeOyxx/jJT37C+973vtjrT58+TU1NzXnHuthzIiIiIiKyyqYG5xtDdB+GnpfBPxnfWJYDSnbawVzV1fZRWL+hl7aebS4Q4t9ODvNUcz+/bBmgd3xuye+tzMvgxqYS3tZUyjV1BaS51l+3WxMIRCrYJglNTBKeXBC8TSwI4CYm7NedHcxNTrLkDfxkyRTYybrR0NBwTgXY2NgYe/bs4Wc/+xnt7e3U1dUldfzbb7+d++67j3vuuYeHHnoo7rEX+uQnP8m+ffsWPTY8PMwdd9zBww8/zE033cSLL75Idnb2ssbdv38/zzzzDNdff/2ix//1X/+Vt73tbXz605/mPe95D2lpaXR2drJnzx4+85nP8Od//uex146MjPBnf/ZnPP7445w8efKic7Asi49+9KP86Ec/WtY8RURERERkGUIB6D8CXdHquRdgtCP+8bKKI8FcJKCruBLSvEmb7nrRPzEX24vu1yeGmA0sfanr3pp8fmdHCTc2ldJQmr0mlrqG5+YIjU8QnhgnNDFBaHyC0MS4Ha6NTxCaiDwXuW0/Z1e/mZmZ1Z5+ajmdOLKyIkcmjqwsnNH7mfbZFwjAf/nqas90EQV2sq7l5eWxf/9+uru7GRoaSiiwO58DBw5w33338dJLLyV13LMVFhby0EMP0dfXx1NPPcW9997LF7/4xWWN8Yd/+IfnffzNb34zb33rW3nyySd544032LdvH1u2bOHIkSPceeed7N69m9zcXE6ePMkDDzzALbfcwrFjx5YdGIqIiIiISBJMDUDXC3Yw1/2iXT0XXHpzg0UcbnuvuVhAtw/yttip0yYTDIV5tWuMp1sHeLplkGO9E0t+b3aai7c0FPG2HaXc0FhMYXZqlroav98O08bGCI2P28fY+DnBW2hinHDs9gThiYmNt5zU6cSZnY0jenizcWYtuL8gfFsUwJ3nsNLSLhmqBru7FdiJJNP4+DiHDx8mKysrKfvMXcjZ++OlgmVZfOlLX+Kpp57i0UcfXXZgdzHR+btc89/yNTU1/I//8T/4u7/7Oz71qU/hcrl47LHHuPnmm5N2XRERERERuYhQwO7U2n14PqQbOx3/eLk1i5e2lu0Bd3ry5rvODE35+FXbIE+3DvKrtkHGZ5feWKCmIJO3NZXwth12V1ePa+lLhGPB2/j4fPg2tuD2+Jh9f9y+H448F94IlW6WZQdlOV47YPN6cWRnRcI3byRwy8K58LY3cjsrG6fXDuSs9PQ1Ubm4mhTYrWMmHCY0Nrba01gSZ14eVoJ7ILS1tcWWrIbDYQYGBnj88ceZnJzkgQceIDc3NwkzXeyHP/whANddd13Sxz6fN73pTbhcLl577TWCweCigC1ep0+f5qmnnqK8vJw9e/YsevxLX/oSzz//PFdccQVZWVl84hOf4L3vfS9//ud/TmFhYcLXFhERERGRBSb7IsFcZHnrmVcguPT90hZxZ0LF3gUB3T7wliV3vutMOGx4vWecp1sGeKZ1gNd7xpe8tZrDgn1bCvidphJubCphW7G94sjMzBDs62V2dNQO3MZGCY1GzmNjBEdHCY+PExwbs4O38XHC09Mp/CpTzO3G6fXaIZrXizPHawdtOV6c3hy70s2bYz8efV1Ojh3I5eTYFW2baP/DVEplYPcZy7IGkjGQMeYvkjHORhMaG+P4m357taexJPXP/xpXQUFCYxw/fpy77777nMc//OEPc+211yY0NiwOBCcnJ/n1r3/NoUOHqK+v5ytf+UrC4y9FWloahYWF9Pf3MzIyQklJYp2YAoEAf/RHf4TP5+Mb3/hGrANtdA+7T3/60xw5coTPfOYz1NbW8tnPfpY/+7M/Y+fOnZfcw05ERERERC4i6I9Uz0UCuq7DMJ5A9VzBNqjePx/OlewCp2pwxmb8/Or4EM+0DPBs2yDD0xdYGmoMmUEfOf7p2FFifFyRA02ZYaodAVzNE4T+bYzQ6CgnxuyzCSy9Km+tcGRn48zJwZGbizMnJ3I7B2dO5H5ujh2y5eTEgjk7nMtZ0vJRWRmp/O7+dBLHUmAn3HzzzTzxxBOx+wMDA/ziF7/gT//0T/n5z3/OoUOHEtrD7nyB4Pbt23nuuecSDs5WQzgc5sCBA/zqV7/ik5/8JH/0R38Uey66h93ZnWALCwv5+7//e06fPh0L65555hne+ta3nvcaDz74IA8++OCix66//nqeeeaZ5H4xIiIiIiJrXbR6ruuQvfdc76vxV895sqFyL1Ttt0O6yn2QpRUwAMYYjvVO8ExzHy+8eorO9h68c1Pk+qe51mefc31T5PpnImf7vtc/g9tcuLFEnLsEpowjKwtnbi6OvNzzBG25OHMjQdyi23YAZyVhpZasvlT9V0xmHKvewHJeJSUlfOADH2BmZobbbruNe+65h+9///txj7cwEOzv7+f+++/n4MGD3HLLLfzyl79MyvLUS/H5fAwPD+N0OilIoCIxHA7z8Y9/nJ/85Cd89KMf5W//9m/Pec3ZYd2FnqutreWuu+465zV33303l19+Oe95z3sWPV5bWxv3vEVERERE1oWz957reiGx6rnCertyrvpqO6QraQKHM3nzXQfCfj+hkRFCIyMER0YJjY4SGh0hODLC7OAwg119TPYPEh4dJXt2ihsCs/zOOogLHFlZOPPycObm4szLxZmXZ1e+5ebizM075zlnpCrOWoF91GVtS0UCcf5SHJEUueaaawA4fPhw0sYsLS3lrrvuoq+vj/vvv5/vfe97fO5zn0va+Bfy/PPPEwwG2bt3b9wBYTgc5mMf+xgPPfQQH/rQh/jv//2/47jEHgI/+tGPLvhcbW1tbKnwQnfffTdXXHHFeZ8TEREREdlQpocWVM8dTqxzq8cLVVfZwVx0eWtmYtsHrUUmHLYbLIyMEBwenj8PDxMcHiE0EjkPDxMcGSE8OXnR8bIix6pxu3HlRQK2/PzF5zwFb5J8SQ/sjDHPJntMOT9nXh71z/96taexJM68vJSNPTo6CthBVbJ99atf5eGHH+ZrX/sat912G16vN+nXiDLG8PWvfx2A973vfXGNsTCse//738+DDz54ybBOREREREQWCIdg4JgdznUdts+jp+Ifr6ghsrQ1Uj1X3Lhuq+fCc3OxgM0O30YIjgwTGrIfiz4XGh4mODoKweBqT/m8LLfbDtsWBW+5OPPzcZ0dxuXn48zLx5GVqb3dZEVpYfM6ZjkcCTdyWO/C4TDf/e53AXjLW96S9PGLioq4/fbb+cY3vsF3v/tdvvzlL8eeO3jwIHfffTd33XVXwlVmIyMj3HHHHTz11FM0Njbymc98ZtljRJfBPvTQQ7z3ve/l4YcfjjWZEBERERGRC5gZsfec645U0PW8DP6p+MZKy4HKqyLNIfbblXQZ+cmdb5KF/X5CQ0MEh4YIDg0THB6K3B+2HxseIjQ4RHB4mPBUnH8uKebw5uAqyMdZUICzoMC+nV+AsyASwBUU2Pfz8nDl52FlKnyTtU+BnawbC7u4AgwODvL000/T3NxMdXX1ojAtyufzceDAgfOOV1RUxDe/+c1LXvcLX/gC9957L9/61rf47Gc/S05ODjBf0bfcpasPPPAATzzxBMYYJiYmaGlp4dlnn2V2dpb9+/fzyCOPxNWd9S/+4i948MEHyc7OpqGhga9+9avnvObAgQPaY05ERERENq9wGIZa56vnul+Aobb4xyusn+/cWn3NmqmeM36/XQU3NExwaNCueIuEbsGhQbsibigSwk1MrPZ0FwlhMenJZDwtm3FPln1Oy2Iq3Ut+RQm12yrZvXMLlbXluAoKcOXna9mpbEgK7GTdOLuLa1paGrW1tXz+85/nzjvvpKio6Jz3BIPBc7qYRm3ZsmVJgV1xcTGf/vSn+eY3v8m3v/3tWAOGI0eO4HA4uPXWW5f1dUQbYzidTrxeL1VVVdx6663ccsstvPOd74x7CWtHRwcAU1NTfO1rXzvva2644QYFdiIiIiKyefgm7eq5rhciFXSHwTce31juLLtza/U18yHdCu49Z4whPD1NcGCQ4GDkGFpwe3DQrowbGCQ0HufXmCKB9EzG0rIZcNrnsTRv5Gwf4wtuT7kzMJb9magiN5237ijhrY0l/Na2QrLSFGHI5mEZk7yuKpZlXbjtZAKMMQm021mbLMuqAroAurq6qKqqWuUZyXKVlpZy/fXX8+ijj672VERERERExBh7r7loc4iuwzBwFEyce13nb11cPVeyE5zJD4xMOGw3ZIgFb0MLArmhRYGcmZtL+vXj4nbjKijAWViAq6AQV2EBzsIiXIUFjHmyOTLr5NCI4V+HQvRZGQSW+OfmcTq4ems+b6kv5q07SqgvydbSVVkR3d3dVFdXR+9WG2O6V3M+kPwKuwR24rwggyoBZY1pa2tjYGCAO++8c7WnIiIiIiKyOQVm4cyrkcq5SEg3PRjfWK50qNhrB3TRkC67JKHpmVCI0MgIgYEBggMDdmVc7PbAfBA3MgKhUELXSgq3G1dhoX0UFeEsKsRVVGzfLy7CGXncVViIIycnFqRN+4L8pn2YX7UN8mzbIB3DM/NjLuGTfF1RFm9pKOYtDUVcW1dIpkcf/0Ug+UGYom/ZFBoaGkhmdaqIiIiIiFzCxJlIMBcJ53pfg3AgvrFyq+cbQ1Tvh7I94FzaPmjGGEJjY4vDt4GBSDC3IJQbGlr9IM7lsivhiqJhW5F9LirEGb1fHAnhcnOXVM1mjKGlb5Jn2wb5VdsgL3aM4g8tvYoxO83Fm7YV8paGYq5vKKa6IDORr1Bkw0p2YPexSzz/GeBqIAA8CbwA9EeeK40893bADbwI3Jfk+YmsK9/5zncYGxu75OvuuOMO8vLyUj4fEREREZEVEQpA/5EFy1tfgPGu+MZyuKHiivlwrno/5FSc/7JT0wQH+gn29xPo7z+3Ki5SGWcCcQaFSeLweu3grbjYPoqKcJUsuF1cjLOoCGduLlace2QvNDzl49cn7Sq6X7UNMjDpW9b7d1fm8JZ6O6DbuyUftzPxOYlsdEndw+6iF7KsvwcOAP8C/AdjTM8FXlcJfB94B/BDY8xtKzLBFaY97GQpamtr6ezsvOTrTp06pWYSIiIiIrJ+zYxA9+H5cK7nJQjMXPp955NVPN8YovoaKL8C4/TYy1P77TAuFsj19RMc6CfQP0Cwv5/w1FRyv67lsCx72WlxsV31VlxsL0mNhnKxx4pwZGSkdCpzgRCHO0Z47vgQ/3p8iGO9y+skW5jliS1zvW57McXetBTNVCQ5NsMedudlWdYt2NV3h4GbjTEXrAs2xvRYlvVu4N+Aj1mW9aQxRrv6y6YU7fwqIiIiIrJhhMMwfAK6fjMf0A21xTeW5SBcsJNgzh6CaXUErBKC02GCp/oJ/KaDYP8hO5wbHITVqopzOiMVcCWRww7g3CUlsUo4V3ExroICLNfq7N8WDhuO9U7w3Ikhnjs+xOGOEXzBpS9zdTks9m7J5/rIMted5Tk4HNoxSyQRK/WvwR9jN4/464uFdVHGmJBlWd8C/l/gk4ACOxERERERkfXIP2NXzEXDue4XYHZ0SW8NhyA44yQw4yQ46yTgzyJolRIIZBOYhuDIJKHREeDZyLGCohVxJcW4i0sWBHKRUK6kBHdJCc6CAiync2XntgRnxmbtCroTQzx/Yojhaf+y3l+Vn8H1DcW8paGYN20rxJu+tD0ARWRpViqwuyxyXs6vTaKv3ZPkuYiIiIiIiEiqjHfPh3Ndh6DvDQgHz3lZOIQdws04F4dyM47Y/ZDvfEHXaORIHUdurl0BV1p6TgAXC+UKC7Hc6yekmpwL8Jv2EZ47Psi/nhiifXB6We/P9Di5ZmtBLKTbWpS1pCYVIhKflQrsvJHzcvpiR1/rveirREREREREZHWEAnYgF2sOcQgmejDhSBg37SQw4yYwm05wxrEonDt/GJdiDoe9/LSsFHdJqR3IlZbgLivDVVKKu9QO6VK9R9xKCITCvNY1Flvm+krXGKHw0vewd1hwWVUeb64v4rrtRVxZk4/HpWYRIitlpQK7TqAB+Ajwz0t8z0ci59MpmZGIiIiIiIgsz8wIpusFQi3/SrD5EIFTrQQmgwRmXHYQN+0kMFNKcM4BZmWrr6yMDNylC0K40rIFt0txlZbhKipck8tTk8EYQ/vQdKxRxG/ah5nynVvZeDFbCjO5bnsRb64v4rfqisjNXD8VhCIbzUoFdv8b+DPg/ZZlvWaM+auLvdiyrP8EfAB737v/tQLzExERERERESDs8xHs7SXQ20vg+GsE2l4m0HmSYF8/gfE5AtNOTChaaZW9InNyZGXhKi+zQ7jI2V1ehqu0DHeZHdI5vN5Nt0RzaMrH8yeHee74IM8dH+LM+Nyy3p+b4ea3txdy3fZi3lxfRHVBZopmKiLLtVKB3V8CfwSUAfdYlvUB4EHsrrED2MFcKXB15HVXRN7XB3xjheYoIiIiIiKyoRljCI2NEThzhsCZMwQj58CZXgJnegj0dBEam7zICMmvuLIyM3GXldnLUqPn8rJFjzm92ikJ7H3oDrWP8OuTQ/zbyWFa+i723+pcHqeDq7bkc129XUW3qyIXp7q5iqxJKxLYGWPGLMu6EXs5bBV2E4pvXeQtFtAN3GSMGUv9DEVERERERNY/Ew4THByyw7czZwj0nJm/HQnmzMzMis3HSk+3g7eKcrsaLloVVz4fzm3GyrilmguEeKlzlOdPDvHrE8O80TO+rH3oAHaUebluexHX1Rexf2sBmZ6VqtsRkUSs2HeqMabZsqxdwJ8DHwfyL/DSUeCHwF8YYyZWan4iIiIiIiJrnQkECPT1RYK4c49gby8mEFiZyVhAfjaUlWGVl+EoK4kcpTjLy3CWleLMy8NhOXA6nFhYOCwHDsuBsRyELAdhLJxhPw4cWNb885tVMBTm9Z5xnj8xxPMnh3mxcxR/MLysMUq8abEKut/eXkSJNz1FsxWRVFrRaN0YMwn8Z8uyvgRcBewBCiJPjwJvAC8ZY/wrOS8REREREZFEGGPwhXzMBeeYC80tvh30XfQxf8hPMBwkEA4Q8vtxD4+TMTBJxtAkmYNTZA/NkD08g3dkDu+4H2t5BVZxm06DoRwYzrEYyoGhyDl6f8QLIecc0BE5IkYix9H4r+2wHDhwxMI+l8OF2+GOHR6nZ/6+86zzRV7ncXhir4uO6XF6SHelk+HMIN2Vbh/OdDJc8/czXBm4HclfDhwOG1r7J3n+5DDPnxji0KmRZTeKyPI42b+1gOvq7X3o6kuyVbEosgGsSi2sMSYA/CZyiIiIiIiIpJwxBn/Yz3RgmunANDOBmdjt6eDi+9HbM8GZWMg2F4yEbgsCt+hjvpBvSXNwhA2FE1A8bigeh5IxQ8n4/P3CSXCsQCAXtmAkG4ZyYTDHss+5FsNeGMq1GPLCbPrqhT5hEyZM2N7tfHkFZinjslyLAr1okHf2/QxXRux+9LFMVybZnmyyXFlMzTppORPgja45Xjo1y8gUwNKrCj1OB3u35PGmbUX89vZCLqvKw+3cvFWJIhuVFq+LiIiIiMiaNxecY8I/waR/kgn/BBO+idj9WOgWCdhigdt5QrigWV710nJZYUPBFJSMLQ7lisehZNwO65wrEMgFnHZ13GCuddbZvm1Xx6kKazmCJshUYIqpwFTyBq2GbGNB2IMJp2PCaRCyz9H7VjiN4qxc6gqLaCotZmdpCfkZQbI9U2S5DYOzc3g9XrLdqqwT2UgU2ImIiIiISMqFTZipwJQduPkWBG+R0G3cN744kIvejrzWH14ju+YYQ/YslI7ZAVzJmB3IlUbORRPgWoGKsBnPudVxgzl2ddxgLoxngVF4sy5YlgGnD8t54SrNMeDlKfvg5Plf47Sc5HhyyE3LJScth1zP/Dk3zT5iz0fO0dsuh6IBkbVG35UiIiIiIrIsoXCIcf84Y3NjjPpGY+fRudFF96PnSf8kU4EpwmaNrG28BHfAXqZaMhYJ5MbnA7mSMchcgewwkO5kLteJLzuAP8NHwBsm6A0Tzg5jskI4PAY3UGYMVQbcGFzG4DbgmjC4xw0uhxtX0Q6cFZfjqLgSq/xKHFnFWJYVawARvW1ZVqzxw6Lb0ecsx7mvi9wHe7lxdBlr2NhH9LGQCdm3FzwXfX7hc7HbC14TJkwoHCIYDuIP+wmEAgTCC47Q+W/7Q/4lvS4QDthLmiNLnGeDs8wGZ5kLzmFYoc0CkyRkQvb3oW902e/NdmfHwruzQ77o7cKMQgrSC8hPz6cgvYAMV0YKvgoRiVJgJyIiIiKyiRljmApMzYdsvjE7eIuGb5H7scd9o0z4JtZdmLGQZQwFk3aVXPWkh/IJJ2XjFkWjYQpG/GRPpHbZLICVmYmnshJ3eRnuPBfutGncphePrw23ewyH23DBArlA5DhbZhHUXAvV+6H6Gii/Atwr0yHUsiyclhMnzhW5XqpF9zucC87FArzonoVD05O83jPIsb5h2gaH6ZucACsAVgDLEQCHH8vygyOAZUXuO3xYDh845yK3V6iT7xJFl/r20LPk92S4MihIL1gU4p19LHzc4/Sk8CsQ2XgU2ImIiIiIbDDGGCYDkwzNDjE8O8zw7LB9e2449lj0POIbIRhOfUCVTJmuTHLScsjx5MT27sp0Z5LlziLTZZ+9YQ+5Iz5yBqbJHJgkrW8Md98wjjMDmN4BCEQDk9mUzNFKT8ddVYm7stIO5iorcVdW2eFcuAfn6BtY3S9A33NgQvNvXPInNAtKmubDueproKCOC6d8shyWZZHmTCPNmQbhTI70jPBv7TP8pn2SY70TGJMGVESOS/OmubimrpA3bSvkt7cXsbU4jdngrB2U+aeYDkwzFVhw9p91PzC96HXRx6YD0yn9c7iY2eAsPVM99EwtLeTLdmdfMNwrzCikKKOI4oxiSjJLyHRnpnj2ImufAjsRERERkXXAGMNMcGZx4LYggDv7sUB4bVXwLOS0nHg93ljgFjsvCOGiS/Ny3PZ54etcDpe9nHJkhEBXF/6uLvynTxM43YW/+ziB06cJDg6e99pJqwt0OnGXl+OuqsJTXWWHcdVVeKqqcFdV4SwowAoHof8InD4EXc/BsRdgoju+67mzoOqqSDh3LVTtg4y8ZH01ssDEXIDDp0b4Tfsw/9Y+zNEzE5hl/sVJdzu4uraAayMh3Z7KXFxndXL1OD3kpuUmNNewCTMdmI7tAznuH7fPkT0hJ3wTix6L3p70TzIbTE1YfSHRoPH05OlLvjbTlUlxZjHFGfZRlGmHeQsfK84sVqMN2dAU2ImIiIiIrLKZwAz9M/0MzAwwMDMQuz04M8jg7CBDs0OMzI2s+Afspch2Z5OXlkd+en7snJ+WT156nn1Oy4sFcdEQLtOVuaQP2SYQINDbi7+1i0DXEfynu+iLBHSB06cJz8yk9GtzFhTYgVwkhIsFctXVuMvKsFxnfZyaHYWuw/Dq/4GuQ9DzEgTinGNOFdRcM189V7obnPr4lgqTcwFe7Bjl39qH+U37MEd6xgkvM6BLcznYV5vPb9UVcm1dIZdV5eFxOS79xgQ5LAdejxevx0tF9tKq/aJ8IZ8d6EWCvLPDvQn/ROz2qG+UkbkRRuZWpiJ3JjhD50QnnROdF31dujOdoowiSjJL7Aq9zPkwryijiJKMEoozi8nx5CjYk3VH/+KLiIiIiKRIKBxiaHaIwdnBRYHcwlBuYGZgVZe1LeRxeOzALRq+pUVuR8O3BSFcQXoBeWl5uJ3uhK4Z9vnsKrnTp/F3nsZ/upNA52k7lDtzBkKhSw8SJys9fUF1XDWeqko7mKuybzuysi78ZmNg6IQdzHX9BrpegMGWOCfihPLLIuFcZIlrblV8Y8klTfmCHO6wK+h+0z7CkZ5xQstM6DwuB1fV5PNb2+yA7vLqXNJc62v/vjRnmh1wZRYv+T3RPS+j4V30GJ2LBHqzI4z45h8bnRslZFL3PTwXmqN7qpvuqYtXrqY50yjNLKUsq4yyrLLz3laoJ2uNAjsRERERkTjMBGbom+mjfzpSDTc7GLsdPYbmhla9M6rX7aUwozC2R1RheuS84H40oMtwZaTkA2t4etpethoN5E5HArrTpwn29bHs9YbL4CwuwlNdg6e62g7laqrtQK6mGmdh4dK/3sAsnHklEtC9YJ9nhuObVHouVO2PVNBdC5V7wXORcFASMj4T4MXOEV44NcJvTsUf0O2tyePaukJ+q66Qy6vzSHevr4AuGSzLilX0bcnZcsnXh02YCd+EHeLNnhXuLTiGZocYmh1iKjCVknn7Qj5OT56+6HLcDFeGHeJllsXCvLPva289WUkrEthZlrXXGPPyMt+zzxjzYqrmJCIiIiJyIWETZnh2mN7pXnqne+mb7uPM1JnY7d7pXsZ8Y6s2v0xXZixwK8oooiC9YD6ES18QxmUU2pvmr4DQxAT+ztMEuk4vqJazA7rQ4FDqLux246mowF1TY1fLVdfYoVx1NZ6qKhyZcX7AnuyzQ7nTh+xz72sQ776Ahdvnl7ZWXwNFDeBI/XLJzWpoysfhUyMcihwtfcvfg87jdHBFTV5sieuVNZszoEuUw3KQl55HXnoedbl1l3z9TGAmVpUc3RJg4e2hmSEGZgeY9E8mfa6zwVlOjZ/i1PipC77G6/GeN9QrzyqnIruC0sxSXA7VRUlypPxvkmVZHwR+aFnW/wD+gzGX/qfSsqxvAP/Jsqw7jDHfS/UcRURERGRzmQnMxIK3haFc73QvvVO99M30rUrnVK/HS2lmKSWZJbEjusF6tEquML1w1ao8QuPj+Ds77aOjMxbIBTpPExobS9l1HV7v4gq56mo8NTW4q6pxl5dhORMMUsIh6D+6uHpu7OJ7Z12QKx0q9i7o3rofsooSm59cVO/4LIfa7XDuhVPDnBxc/hJzt9Piyup8rq0r4NptheytyVdAtwoy3ZnUuGuoyam56OvmgnPnBnsL9vwcmBlgaHYo6b9YmfRPMumf5Pjo8fM+77SclGaWUumtpCKrgkpvJZXZ80dxRjFOh/5eydKsRPR7M+AGPgqkWZb1R8ZceF2AZVnfBv4UsIB3WZZ171JCPhERERERsPdYGvWN0jPZQ890D71T54Zy477xFZ2Ty3JRnFkcC+HODuWiR4YrY0XndT6hqWn8nR0EFgZzkduh0dGUXddZVISnpsY+ttQsqpRz5uUld6nu3Dh0H54P57pfBH+cS/GyS+1gruZa+1x2Gbg8yZurLGKM4fTIzHxA1zFM18jym7G4nRaXV+XF9qDbW5NPhkdBynqR7kqnyltFlffiez36Q/5YgNc33WcfM33zt6f7GJ6Lc2n7eYRMiDPTZzgzfea8z7scLsqzyheFeBXZFbHbRRlF2kdPYlYisPsjIAR8GHg/dmj3fmPMOb+ytCzrPuCPscO6fwL+vcI6ERERETnbdGCa7slueqZ65o/JHrqnujkzdYaZYGq7hy6U48k5bwgXvV+cWUxBegEOa+0sgQzPztrVcdEwrqNjPpQbSt3yVVdZ2XwgV1ODp2aLfbuqGmd2ivZwMwZG2ufDua4XYOAYEMfHDMsBJbsWdG/dD3lbQB+wU8YYw/GBqUj1nF1B1z/hW/Y4HpeDK6vzuGZrAfu3FrJ3Sx6ZHi1d3Og8Tg8V2RUX7aDrD/npn+mPBXgLb0cDvmT9kicYDtI12UXXZNd5n09zptmBnreSyqxKu1Ivu4LKrEpqcmrITctNyjxkfUj5v1DGmLBlWR8FfMB/AP4d8L8sy/r3xhh/9HWWZf0A+Bh2WPcY8D5jTJybRIiIiIjIeuYP+emd7o2Fct1T3XbFXCScW6n941wOF2WZZZRnl1Oetfgoy7b3MVqrm5CH/X67+2pHR+SYr5QL9ven5qIOB+6KCnu56pb5QC66nNWRnp6a6y4UmIPeVxcvb50ejG8sjxeqr57fe67yKkjPSep0ZbFQ2NDcOxFb3nq4Y5SRaf+l33iWTI+Tq7bkc83WAq6pK+SyqvXXxVVWhsfpodpbTbW3+oKvmQ3OXjDM65/uT9ovinwhHx0THXRMdJz3+RxPDjXeGqpzqqnx2kuHa7w1VHmrKExfRhMdWReslSxgsyzrvwGfxv511i+AP8AO8h4EPogd1j0KfMiYFPZ+XgMsy6oCugC6urqoqlLbdhEREdk8jDEMzg5yeuL0oiq5aEA3MDOAiacCapny0/JjG4ZHQ7nY/axyCjMK11Rl3NlMOEywrw9/Rwe+jg78pzpiAV2gpwfCKehQ63TirqzEs2XL/FFTbVfMVVZieVZ4OehkfyScixxnXo2/OUT+1vnKueproKQJtN9USvmCId7oHueFjhEOnxrhxY5RJn3L3z8yJ93F/q0FXLO1kP1bC9hVkYPLuXa/d2VjMcYw7htfXPUdOc5MneHM1BnmQnMpnUOmK5OanBqqvfNhXvR2cWbxmv5/2VrQ3d1NdXUstK02xnSv5nxghQM7AMuy/hq4Azu0ew4YAP595OmHgQMX2+Nuo1BgJyIiIhtdKByib6aPrskuTk+cjp1PT56me7I75R9enJaTsqwyKrIrYgFcRXZFLJAryypbE3vGLUVobMwO5RYEctFlrGYuBX+OloW7vBxP7RY8tbV4tmzBHQ3nViOUiwqH7OWsC7u3xtscwumBiivnw7mq/eAtTe585RzjMwFeOj3C4Y5RXuwY4bXucfzB5X/8K8r2LAroGku9OByqLpK1yRjD8NxwLMBbuJXDmWk70AvE+4uGJUh32nv+1XgjIV7O/Lkss0yNMFBgN39Ry/o68EUWbxzxQ+ATm2XPOgV2IiIishEEwgHOTJ1ZHMpNno5VzqXyAwhAcUaxvVl3pBNfVXZV7H5pZikux/rZoyo8N4e/8/R8GHfqVOx2qjqwusrKFlfK1dpnd3U1jrS0lFxzWWbH7IYQ3UloDpFVPL+0tfoaKL8c3CuwRHeT6xmb5cWOEQ532NVzrf2TxPOJryI3nWvq7HBu/9YC6oqytPxPNoywCTM4M3hOZV70dt90H6EULUJ0OVxUZVdRm1NLbW7tonNBesGm+T5TYBe9qGWlAUeAOuxlsENAvTFmZdt1rSIFdiIiIrJe+EI+uie7FwVy0YCud7o3ZR8iwN6vpzK7kipv1aKuepXeSiqyKkh3ra/AxRhDsL8ff3s7vlOn7CWs7e32EtbeXuJKMi7BWVQUC+I8W2ojwVwtnppqHBlrqMLQGBg+uWB56wsw2EJczSGwoHTXfPVc9X57uesm+eC5WsJhQ9vAJIc7RiPLW0c4Mx5fBejWoiz21xbEArqq/IxNExyInC0QDtA71Rv7hVi0cUW0Yj1Vvxzzerxszd1KbU5t7FybU0tNTg0e58bqhr0WA7sV/5WjZVkZwP9hPqwDKAT+xbKsdxhjUtcrXkRERETOKxQOcWb6DB3jHXROdMY2ve6c6KR/uj9l+8mlOdPsqjjvfBi38L7X403JdVMtPDsbq5LztZ+yq+VOncLX0YGZSX4HW0dmJp6tW+0grrZ2we0tOLOzk369pPDPwJmXI40hIhV0syPxjeXxQtW++XCuah+kq5tiqs0FQrzePR6pnhvhpc5RJuaWv/+cZUFjqZerFwR0pTnrK4wXSSW3w203mMipgcrFz4XCIfpn+s8b5nVNdCW0/cSkf5LXB1/n9cHXFz3usBxUZFXYIV6kGi8a6BVlFClcT5KVbjqRBfwj8BbsX5X9DXAa+OvI/deB3zXGpK6X/BqhCjsRERFZacYYRn2jdiA3bgdy0YDu9OTplP2GPsudtWjfnGhHu/W+EXasWu7UKXzt7bFqOV/HKYJnepN/QZcLT3X1glCuNnbbVVy89j8gjXcv7tza9waElx/uAJC3BWquXdAcYqeaQ6yAsRk/L3WOxvafe717HH9o+fvPeVwOrqjO4+rafPbVFrC3Jp/cDHcKZiyyuS1s8LRwy4ro7enAdNKvme3OZkvOlvmKvAXLbNOca2CrhQvY1BV2lmV5gZ8DvxV56C+NMV+OPOcD7gUuA562LOtGY0yKes2LiIiIbGyzwVlOT5yOVcotDOgm/BMpuWZuWu65m1lH7q/3PXDCc3N2tVx0GWu0Yq6jg3AKquVcpaXnBHJptbW4q6qwXOtkT75QAPpenw/nul6AiZ74xlJziFVhjKF7dJYXO+cbRLT1x7d/YF6mm31b7HDu6tp8dlfmkuZSwCqSapZlUZJZQklmCfvK9i16LvpLvGgzqOjPCafGT9E50Rn3L/GmAlMcHT7K0eGjix53WA6qsqvYlreNbXnbqMutY1veNrbmbl03DaBW2opU2FmWlQc8CUT/hnzFGPP1s17zceAB7GWybcDbjDFnUj65VaIKOxEREUlE2ITpm+7j1PipRZVyHRMd9E6noLoLKEwvPCeMi97PTVv/yw+Do6N2KHfyJP72U/ja7XOgpyfpe8tZmZmkRZeu1tnLV9O2bsWzZQuOrKykXmtFTA1GGkNEjjOvQHA2vrGySxc0h9hvN4dwrd2qjI3CFwxxpGeClztHealzlJdOjzI46YtrrOqCDK7eUhAL6LYVZ6uDq8g6snCbjOjPGNHzwOxAUq9lYVGZXWmHeHl1bMudD/Qy3ZlJvdbFrMUKu5QHdpZlFQJPAZdHHvqCMebbF3jtB4EHAQfQDvyOMaYrpRNcJQrsREREZCkCoQCnJ0/TPt7OqfFTtI+30z7WTsdEB7PxBiIX4fV42ZqzlS05W6jNrWVLzha25Gyh2ltNlnsdBklnMeEwgTNn8J88ae8t195uL2dtbyc0mvytlN0VFXYoFwnm0iK3XaWl67fqMBSEgWOLA7rRU/GNZTmhbLddNRcN6PJq1BxiBQxO+nj59Cgvd47yYucob8S5vNWyoKksJ7a8dV9tPuW5qpYR2aim/FN0TnRyauLUOdtrJLJf3vlUZFUsCvGiQV62J/l7s27WwO5Z4M3Ye9T9iTHmby/x+n8P/AR7uW4LsNusRivbFFNgJyIiIgvNBGbmA7lIKNc+3k73ZDdBE+c+Xxfgcrio8dZQm1PLltwtiwK6/LT89RskLbBoGWv7KfztJ2PNH4wvvqqhC4lVy9XV4dkaqZSrq7Or5dZSF9Z4zYxA94uRgO4Q9LwM/viWRpKeF1naGgnoKvZC2hptirGBhMKGtv5JXuq0A7qXTo/SORzfcu40l4Mra/K4utauoLuyJo+cdO0/J7LZRSv/O8Y7Fod5Ex30Tfcl9VqlmaWx8G573vZYdV6OJyfuMTdrYLcLe++6/8cY86Mlvufd2Mtj/9AY828pnN6qUWAnIiKyOY3MjcTCuIUBXbJ/mAX7B9rYZs85tbFQrjyrHJdjneyFdgmhiQl7CevJk/hOttvLWE+2p2QZq6uinLStdecEc66Skg0RcgIQDsNQq101F62gG2qLf7yixsUBXWE9ONZnk5H1ZHIuwKtdY/bS1s5RXj09xqQvvuC/MMvDlTX57N9qV9DtrsjF49J/QxFZuugvJU+On+Tk2PzRM9WT1C70ZVll1OfVU58fOfLqqcutw+289C8VNmVgB2BZVroxZlm1kfG8Zz1RYCciIrJxGWPon+nnxNgJTo6djAVzp8ZPMeYbS+q1st3Zse5r0UCuNqeWGm/Niu79kkrGGEIjI/hOnMR38gT+k+2xkC44OJjUa1lut93oYds20uq24qmLnGtrcWRujD/PReYmoOdF6DocqZ57EebG4xvLnQVVV803hqjaB5kFyZ2vnMMYw+mRmVg491LnKK39k3Hl1ZYFDSVe9m7J56ot+ezbks+WwsyNE0iLyJoyG5ylY7yDE2MnaB9v5+TYSdrH2+ma7CJslr9E/3xclova3Frq8+tpyG+gPs8+l2WVLfq3bdMGdnIuBXYiIiLrnzGGwdnBWDB3cuxk7PZUIM4lgxdQlFFEXW4dW3O3UpdbR11eHXW5dRRnFG+YD9PGGIJ9ffhOnLSXsJ44ae8vd+IEofE4Q6QLcOTkkFZXh2dbnX2us8/uqios5wbtXmkMDJ9cvPfcwDGIt7ohf+t89VzVfijZCc6NUbm5ls0FQrzRM84rp6MB3RhDU/Et887yOLmyJj8W0F1RnUduhpa3isjqmgvO0TnRGfu5KhrmdU12ETKhpFzD6/ayPX97rCIvZzaHm/feHH16TQR2+j+qiIiIyBIMzw5zYuzEOeHchH8iadewsKjyVs2HctGALsF9WdYaEwoR6O7Gd/KkXSkXDeZOniQ8E9++WhcSW8Z6VjDnLCzcMEHnBfkmoeclu3qu+wXoPgyzcTbWcKXb+81VXx2poLsaskuSO185R7R67pXTY7xyepRXusY4dmaCYDi+kLW6IIOrauxwbu+WfHaU5eBU91YRWWPSXek0FjTSWNC46HF/yB8L8qLLa9vH2umc6Fz2fr+TgUleGXiFVwZeASAwEkja/JNFgZ2IiIjIAqNzo7FQbmE4N+pLXgdRj8PDltwtsVAuGszV5taS5kxL2nVWmwkG8Xd14TtxAv+JE3bF3IkTduMHvz95F3K58GzZMl8xt22bHczV1uLIWv+dbZfEGBg+Edl77rB9DByDeJcU5VbboVz1NXZIV7oHXJ7kzlnOMeUL8nrXGC+fHrVDuq4xRqbj+15xOy12V+ayL1I9t7cmn5Kc9CTPWERk5Xicntj+dAsFQgFOTZzi+Ohx2kbbOD56nONjx1OyP/BK2rSBnWVZJcD+yHF15CiMPP2gMebAKk1NREREVsCkf5ITYyc4Pnp8UcXc8Nxw0q6R6cqMdTGLLmGty62jMrsSp2PjLLs0wSD+0134Thy3mz8cP2FXziU5mLPS0vBs3Uratm2kbd9m7y+3fRuemhos9yZbxpfM6jmHGyqusJe1Rpe45lQkdbpyrnDYcHJwKhLM2QFdvHvPgd0c4qpIOHfVlnx2V+aS7t44/86IiFyI2+mmIb+BhvwGbia2rJUJ/wQnRk/EArxooJfsbUtSZdMGdkD/ak9AREREUi8QDtAx3hH7YS36m9fe6d6kXSPDlUFdbh3b8raxPW872/K2UZ9Xf86GxuudHcydxnfiRKRqbkHFXCB5S0kcWVl204dt20jbVhe77a6s3Lj7y11MsqvnssvsqrmqSOfW8svBrcqrVBub8fNK11hseeurXWNMzsXXudVhQWNZDldU57FvSz77avOpKVBzCBGRhXI8Oewt3cve0r2xx4wx9E33LfqZ8PjYcVrHWldxpue3mQO7hU4DLcDbV3siIiIiEp9oZ9boD19to20cHzvOqfFTBMPxfSg+W5ozLRbMRUO5bXnbqMiuwGE5knKNtSAWzB0/YXdljSxnTXYw58zLw7N9G2l1iyvmXKWlmzt4SGr1nAvKLos0hrjaPudW2+1AJWWCoTCt/ZO8HA3nTo/RPjQd93iFWR6urMnnypo8rqzJ47KqPLLT9FFORGS5LMuiPLuc8uxy3lL1ltjjpzpPUXdH3SrO7Fyb+V/5vwAOA4eNMf2WZdUCp1Z3SiIiIrIUC5ezLvzt6KR/Minjux1utuZuXRTKbc/bvvGWskabP5w4ge/4cTugO348+cFcYWFkGet2O6Dbtp20+u24CgqSdo11KxyG4eMLqudeTKxz68Lquaqr7aWu7oxkzljOYoyhb2KOV0+P8Wr3GK+eHuP17nFmA/F1MnQ5LHZV5MQCur01+VTlZ2zuEFtEJMXczrW3tUbSAzvLsn4/cvMXxpj4f42UYsaYu1Z7DiIiInJxC5ezRivmkrmc1WW5qM2tjQVy0eWs1d5qXI6N83tNYwzB3l47lDtxAl/bcft2eztmbi5p13EWFpK2fXvkiAZ023Hl5yftGuvezAj0vDxfOdf9EvjG4xtL1XOrYmIuwBvd47zaNcarXWO81jXGwKQv7vHKc9PZu6B6bleF9p4TEZHUVNg9BoSBy4BjKRhfRERENqDRuVFaR1tpHWmlbbSN1pFWTo6fTNpy1tLMUhryG2Ldxerz6qnLrVuTv1GNlzGG4OCgXSV34gRzx4/jP27vNxeeTt7vUZ1FRXYot20bafX2WcHceYSCMNhsB3Ndkb3nho/HP56q51acPximpW+C17rGeLVrnFe7Rjk5GP/3UprLwWVVuXb1XHUeV9TkUZ6r/4YiInKuVP3qWL/WExERkfMKhUN0TnTGwrnW0VbaRtoYmB1IyvjZ7my2521fFM5tz9tOblpuUsZfK4Kjo5FlrMfnK+eOnyA8Hme11nk4i4vs5asLK+a2bVMwdyFTg/NNIboP25V0gTjDHVXPrThjDJ3DM7zWbTeGeK17jKNnJvAH42zuAWwpzOTK6rzY8tam8hzczo2z36WIiKTOxlnrISIiImvOhH+CtpE2O5SLVM2dGDuBLxT/8rGo6HLW+vx6O5zLs8O58qzyDbXXU3hmBt/Jk/ja2iJLWduYO36c0OBQ0q7hzMsjrb7erparryetvl7B3KUE/dD/hr3nXDSgG+2If7ycSqjaZ4dzVVdHOreq8iqVhqd8vNZtV8691mUHdGMz8e/d6E13cUV1HpdX2Utbr6jOozA7LYkzFhGRzUSBXYpYllV1iZeUrchEREREVkDYhOme7D6nau7M9JmkjL8plrMGAvg7O/G12YFcdJ+5QFcXmDgbEJzFkZ1tB3Lbty8K6JyFhRsq5Ew6Y2C8O1I195J97n0NgnHu/+dMg4orFwd0uZXJnbMsMusPcfTMgn3nusfoGpmNezyP00FTRQ5XVOVyebUdztUWZuFw6PtIRESSQ4Fd6nSt9gRERERSYS44x/HR47SMttAy3ELraCvHR48zE5xJeGyPw8P2/O005jfSWNBIQ34DDfkNG2o5qzGGQM8ZfMfb7K6sbW32nnPt7UnrzGplZET2l4uEcw121ZyrtFTB3FL4puDMK4sDuqn++MfL2zK/tLVqH5TuAZcnefOVRaL7zr3ePc7r3XbH1uMDU4TC8QffdUVZsWDu8uo8msq9pLnUGEJERFJHgZ2IiIhc0NjcWCyYi55PTZwibOLf0ymqOKOYhoIGO5yLBHRbcrZsqO6swdFRfK12IGcvaW1LagMIy+3Gs23bORVz7spKLIf2yVqScBiGWueXtva8BAPHIN6/4+4sqNw7XzlXtQ+yS5I7Z4kJhsIcH5jije5xXuse442ecVp6J/GH4v83qijbE1vaekVNHpdV5pGbuXGqeUVEZH3YOD8Rrz3Vl3i+DDi8EhMRERG5FGMMZ6bPLArmWkZb6JvuS3hsl8NFXW7doqq5xoJGCtILkjDztSHs8+E/eZK51kgo19rK3PG25O0zZ1l4amoilXIN9rmhAU9NDZZLP84ty9Qg9Lw4H9CdeQV8E/GPV1g/H8xV74fiJnDqv0kqhMOG9qFp3ugZi1TPjXP0zDhzgfjDuQy3kz1VubGA7vLqXCrzMlSJKiIiq04/TaSIMab7Ys/rhwAREVktgXCA9rF2WkdbaR5upnW0lZaRFib9kwmPnZ+WP181V2BXzm2kveZMOEzgzJn5UK6tDV9rG/7OTgiFknINV0kJaQ0NdsVc9LytDkeGGhAsW9AHfW9EmkJEArqxzvjHS8+zg7nKfZHzVZC5cYLntcQYQ/forF01F6meO9IzwZQvGPeYDgsaSr1csWBpa31JNi51bRURkTVIgZ2IiMgGNhOYiQVy0ePE6An8YX9C41pYbMnZwo6CHbFgrrGgkeKM4g3zS6nQ+LjdACISykWXtIZnEt+rD8Dh9UYCue2kNTSQHunO6szLS8r4m44xMNIOPS/PV9D1vQ6hOP+uO1xQusuunquMNIco3AYb5O/3WmKMoX/Ctyice6NnPKGOrWDvO3dZVS57qvK4vCqXnRU5ZHr08UdERNaHVP4f6zOWZQ0kYyBjzF8kYxwREZGNbNw3TvNIM83DkWOkmc6JTgyJdRj1ODzU59ezo2BH7GjIbyDTnZmkma8u4/fjO3UqFsjNtbbiaztOsC/x5cAAlseDZ/s2O5BbUDmnBhAJmhmJNIR40Q7oel6C2dH4x8upgqqr5gO68svBszH+jq8l0XDuSM84b/SMc6RnnNd7xhmc9CU0blV+BpdX5bGnKpfLKnPZXZVLTvrGqOwVEZHNKZWB3aeTOJYCOxERkQWGZoc4NnyM5uFmWkZaaB5ppmeqJ+Fxczw5NBU00VjQGAvntuZu3RCNIIwxBAcHI9Vyrcy1tOJrbcXX3g7B+JfZLeSurrZDuYZ60hsbtc9csgTm7KWt0WCu+0UYPRX/eO5MqNi7OKDLKU/efAWwv+d6x+diwZwd0k0wNJVYOFeak8aeSrtqbk9VLpdV5VGQpa67IiKysaTqp8dk/ro4sbIAERGRdcwYQ+90b6xiLlpBNzg7mPDYFVkVNBY0xgK6poImyrLKNkTVV9jnw3fihB3OtbbaVXOtrYRGE6jAWsCRm0t6Q4MdzjU2kN7QgGd7Pc7srKSMv6mFwzBycnH1XN8RCCewPLKoMdIYIhLQqTFE0kX3nDvSM86RM3Ywd7RnnOHpxJbf52e6uawqj8siwdxlVbmU5qQnadYiIiJrVyp+UnlrCsYUERHZ8MImTNdkF83DzRwbORYL6cZ94wmN67ScbM3dumhJ646CHeSm5SZp5qvHGEOwry8SyM2Hc/6OjuQ0gXC7Sdu2za6Ya2ggLVI15yop2RDB5powNWiHc9F95868DHMJ/J3PLFrQGOIqu5IuIy9p0xX7++70yAxHeibmq+fOJL7nnDfNxe7KXC6rzuWySjucq8pXx1YREdmckh7YGWOeTfaYqWBZ1nXA9gUPFS24vd2yrAMLX2+M+dEKTEtERDaJYDjIqfFTsYq5Y8PHaB1tZTowndC4HoeHhvwGdhTuoKmgiZ2FO9met5101/qvSAnPzOA7cWI+nGtpYa6tjfDERFLGd1WUk97QGFnS2kB6YwOe2lost/bBShr/NPS+HgnoIiHd2On4x3NlQMUVdrfW6JFXo8YQSRQOGzpHZnijZ5yjC/adm5hLbBl5dpqLXRU57K7MZU9lLpdV5VJbmIXDof92IiIisLm7xN4GfPQCz/125FjoRymdjYiIbFjBcJD28XaODR+LHa0jrcyF5hIaN8OVwY4CO5hrKmyiqaCJurw63I71HTAZYwj29kb2mGuxzy0t+E+ftjuBJsjKzJyvlmtssPeaq6/HmZOThNlLTCgAA812MHfmZbt768AxMOE4B7SguHG+cq7yKijZCc71/fd9LQmGwrQPTXP0zDhHI9Vzx85MMOlLLJzzprvYXWHvN7e7MpfdFTkK50RERC4h6YGdZVmXG2NeS/a4IiIi60EgHKB9bEE4N3KMtpG2hMM5r8fLzoKdsWCuqbCJGm8NToczSTNfHeG5OXzHT8wHc5ElrcmqmnPX1NiB3IJwzl1VheVwJGV8iTAGRtrtUO7My3ZI1/saBBP4e59dFlnaGgnnKq6EdIWqyTIXCNHcO8HRMxMci5xbeifwBeMNVG25GW72VEaCucoc9lTmUlOQqWWtIiIiy5SKCruXLcvqAv4ReBz4pTEmsd1mU8AYcwA4sMrTEBGRdSwQDnBy7OSiyrm20TZ8ocQ6IBakF7CzcOeiyrnK7Mp1/YHXGENwYHBRxdxcayv+U6fsJgMJcni9keYPdjiX3thAWn09jiw1gUiJyf75YK7nJTuomxuLfzx3lh3IRSvnKvdBToWWtibJ+EzArpo7MxE7nxycIpxgwWpBlidWMRcN6bTnnIiISHKkIrCzgBrgU5FjxrKsp7DDu380xvSn4JoiIiIpFQgFODF24pxwzh9O7HdSZVll7CzYyY7CHbEKuuKM4nX9gdf4/fhOnpwP5tpa8bUkqUOrw4GntnZ+KWuDHc65KirW9Z/ZmjY3Ab2vzgdzPS/DRHf841lOeylr5ZWR5a37oHgHrPNq0bXAGEPfxBxHeyYWhXM9Y7MJj12U7YntN7c7clTkpuv7TkREJEVSEdhVAe8C3g28DcgC/gD4fcBYlvUSdnj3uJbOiojIWhQIBzgxeoKjw0cXhXOBcGIdEMuzytlZuDN2NBU0UZhRmKRZr47g6KgdyjW32NVzzS342tshmNieV2BXzaU3NpK2YwfpOyLLWrdvx5GRkYSZy3kF5qD/6Pyecz0vwVAbkEApVv7WSNXcXvtcdhl4MpM25c0qFDaciuw3d+zM/NLWkenEF7aU56azqyKHnRV2QLenMpfSnDSFcyIiIivIMknYvPmCg1tWBnAjdoD3LqA88lT0ot3ML539xVpcOpsqlmVVAV0AXV1dVFVVrfKMREQ2p2A4GFvWGg3oWkdaE66cq8yuXBTM7SzcSX56fpJmvfJMOIy/s9PeY665xQ7pWloI9iehcN6ycNdUk964g7QdjaTv2EF6Y6Oq5lItFIDBlvl95868Av3HIJFgOqt4wZ5ze+2QLrMgeXPepGb9IVr7J2nunYiEc+O09E0y4w8lNK5lQV1RFrsqctlVkcOuilx2VuRQkOVJ0sxFRETWh+7ubqqrq6N3q40xCSwnSI6Udok1xswSqaYDsCzrKuzKu3cBe4Fq4I8jh5bOiohISoXCIU6Nn+Lo8NHY0TrSmvCecwvDuZ2FO9lZsJO89LzkTHoVhGdm8LW1MdfSylxLM76WVuba2jAzMwmP7cjMtCvldjSS3hipnNNec6kXDsPwifnKuTOvQN/riTWF8GTb+85VXDkf0uVWad+5BBhj6J/w2cFc5GjunaBjaDrh/eY8TgeNZd5IMGdXzzWVe8n0pPTjgIiIiMRpRf8PbYx5CXgJOGhZVgXzS2d/By2dFRGRJAqbMB0THRwdOhqrnmsZaWE2mNheTlXZVYvDucKd5KblJmnWK2tRI4jmllg45+/osLt+JshdWWkvZ40GdDt2qEPrSjAGxjoXVM69ah/+yfjHdLigdPd8MFe5F4oatO9cAvzBMCcGpmiOhHLNfXb13OhMYkvvAbzpLnaWz1fM7arIYXtJNm6nvvdERETWi5QuiV3yJCwrHXvpbLT67uylsz3Y4d39xpg3Vn6GyaclsSIiyRM2YU5PnI4Fc0eHj9I83MxMMLGKsGpv9Tl7zq3bcC4YxH/qFHPR/eZamplraSU0MpLw2FZaGmn19aQ37SCtcX6/OafXm4SZyyVN9C6unDvzCswm8t/VgqL6xZVzpbvBnZ60KW82I9P+WDBnV81NcmJgkkAo8Z/DS7xpseWs0XN1gTq1ioiILMemWxK7VMaYOeCJyBFdOhutvtuL3cjiU0A/sCECOxERiY8xhu6pbnu/uaH5feemAlMJjRtd1rqrcNe6r5wLT08z19pmV8w1N9sBXVsbxp/4VrHOwkLSm5rsUG6HffbU1mK51sSPFBvf1KAdyPW+ap97XoapvsTGzNsSCef22vvOlV8O6TlJme5mE20EEauai4RzfRMJLD2OsCzYWpRFU3lOpHrODueKvWlJmLmIiIisNWvyp+sFS2fvjiydfTdwM5D45jkiIrJuGGPon+m3q+aG5vedG/eNJzRuWVYZuwp3xY6mwqZ12RDCGENwcDDWpXWu2Q7o/KdPJ76k1eHAs3Ur6TuijSDscM5VXJycyculTQ9FlrMuCOgmehIb01tuh3IVV0LllVB+JWSt707Fq2V02k9L3yStfRO09E3SHLk9FwgnPHZ2mosdZV6aynPsgK4ih8ZSLxkeLUEWERHZLNZkYLeQMeYM8HeRQ0RENrCh2SF7WWsknDsydIThueGExizJLIlVzkWr5woz1l9AYUIh/J2ddijX0sLcsWbmWloIDSf25wORRhA7dsyHc01NpG3fjiMjIwkzlyWZHobeVxYEdK/BeFdiY2YURKrmrpwP6XLKL/0+WcQfDHNycIqWSDDX0jtJa19yquYAqvIz5oO5ci87y3Opys/A4dCSVhERkc1szQd2IiKyMY37xs+pnOubTmxpX2F6IbuLdi9a2lqcuf4qwsKzs3aX1kjV3FxLM77WNsxc4gGBq7yc9MZG0nc22fvNNakRxIqbGZmvmIs2hBg/ndiYHi9UXLFgaeuV9lJX7WO2ZMYYesfnaO2bpLlvIhbMnRycIphoi1bA43LQWOplZ3kOTeV29dyO8hxyM9xJmL2IiIhsNGs2sLMs66PAfweMMWbNzlNERC5tyj9F80jzonCuazKx6qH8tHx2Fu1ctLS1JLNk3W20HhwdZe7YsfmqueZmu0trOMFldU4naXV1pDXtsJez7mwirbERV/76W/q7rs2OnrWs9VW7g2si3JlQdlkkoIuEc4XbQaHrkk35grT2TdLSN2Gfe+3bE3PBpIxf7E2L7TXXVG6HdFuLsnCpS6uIiIgs0VoPwtbXpy4REWEuOEfLSEtsSevR4aN0jHdgiL9Cxev2LgrndhftpjyrfF2Fc8YYAj09sX3moktag30JNgzgrCWtTTtIb9pJWv12HGnajH5FTQ9D32v2ctYzr9oB3WhHYmO6MqD8Mii/IrK09QooagCH9jJbilDY0DE8HQvkWiIhXdfIbFLG9zgdbC/JZkeZl8YyLzsr7KWtRdn63hMREZHErPXATkRE1rBAKEDbWNt85dzQUU6MnSBkQnGPmeHKoKmgiV1Fu9hduJtdRbuo9lbjsNZPZYoJBPC1n2Ku+VisS+tcSwvhiYmEx3aVlMxXzTU12Utaq6u1pHWlTfbbwVzvq5FzEvacc6VD2R47mIsGdEUN4NSPa5dijKFnbJa2/kla+6Yi50lODE7hDybeBAKgMi+DHWVedpR7aSzLoanMS21RFm5VzYmIiEgK6CdAERFZklA4RPt4e6xy7tjwMVpHWvGH/XGP6XF42FG4Y9Gy1q25W3Guo+qh8PQ0c61tdjgXWdbqO34c44//zwVY1KU1vWkHaU1NpO/Ygatw/TXMWNeMsTuznnl1PpjrfQ2mEqyMdKVD6e75qrmKK6GoUeHcJRhjGJryxwK5tv5JWvsnOd4/xZQvOctZox1aG8u87CjPYUeZl4ZSr/aaExERkRWV9J8KLcv670kaanuSxhERkWUyxnB68jRHh45yZPgIR4eO0jzSzGww/mVkLstFfX79osq5bXnbcDvWz4fg4MhIZJ+5Y7Flrf7OTjvUSYCVlkZaY2OsYi69qYm0hgZ1aV1pxsDoqcXBXO9rMJNgJ15nGpTtXlA5dwUU7wDn+vm7vxrGZwK0DdihXFufHcy19U8xMp1gGB7hdFhsLcqyq+bKvOwoy2FHuZfKvIx1tdxeRERENqZU/Br3ACSwUZGIiKwoYwx9032L9pw7OnyUSf9k3GM6LAd1uXV21VwkoGsoaCDNuT72dbL3mzuzKJiba24m2N+f8NiO3NxIMGc3gkhvasJTW4vlUmXVigqHYeTk/F5zva9B7+vgG09s3Oiy1vLLI40hroSSJoVzFzHjD3JiYGpBxdwUbX2T9E0k3hU5qtibtiiYayzzsr0km3T3+qnmFRERkc0llZ8O9KtJEZE1aHh2eFE4d2ToCCNzIwmNuSVnCzsLd8Yq55oKmsh0ZyZpxqllQiH8p04xFw3mjh2z95sbTzC4AVwV5aQ37VxUOecqX1/NMjaEoA8GmqHvdTuU63sd+o5AYDqxcT3ZdihXfvn8oT3nLmguEOLk4BQnBuw95tr67fPpkZlEi1RjvOkuGku9NJR57XOpl4bSbArVBEJERETWmVT8RDkMFAD/DHwqgXFuAf5rUmYkIrJJTfgnFjWEODJ8hL7pxPbeKssqiwVzuwp3sbNwJ7lpuUmacWqFfT58bW2xZa1zzc34WtswcwlW8jgcpG2ri+wzF6mc27EDZ15eUuYtyzA3AX1vLAjn3oDBZggnuL9Zeu6CYO4K+1ywDdTs4xyzfjuYOz5gh3LH+6c4MWAHc+EkBXPpbgf1JXYg11iWHTl7KctJVyAuIiIiG0IqArvDwE3ADmNMZ7yDWJY1lLwpiYhsfDOBGVpGWhYta+2ciPufYQAK0gvYXbQ7FtDtLNxJUUZRkmacWqGJCbs764Jlrb72dgjF38EWwEpPJ62xIVI1t5P0nU2k1dfjSE9P0sxlySb7I8Hca/MB3eipxMfNLJwP5aJHfi0oCFokupT1eP8UxwemON4/yfGBKbpGk1cx53JYbCvOjlTMzQdzVfmZOB367yEiIiIbVyoDuxrLsoqNMYMpuIaIyKbmD/lpG22LVc0dGTpC+3g7YROOe0yvx8uuwl3sLtodO5dmlq6LapXg4GBkSeux2H5zga6uhMfVfnNrRDhsB3ELl7T2vg7TA4mP7S1fHMyVXw45lQrnFpj2BWPLWKPn4wNTdI/G34TmbJYFWwoyY4Fc9FxbmIXHpSpGERER2XxS8YnjhQW3rwb+KQXXEBHZNILhIO3j7XY4F6meax1tJZjAEr8MVwZNBU2xhhC7i3ZT7a1e8+GcMYZAd/f8ktZj9rLW0GDiRdmusrJzwjlXRcWa/zPZcII+GGyx95hbuKw1gSYoMQV1dkOI6L5zZZeBtzTxcTeIibkAJ2MVc5ORqrkpesaSF8wBVOVnUF+STX3p/D5z20uyyfCoAYSIiIhIVCoDO4vEArsTwINJmZGIyDoRNmFOT5zmyPCR2N5zLSMtzAbj/8DsdrhpzG+0w7lI9Vxdbh1Ox9r+cGyCQbsZxIKqubnmZsKTCQY3loVnyxZ7KWtTE+k77aYQroKC5Exclm562A7l+o9EAro3YKg18f3mHC4oboLyyyLh3GVQuhvSc5Iz73XMGMPApI8TA3bzh2gTiBMDUwxM+pJ6reqCDBpKvGwvzY7sN5fNtuJsstJUoSoiIiJyKUn/iSmyBDbhtQvGmF8Dv058RiIia5MxhjPTZ+b3nBs6yrHhY0wFpuIe02k52Za3LRbM7SraRUNeA26nO4kzT75FzSCORZtBtGJ8CQYIbjdp9dsX7TeX3tiIIysrOROXpQmHYKQ90gzijUhA9wZM9iY+tjsrUjW3Zz6gK2kC1+buChoMhTk9MsPJwelYIHdicIr2gSkmfQkGogtYFtQUZFJf4qW+NJv6EnufubriLDI9CuZERERE4qWfpEREVsjAzEBsz7mjw0c5NnSMUd9oQmPW5tQuWtbaWNBIhisjSTNOjdDUVKQJxHzlnO/kycSbQWRmkr5jR2RJa6QZxLZtWB5PkmYuS+KbgoFjduVctGpu4BgEZhIfO7NocdVc2eX2MtdN3Kk12pH15OAUJyOh3ImBKTqGZvCH4t/T8mwOC7YUZkWWsmbHArptxdmku9d2ta6IiIjIeqTATkQkBUbnRjk6PL/n3LGhYwzMJrZBfkVWBbuKdsUaQuws3InX403SjFMjODy8qGpurvkYgc7TCY/rzMubD+Ui1XOe2i1Ymzi4WXHGwMSZSMVcpHKu74hdSUcSWoTm19rLWKN7zZVfZjeI2KR7Co5M+xctX40uZ+0Zm01aR1YAp8NiS0Em9ZGOrNtL7HCurjhLwZyIiIjIClJgJyKSoEn/JMeGj8UCumPDx+iZ6klozKKMInYX7mZn0U57aWvhLgozCpM04+QzxhA8c+acTq3B/v6Ex3aVlcX2mUvfFdlvrqxMzSBWkn8GBpuh/+iC4wjMJlYhCoArHUp2QtluO5gr3Q2luzblfnP+oL2MtX1wipOD07QPTtE+ZJ9HZwJJvVaG28m2kiy2F9tVcttL7GOLurKKiIiIrAkK7ERElmEmMEPzSHOsIcSx4WN0THQkNGZuWq4dzhXujC1vLcksWbOBlAmF8Hd2LurU6jvWTGh8PLGBz9cMYudOXPn5yZm4XJoxMNa5OJTrPwrDJ0lK1VxWSWS/uQXhXOF2cG6eH0eMMQxP+2lfEMidHLDPp0dmCIWTWC4HFGR57FAuEshtK85ie0k2FbkZOBxr898YEREREVFgJyJyQbPBWVpHWmPB3NGho7SPt2MSCC6y3FnsLNwZq57bXbibyuzKtRvO+f34TpyIVM5FqudaWzEzCe5H5nKRtn374v3mGnfgzFYziBUzNwEDzfOhXPTwJ9iFF8ByQFGDHchFA7rSPeAtTXzsdcIXDNE5vLBabpr2IXufuYm55DV9iKrKz4gEcvPVctuKsynI0h6OIiIiIuuRAjsREcAf8tM22harnDs6fJSTYycJmfgbIaQ709lRsCO239zuot1sydmCw1qby83CMzPMtbTGqubmmpvxHT8BgcSW4lnp6aQ3NpK+a2dsv7m0hnocagaxMsIhGDl1VjB3xK6kSwaPN1Ixt2c+oCtpAvfabn6SDMYYBqd8tA9Oc3JwalHVXNfIDEkulsPjdFBblGkHcpGquW2RJa0ZHu0vJyIiIrKRKLATkU0nEA5wYvRELJg7OnSU42PHCYbjr3pxOVw05jeyu2g3uwp3sbNwJ9vytuFyrM1/ZkNjY+fsN+c/dYpEd6935OQsqppL37kTT20tllNhQsoZA9ODdiA30AwDR6H/mH07OJuEC1h2R9bSXfP7zJXugrwtG75L6/hsgI6haU4NTdM+NB27fWpomilf8qvlirLTqCvOYltxFnVF2dQVZ1FXnE11fgYu58b+sxYRERER29r8JCkikiTBcJD28fZFe861jrTiD/vjHtNpOdmetz3WsXVX4S7q8+vxONdexZgxhuDAAHNHj9mVc5GQLnimN+GxXcXFpO/cSdrOpkhItwt3ZcWaXd67ofgmI6HcsUgoFzlmhpMzfnre4lCudDeU7ADPxl2yPBcI0TE8zanBc0O54en4/724kGi13LbiSCC3IJjLzXAn/XoiIiIisr4osBORDSMYDnJq/BTHho/Fura2jrQyF5qLe0yH5aAut85uCFG4i11Fu2jMbyTdlZ7EmSeHCYcJnD69eL+55mZCIyMJj+2url5cOdfUhKu4OAmzlosK+mDo+HwgN9BsB3Tjp5MzvsNl7zVXsnNx5VxOBWzA4DUQCtM9OsupIXv5asdwJJQbnObMePz/TlxMiTctFsRFw7ltRdlU5mfgVNMHEREREbkABXYisi6FwiFOjZ+KVc0dGz5G62grswku/avNqV1UObejYAeZ7swkzTp5TCCA7+TJ2HLWueZj+JpbCE9PJzaw00laXd3iTq1NTTi93uRMXM4vHIaxjvklrAORZa3DJyCBpdqLZJcurpgr3WWHda605Iy/RoTDht6JOTrOs3y1a2SGYLI3lgPSXA62FmXNV8sV27e3FmXhTVe1nIiIiIgsnwI7EVnzouHcsZFjsW6tyQjnqr3VsWBuV5Edznk9ay+YCs/MMNfaGlvO6jvWjO/4cUyizSA8HtIaGxd3am1owJG+9qoHNwxjYOIMDDbDQMt8ODfYCoEEO+9GuTLs5aslu+zmD2W77dvZG6ciMhQ2nBmbpWN4mo7hGTqHpmO3T4/M4A+Gk35Np8OiOj+D2qIsthZlUVeURW1RFrWFWVTmZeBQtZyIiIiIJJECOxFZU0LhEB0THYsq51pGWhIO5yqyKthVtCu2tHVn4U5y03KTNOvkCY6O4mtunl/W2tyMv6PDrsBKgCM7m/QdO+z95nbutDu11m3Fcqv6JyWMgcleO5AbbJk/D7aCbyI517CcUFRvh3IlOyNHE+TXgmP9N/kIhML0jNqhXOfwzPx5aJqu0RkCoeRXygGU56azNRLG1UXCudqiLKrzM/G41PBBRERERFaGAjsRWTXRcG7hnnPJCOfKssrYWbAzFtDtLNxJQXpBkmadHMYYgn19i4K5uebkNINwFhaes9+cu7oaa4N38lwVxsBk33zFXOzcCr7x5F0nt8YO40p3zodzRfXrfjmrPxima3SGzuFpOobs86lh+9w9OksoBctXAQqyPHYQV2gvX90aCea2FGaS6dGPRiIiIiKy+vRTqYisiGi31mPDx2gebqZ5pDmp4dzOQjugaypoojCjMEmzTg4TCuHv7GSuudmunosEdKHR0YTHdldWzu83FwnpXCUl6tSabMbAVP95KuZaYC6JwVxm4XwgFw3nindAek7yrrHCZvxBTo/M0Dk8w+nhGTpH7HCuY3iaM2OzpCiTI8vjZGtxFluLstlamLngdha5maosFREREZH/r707D45svev7//lKvam1tzSj2TSr1hvjBDAGY34/uJgyJCYph0AgELAJm+NUCL/AL2Sr4JBUdlI2ASoJENssFQwUDmBIbJY7xlwTMISLQ+5om1WjGc1oa+3q9ckfz2mppdGubvWR9H5VnTrndJ9+ztHcR+dKH32f84QbgR2AissVchpLj/lwbvaOXp95XSNzI8oUMkdqtzycKy1hC+eKmYwyI6Nau/N6ENANaW14WG71aMGk6uoUu3lDicGX1ieCSAwOqL41fMN6T7TSM+amh6WpkbKKuSFpLV2588SapXP9m5811/VnpMZzJ252VuecppYyehQ8P+5hsC5tTy8d7ft+N83xiH+OXGejrnckda1jY93ZFCO4BgAAwIlFYAfgSDKFjEbnRteHtb4+87pG06PKH3Fmy65k16bnzYUxnCvMz2vtztCmWVoz9+5JhcKR2t08GYSvnIv39amuoaFCVw4V8lL64cZz5aZHgvWolF2s3HliTT6YOzfow7lzg36/9cqJCuay+aIm0qt6OONnWn04s6KHsysaD4K5lezR+vxu2pLRTUHcjc5SMNeo9mSUUA4AAACnEoEdgH1bya1oZG5kU+Xc3fRdFdzRflkvhXPlAV2YwrkXnjc3dEeZ1+8o9+TJkduua25WYmBgY5bWwUHFb96URbg9V0RuTZoZ3RLKjUgzY1IhW7nzRBuDirlBP4T13IAP6Fq7T0wwN7+aKwvjyoK5mRU9na/e0FVJ6miM6VpHUtc7Gn0Y11naTqotGaveiQEAAICQ4jdCANtayi5paHZId2bv6M6MD+fuL9xX0R1tttLLTZc1mBrUYMegXup4SQOpAXU2dFboqo/O5fPKPniwOZy7M6RCOn3ktiPnzys+OBAMZ/UBXfTKFSqEKmFt3g9hnR7eHM6lH0pH7LObRJNSZ99GMFdat3ZLIZ/UI5MvaGJuVeNzqxqfXdH4nK+QG59d1fjcitIruaqev6slrquppK6mNlfJXe1IqrWBZ8oBAAAA5QjsAGh6dVpDs0Mamh3S6zOva2h2SOOL40du92rzVQ12DGow5cO5wdSg2hJtR7/gCikuL2tteGQ9lFsbGlJmZEQuc8Rnbpkpdu2ar5gbGFx/3lykMzzB5IlULEqLT3wYNz22UTk3NSwtTVb2XNFG6Vyf1Nm/MZT1/ICfrTWkwVyh6PRsYS0I4zZCucezq3o0u6Jni2tyVaySi9XX6UqqQddSSR/MdTT67Y6kutuTaojVV+/kAAAAwClDYAecIc45TSxNbKqcG5od0tTq1JHaNZmutVzbNBlEf6pfLbFwzGzpnFN+asrP0FoK5u7cUfbRIx01wbBoVPG+vs2Vc/19qmtsrNDVn0HZZT9kdXrULzOl9ZiUW6nsuZIdPpQrhXOldcvl0AVzzjmlV3Ian/PPjStVxo3Prujx3Kom5laVLVSwmnAbbcmorqWS6k4lda0juV4xd60jqa6WhOrrqBYFAAAAKoHADjil8sW8Hsw/0J3ZO+vVc3dm72jxiA/Ur7M63Wy9uV4xVwrnGqPhCKhcoRAMaR1SZmgjoCvMzBy57Y3nzQWVcy8Fz5uLMpzvwLarlittLzyu/PlarmwO5c4N+O3G8DwrUfLPkZuYW9XjuRVNpFdfCOWWMkebzGUvdSZdbG3QtQ4fyHWnkroWBHLdKYauAgAAAMeFwA44BTKFjMbmxvT67OsamvHh3MjciNYKa0dqN2IR3Wq75cO54Jlzfe19aoiEY7bS4vKy1kZGlBka2qicGxmRWzva1y35580lBgcVf6k0pJXnzR3KcVbLWb2UuhGEcX1+EojOPr/Emyp7rkNwzml+NafHQSDn136ZSPvXFteqG8hJvkquuz2p7lSDulPJYNtXy11ua1AsEq7KQgAAAOAsIrADTpj5zLyGZ4c1NDuk4blh3Zm9o3vpe0eeqbUh0qC+9r71CSEGUgPqaetRrL72MzSuz9I6NKTM8LDWhoaVGRpS9uHDIw9pVX294jdv+Iq5gQElBgcUHxhQJJWqzMWfBfmsn9xh5q4P4maD9cy96lTLxZqkjh6ps3cjkDvXL6VuSZHa9VfnnGaXs2Uh3MZQ1VJIt5w92vfpfiSideshXHe7D+WutPtArjvVoOYEVXIAAABA2BHYASFVet7c8OywhuZ81dzw7LCeLj89ctut8VYNpAb0UsrP0jrQMaBrzddUX1f7h8IXMxllxsaUGRrW2vBQsB5WcX7+yG3XJZOKDwwoMTDgnzk3MKh4b4/qEokKXPkpVyxI84+DQO5eEMgFwVz6kXTEwPhFJrV1Sx29QTDXu7HdfFGqQaVjseg0tZTRRHpzCOer4/xrq7nqB3L1daZLbQkfypVVypVCuc6mGJWgAAAAwAlHYAeEQLaQ1d303fWquVI4t5RbOnLbXckuDaYGNdAx4KvnUoO60HghFL/Q56emfLXc8ND6OnPvvlQ4eugR6eraFMwlBgcU7e6WhWwigVBxTlqcLKuQu+uX2bs+pCtkK3/OWNPmMK603XFLih7v0OuVbF5P0quaSK/pSXrVbwfDVZ/Mr2pyfk25QhWnWQ2YSV3NCV1ub9Dltob1yrhS1dzF1oQi9fRjAAAA4DQjsAOOWXotvSmUG5ob0v30feXd0Z5dVZqpdSA1oIHUwHpIl0rUfminy+WUuXd/I5gbGtLa8HBFJoJgSOsBOSctT/kAbvb+i0NYc8tVOGlQLdfZFwRzPRvbzReOpVquWHSaLlXHBWHck/Ta+vZEelXplVzVr0PamNjhcluDrrT75XJ7g660+2fIXWxLKB6pfbUrAAAAgNohsAOqpOiKmliceCGcm1yePHLb0bqoett71d/er/5UvwZTg6GZqTU/O+ufMzc8rMzwiNaGh5QdHZPLHT0MqWtuVry/T4n+AcUH+v2Q1r5e1cXjFbjyU6Q0A+vsvY1grrSeuy9lj165ua1kp3+2XMetYOnxz5U7hmq55UxeT+c3KuNKlXIT6RU9Sa/p6fzqsVTHSX7I6sXWRBDGJcuCuaSutDfoQmtCUSrkAAAAAOyCwA6ogOXcskbnRjUyN6Lh2WGNzI1oZG5EK/mjz4JZet7cQPuA+lP9GkgN6HrrdUXravvg+GI2q+zdu+vBXGZ4WGsjIypMT1ek/ejVq0r09wfB3IDi/QOKXr4UiqG8oVDI+WfHlUK48nBu7oFUyFTnvPGWLWFcj9Rx0283tFXllKvZgp7Or64HcpPza3oy70O4yeC1hWOYXbUkVl+ni21BINeWDKrjgnCuvUFdzXGGrAIAAAA4EgI74ACKrqiJpQmNzPpAbnjOh3Pji+MVab+7uVsDqQH1t/tgrj/Vr65kV01DKuec8k+f+mBuZDQI5oaVvf+gIs+as2RSid7eYDKIfsX7BxTv61N9U+2rBWsut+rDt1KFXHkwlx6vwkQPgUiDlLq5EcyVB3SNnRUdwrqWKwQBnA/ftgvljmuoakmqMaZLbQldam3QpTY/dPVyu9++1JZQZ2NcdXUExwAAAACqh8AO2MF2VXOj6VEtV+AZX7G6mHraezaFc33tfWqKNVXgyg+vsLSszOiIr5gbGdHaiK+eKy4uVqT9yKWLG8NZ+31AF7169exOBFEsSkuTPpSbeyDNPdzYTj+UFo8+I/CO6mNS+/UgmOvZWHfckpovSRX4b7KWK+jZgg/hykO50hDVp/Nrml2uwkQWu4jWmy62+uDtUluDrrSVgriNQC4Z43+NAAAAAGqL30pw5q1Xzc2NaGS28lVzbfG29WAuLENaXT6v7MOHyoyOBsGcD+ly45X5mi2RULy3V/G+3rKArl/1ra0Vaf9EWZvfCOLSDzeHc+lH1Ru6KknRRil1I1huSu3BOnVTarkk1R1uYgPnnOZWcpqcX9OzhTVNLvhAbnLeb5deO+7KOElqS0Z1qbVhfYbVUjBXCuc6m6iOAwAAABB+BHY4UxayCxqdG11fKlk1V2/1ut5yXX2pPvW1960HdOcaztVsSKsrFpV78tRXzY2OKTMyoszoqLL37lVkEghJinZ3+4kg+voV7+tTvL9PsatXZfVnZJbLQk6aH9++Qm7ugbQ6V93zJ9o2QritwVzT+QMPX83mi3q+uLapMs4HcBk9CwK5yYU1ZfPF6nw9u2hJRHSx1c+ierG1QRdbE7rY6gO5C8E21XEAAAAATgN+s8GplCvkdH/h/kYoNzeq0fRoRWZolfxEEP3t/T6YS/n1rbZbitfXZrZS55wK09O+Ym50VGvBOjs6puLK0Se+kMpmaO3rV7y/X/G+XsV7z8Cz5go5af6xr4abH/frdGn9SFp4LLkqh1dNXVsq5IKqufYbUjK1ryaKRae5layeLWT0fHFNzxcy65VwpXDu2cKappeOd4hqSXM84kO3tgZdak3oQqt/hpwP53xA1xjnf1kAAAAAzgZ++8GJ5pzTs5Vn67OylgK6BwsPlC8efdbI7arm+tr7dD55vmZVc4WFBWXGxvwEEEEwlxkZUSGdrswJ6usVu3F9I5jr71Oiv1+RCxdO5wyt+UwQyD3cHMaVwrnFp9UP5CIJ/zy5tmt+3V5aB6/Fd362YSmIe77oA7jnQSD3LAjkni9m9DxY54uuul/HDhpj9T6Aa/NVcRdafSh3sW2jSq45UdtZjwEAAAAgTAjscGIsZhc1lh7bXDU3N6rFXGUmRCivmitVztWyaq6wtKzsvbvKjN31AV0QzuUnK1MlKEmR8+cV7+nZFMzFbt5UXbw2X3NVZFeC8G3ch3LzZdVx6XE/6UPVmdRyeSOIaysL5Nqv+Qq6LWFo6Tlxz2bX9Gzh+Xrw9qwskHu+sKappYxyhdoEcWZSZ1NcF1oS6mpJ6EJrXBdbG/x2sN/VQhgHAAAAAAdFYIfQyRVyerDwYH0YaymYe7L8pCLtR+oiutF6Q71tvepr71Nve6/62/trVjVXmJ9X5u49Ze6OKTt2V5m7fsk/rdwMoXWtrYr39ije26tEX5+fEKKnR/VtbRU7R00UC9LSM2l+wgdxCxO+Wq58WZk+nmuJt5ZVxpVXyF2X2rqliA9B13IFTS1mNLWU8esnGU0tjm7sB8vzxbWaBXGSFI/U6UKrD+IutibKQrmN9fnmuKL1Z3SGXwAAAACoIgI71EzRFfVk6cl61VwpoKvUcFZJutB4wYdybb3qbffLjZYbitYff8VPfm5O2bExH8iN3V0P6PJTUxU7hzU0+Iq53t5NS+R87Sa+ODTn/IQNW0O4hYkgoHssLT6RKtRX9hRrltquBku3X7d2S+3XVGy9rlmXLAvbguBtMqOppUVNLf6v9fcW1o7pendgJnU0xtXVEtf55vhGANeSUFfrRjjX2hA9eX0GAAAAAE4JAjsci9m1WY3OjW4K58bSY1rJV2ZChKZokw/kgmCur71PPe09aom1VKT9/Vqf/GFLKJe5e1eF2dnKnSgSUfzGDR/I9W0Ec9ErV2R1J6TiKbssLTz1kzbMP96mSm5CqsDsvfuWaCsL5K6q2HJFK8nLmo12adK69DwX1/RSdiOMe1aqhpvRzPJTFWr0fLiSUhB3vtmHcV0tvgLufFAZ519PqLMppghVcQAAAAAQagR2qKiV3Irupu9uDGUN1rNrlQmrIhbR9dbrfjhraqNy7mLjxWOtBnL5vLLj48ref6Ds/fvK3L+n7L37yty9q+L8fOVOVFen2NWrit26tT6kNd7bq/j167JYrHLnqSTnpJUZaeGJn7BhYcIHc4tP/Gul7bUK/jvtR7JDxdaryjZe1lLDJc3FLmiq7rwmdE4Pi516shLR1FJGM8+ymr6b0exyNpikYTZYaqezKabzzQmdb4mrqzmhrpa4zrUk1BWEcOdb4upsYngqAAAAAJwWBHY4lHwxr0cLj9ZnZy1Vzj1eelyxc3Qlu16omrvRekOx+uMLqgrptDL37it7/76yD+5vbI+PS7lc5U4UiSh2/Zrit3oUv3VL8Z5bit3qUez6tXBNAJHP+kkaNgVwpWCutD0pFTLHelmuLqZM40WtJLqUjl3QdF2nJtWp8UJKd7PtGl5r08RKndKz2/03K0h6dqzXK0mxSJ3ONcV1rrlsaYqvh29dLT6YI4gDAAAAgLOHwA57mlmdWQ/mSjO03k3fVbaYrUj7LbEW9bb3qqetxw9lbes51uGsLpdT9vFjH8Tdv6/M/fvKBsFcYW6uoueyaFSxGzd8INfT4wO6nluKXb0qi9ZwJs1iQVqe8mHb0rPN64UnQTj31B+j4x366WRaiXUoHTmvqfpzeuI69biY0r1su0bXWvUwn9KMmuVWdgu1CsFSXWZSKhnbHMIFQVxp+3xzQuea42pJRHhGHAAAAABgWwR2WJctZHVv/p4P52ZH1kO6mbWZirQfr4/rZuvNTVVzPW09xzI7q3NOhbk5ZR88VPb+vSCYe6DsvXu+Wi5f2YkALB5X7NbNLRVztxTr7pZFjvHbLp8JgrdnvjJuu0Bu6ZkP4lzx+K6rzLI16pmd0xOX0sN8ShPFlJ64Tj11HZpQh565lHJrtb1VNSci6myKq7MpVlYJl3ihQi7VGKMaDgAAAABwZAR2Z5BzTs9Wnq0HcqXKufvz91VwR69CqrM6XW2+uh7M9bT3qLetV93N3aqvq6/AV7A955zyz6eUe/RQ2UePlH34SNlHj5R75NfFpaWKn7O+vV2xGzcUu3Fd8Rs3/LPmenoUvXRJVl+lr9U5//y35Slp6XkQxD3bfr1a2QrBgyjKNO1a9dSl9My1a9KlNFlaa+O1ZTUc+7XVmZRq9AFcKYjraPLDTzuaYjoXrDubfAiXiFav3wIAAAAAsBWBnSQzuybpuyW9Q1K3pIyku5J+XtKPOucqM5VpDazkVjSWHtsUzo3MjWgxu1iR9s83nFdvanPF3M3Wm0pEEhVpfytXKCg/ObkpkMs+eqjcw0fKjo/Lra1V/qSRiJ/44cYNxW/eUOz6jfWQLtLeXplzFAt+ooal59Lyc2l5Otie2gjmStvLU1KhMsORD2vNRTXpUnomH7ptDuX8MqVW5Y/xFhOP1PnwrTmuzsbYevi2OYTz4VxbMqb6OoajAgAAAADC6cwHdmb2FyX9jKTyB6YlJb0pWL7dzN7hnBurxfUdlHNOQ7NDuv34tm6P39admTtyFXjmWKI+4Z8xl+pTX7tfett61ZZoO3LbW7lcTrmJCT8L68OyQO7RI+UeP5ar5GQPZepTqW1DudiVK4d7vlx2RVqZDgK3Utj2fPN2KZhbmdFxPxtuO3lXp2m16rlr21jUrqeuY1OVXFpNkqobeCVj9Uo1xtTRGFOqMaZUow/eUqX9ZEyppo33m+I8Ew4AAAAAcDqc6cDOzD5X0kckNUhakvQvJb0S7H+DpO+Q1Cfp18zsTc65ypSlVVi2kNVnJj+jV8Zf0Scff1KTy5NHau9K05X1WVlLSyWHsxazWeWfPlVuYkK5J0/8MjGh3ESw/eyZVKjSBAHRaFAtd13xGzc3DWetb2vb+XP5rLQ664O1TUvw2vL0i6/lV6vzNRxCxkU0pVII114WxpXvt2tWzSqqOs9ga0lE1BEMMd0cxMXKXouvh3AMQwUAAAAAnFVnOrCT9AH5cC4v6e3Oud8re++3zWxU0r+RD+2+V9L7jv0Kd5BeS+tTE5/SK+Ov6NWJV7WSP/io3aZok6+UKwvnett71RhtPNK1FVdWNkK49UBuYz8/NXWk9vdi8bhiV68qeu2qYlevKXa12+9fvaboxQuyYk5aS/vnu63OSSsT0t3P+mq4lR1CucxCVa/5sBZdg6Zc655h3LwaVcmKuJZERO2NfmhpKhlVe9Jvtyejam+Mqb1su6MxpnYmYwAAAAAAYN/MudoPw6sFM3uzpN8Pdv+Tc+492xxTJ+lPJQ1KSks675yryHhMM7siaVySxsfHdeXKlT0/82D+gW6P39Yr46/otanXVNznrJ51VqdrLdc2Vcz1tffpYuPFAw8hdMWiCum08s+evVgZF+wX0ukDtXkYdY2Nil65pNil84p1tSt2rlnRjoRirRFFEjlZZt6HcevBXHpjO1+F59xVSNGZ5tSkadeqGdeiabVq2rVqOtiecS3Bfqum1aqMYkc6X32dqa2hFLJFtw3d2pK++q203dYQVYTwDQAAAABwSjx+/Fjd3d2l3W7n3ONaXo90tivs3lm2/cHtDnDOFc3sp+SHyrZJelnSJ6p+ZYFCsaA/mfqT9ZDuwcKDfX/2StMVvXz1ZX3ZlS/TG8+9cc9JIFw+r/zMjPLPp5Sf2mWZnpby+aN9YftUn4z5EK4tomizU7Qpp2hiWbH4gqJ1T+QLIANTwRJCWVevGQWhm2sNtjf2y4O4WTWroIMPBY1H6tSWjKq1Iaq2hphaGqJl+1G1BtulJRVUxzXHI6pj8gUAAAAAAELlLAd2XxKslyX90S7HfbJs+62qcmC3nFvWp598WrfHb+t3Hv+O0pn0vj5nMr3x3Bv1Zd1fppe7X9bN1psyMxUzGeUnp7SyRxBXmJ2Vjrnasi5aVLSxoGhjXtFkIdguKJosKNaUV308nNWfc65Js65Zc2rWnGte354J1rMueF3NmnNNWtjncNQ6kw/YkkHgFoRrbVvCtrZk7IXXed4bAAAAAACnx1kO7AaD9ZhzbreSsaFtPlNRz1ee69WhV/XK41f0B0//QLliTnJOsbzUmpGSGakhKzVknJJZqSHjl9ZcRLeiF3W9rlMXXJMiKxkVlz6uwtIvaWx5RYXFRbmlgz/brlLq4xsB3HoYVxbO1cdqH8gtugYfwKk8ZGvWrGsp2954fV6NO1bAxSN1ammIqjkRUUsiqmsNUb0h2G5JRNTS4NfNiahaGvzrpe3mRFSNsXpmOQUAAAAAAGczsDOzhKTOYHfXccnOuTkzW5bUKKl7t2O3nGOvh9J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+ "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# B0, massless lepton\n", + "fig, ax = plt.subplots(dpi=200, figsize=(6.4, 2.2), nrows=1, ncols=1, sharex=False, sharey=False)\n", + "for key in dict_d.keys():\n", + " m_D = pdg.get(dict_d[key]['pdg']).Mass()\n", + " rate = dict_d[key]['rate'](\n", + " Vcb=40e-3,\n", + " m_D=m_D,\n", + " m_B=m_Bzero,\n", + " m_L=0,\n", + " )\n", + " w_range = np.linspace(*rate.kinematics.w_range_numerical_stable)\n", + "\n", + " total_rate = rate.Gamma()\n", + " w_rate = [rate.dGamma_dw(w) / total_rate * (max(w_range) - min(w_range)) for w in w_range]\n", + "\n", + " ax.plot(w_range, unp.nominal_values(w_rate), label=f\"BLR, {pdg.get(dict_d[key]['pdg']).GetName()}\", ls=\"solid\")\n", + "\n", + " ax.set_xlim(1, max(w_range))\n", + "\n", + " ax.set_ylim(0, 3)\n", + "\n", + " ax.set_xlabel(r\"$w$\")\n", + "\n", + " ax.set_ylabel(r\"$1 / \\Gamma \\times \\mathrm{d} \\Gamma / \\mathrm{d}w$\")\n", + "\n", + " ax.legend(loc=\"upper left\", frameon=False, fontsize=\"x-small\", ncol=1)\n", + "\n", + " add_watermark(ax, px=0.01, py=1.05, fontsize=8)\n", + "\n", + " plt.tight_layout()\n", + "\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "code", + "execution_count": 6, + "id": "bd8d0e06", + "metadata": { + "scrolled": true + }, + "outputs": [ + { + "data": { + "image/png": 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "# B0, tau lepton\n", + "fig, ax = plt.subplots(dpi=200, figsize=(6.4, 2.2), nrows=1, ncols=1, sharex=False, sharey=False)\n", + "for key in dict_d.keys():\n", + " m_D = pdg.get(dict_d[key]['pdg']).Mass()\n", + " rate = dict_d[key]['rate'](\n", + " Vcb=40e-3,\n", + " m_D=m_D,\n", + " m_B=m_Bzero,\n", + " m_L=m_tau,\n", + " )\n", + " w_range = np.linspace(*rate.kinematics.w_range_numerical_stable)\n", + "\n", + " total_rate = rate.Gamma()\n", + " w_rate = [rate.dGamma_dw(w) / total_rate * (max(w_range) - min(w_range)) for w in w_range]\n", + "\n", + " ax.plot(w_range, unp.nominal_values(w_rate), label=f\"BLR, {pdg.get(dict_d[key]['pdg']).GetName()}\", ls=\"solid\")\n", + "\n", + " ax.set_xlim(1, max(w_range))\n", + "\n", + " ax.set_ylim(0, 3)\n", + "\n", + " ax.set_xlabel(r\"$w$\")\n", + "\n", + " ax.set_ylabel(r\"$1 / \\Gamma \\times \\mathrm{d} \\Gamma / \\mathrm{d}w$\")\n", + "\n", + " ax.legend(loc=\"upper left\", frameon=False, fontsize=\"x-small\", ncol=1)\n", + "\n", + " add_watermark(ax, px=0.01, py=1.05, fontsize=8)\n", + "\n", + " plt.tight_layout()\n", + "\n", + "plt.show()\n", + "plt.close()" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "id": "7afe4b10", + "metadata": {}, + "outputs": [], + "source": [] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Belle2 (light-2311-nebelung)", + "language": "python", + "name": "belle2_light-2311-nebelung" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.8" + } + }, + "nbformat": 4, + "nbformat_minor": 5 +} diff --git a/effort2/formfactors/BLR.py b/effort2/formfactors/BLR.py new file mode 100644 index 0000000..28f43e0 --- /dev/null +++ b/effort2/formfactors/BLR.py @@ -0,0 +1,555 @@ +from ast import Lambda +import numpy as np +from effort2.formfactors.DStStAlphaSCorrections import DStStAlphaSCorrections + + +class BToDStarStarBroad(DStStAlphaSCorrections): + """ + A class to compute the form factors for the two broad D** states (D0* and D1') + """ + + def __init__( + self, + m_c: float=1.31, + m_b: float=4.71, + params: tuple=(0.70, 0.2, 0.6), + alphaS: float=0.26, + LambdaBar: float=0.40, + LambdaBarPrime: float=0.80, + LambdaBarStar: float=0.76, + chi1: float=0, + chi2: float=0, + ) -> None: + super().__init__(m_c, m_b) + self.m_c = m_c + self.m_b = m_b + self.alphaS = alphaS / np.pi + self.LambdaBar = LambdaBar + self.LambdaBarPrime = LambdaBarPrime + self.LambdaBarStar = LambdaBarStar + self.chi1 = chi1 + self.chi2 = chi2 + + self.Z1, self.zetap, self.zeta1 = self.set_model_parameters(params) + # Scale mu = sqrt(mc*mb) + # Certain values depend on renorm scheme + # The chromomagnetic terms chi1/2 are neglected in Hammer and certain Approximations. + # I'm not sure whether they should be set to 0 with the most up-to-date fit of the 3 zeta parameters. + + def set_model_parameters( + self, + params: tuple, + ): + """ + Sets the input model parameters zeta(1), zeta' and zeta1 (cf. Table V in arxiv:1711.03110). + Expects the parameters in that order. + + Args: + params ([tuple]): input parameters for the broad D** form factor. + """ + Z1, zetap, zeta1 = params + return Z1, zetap, zeta1 + + def Gb( + self, + w: float, + ): + """ + Used in all B -> D** broad form factors + """ + LambdaBar = self.LambdaBar + LambdaBarStar = self.LambdaBarStar + zeta1 = self.zeta1 + return ((1 + 2 * w) * LambdaBarStar - (2 + w) * LambdaBar) / (w + 1) - 2 * (w - 1) * zeta1 + + def gP( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarStar = self.LambdaBarStar + chi1 = self.chi1 + chi2 = self.chi2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + zeta1 = self.zeta1 + CP = self.CP(w) + Gb = self.Gb(w) + return (w - 1) * (1 + alphaS * CP) + epsilonC * (3 * (w * LambdaBarStar - LambdaBar) - 2 * (w**2 - 1) * zeta1 + (w -1) * (6 * chi1 - 2 * (w + 1) * chi2)) - epsilonB * (w + 1) * Gb + + def gplus( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarStar = self.LambdaBarStar + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + zeta1 = self.zeta1 + CA2 = self.CA2(w) + CA3 = self.CA3(w) + Gb = self.Gb(w) + return 0.5 * alphaS * (w - 1) * (CA2 + CA3) - epsilonC * (3 * (w * LambdaBarStar - LambdaBar) / (w + 1) - 2 * (w - 1) * zeta1) - epsilonB * Gb + + def gminus( + self, + w: float, + ): + alphaS = self.alphaS + epsilonC = 1 / (2 * self.m_c) + chi1 = self.chi1 + chi2 = self.chi2 + CA1 = self.CA1(w) + CA2 = self.CA2(w) + CA3 = self.CA3(w) + return 1 + alphaS * (CA1 + 0.5 * (w - 1) * (CA2 - CA3)) + epsilonC * (6 * chi1 - 2 * (w + 1) * chi2) + + def gT( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarStar = self.LambdaBarStar + chi1 = self.chi1 + chi2 = self.chi2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + zeta1 = self.zeta1 + Gb = self.Gb(w) + CT1 = self.CT1(w) + return 1 + alphaS * CT1 + epsilonC * (3 * (w * LambdaBarStar - LambdaBar) / (w + 1) - 2 * (w - 1) * zeta1 + 6 * chi1 - 2 * (w + 1) * chi2) - epsilonB * Gb + + def gS( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarStar = self.LambdaBarStar + chi1 = self.chi1 + chi2 = self.chi2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + zeta1 = self.zeta1 + Gb = self.Gb(w) + CS = self.CS(w) + return 1 + alphaS * CS - epsilonC * ((w * LambdaBarStar - LambdaBar) / (w + 1) - 2 * (w - 1) * zeta1 + 2 * chi1 - 2 * (w + 1) * chi2) - epsilonB * Gb + + def gV1( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarStar = self.LambdaBarStar + chi1 = self.chi1 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + Gb = self.Gb(w) + CV1 = self.CV1(w) + return (w - 1) * (1 + alphaS * CV1) + epsilonC * (w * LambdaBarStar - LambdaBar - 2 * (w - 1) * chi1) - epsilonB * (w + 1) * Gb + + def gV2( + self, + w: float, + ): + alphaS = self.alphaS + chi2 = self.chi2 + epsilonC = 1 / (2 * self.m_c) + zeta1 = self.zeta1 + CV2 = self.CV2(w) + return - alphaS * CV2 + 2 * epsilonC * (zeta1 - chi2) + + def gV3( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarStar = self.LambdaBarStar + chi1 = self.chi1 + chi2 = self.chi2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + zeta1 = self.zeta1 + Gb = self.Gb(w) + CV1 = self.CV1(w) + CV3 = self.CV3(w) + return -1 - alphaS * (CV1 + CV3) - epsilonC * ((w * LambdaBarStar - LambdaBar) / (w + 1) + 2 * (zeta1 - chi1 + chi2)) + epsilonB * Gb + + def gA( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarStar = self.LambdaBarStar + chi1 = self.chi1 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + Gb = self.Gb(w) + CA1 = self.CA1(w) + return 1 + alphaS * CA1 + epsilonC * ((w * LambdaBarStar - LambdaBar) / (w + 1) - 2 * chi1) - epsilonB * Gb + + def gT1( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarStar = self.LambdaBarStar + chi1 = self.chi1 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + Gb = self.Gb(w) + CT1 = self.CT1(w) + CT2 = self.CT2(w) + return -1 - alphaS * (CT1 + (w - 1) * CT2) + epsilonC * ((w * LambdaBarStar - LambdaBar) / (w + 1) + 2 * chi1) + epsilonB * Gb + + def gT2( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarStar = self.LambdaBarStar + chi1 = self.chi1 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + Gb = self.Gb(w) + CT1 = self.CT1(w) + CT3 = self.CT3(w) + return 1 + alphaS * (CT1 - (w - 1) * CT3) + epsilonC * ((w * LambdaBarStar - LambdaBar) / (w + 1) - 2 * chi1) + epsilonB * Gb + + def gT3( + self, + w: float, + ): + alphaS = self.alphaS + zeta1 = self.zeta1 + chi2 = self.chi2 + epsilonC = 1 / (2 * self.m_c) + CT2 = self.CT2(w) + return -alphaS * CT2 + 2 * epsilonC * (zeta1 + chi2) + + +class BToDStarStarNarrow(DStStAlphaSCorrections): + """ + A class to compute the form factors for the two narrow D** states (D1 and D2) + """ + + def __init__( + self, + m_c: float=1.31, + m_b: float=4.71, + params: tuple=(0.70, -1.6, -0.5, 2.9), + alphaS: float=0.26, + LambdaBar: float=0.40, + LambdaBarPrime: float=0.80, + LambdaBarStar: float=0.76, + eta1: float=0, + eta2: float=0, + eta3: float=0, + ): + super().__init__(m_c, m_b) + self.m_c = m_c + self.m_b = m_b + self.alphaS = alphaS / np.pi + self.LambdaBar = LambdaBar + self.LambdaBarPrime = LambdaBarPrime + self.LambdaBarStar = LambdaBarStar + self.eta1 = eta1 + self.eta2 = eta2 + self.eta3 = eta3 + + self.T1, self.taup, self.tau1, self.tau2 = self.set_model_parameters(params) + + def set_model_parameters( + self, + params: tuple, + ): + """ + Sets the input model parameters tau(1), tau', tau1 and tau2 (cf. Table V in arxiv:1711.03110). + Expects the parameters in that order. + + Args: + params ([tuple]): input parameters for the narrow D** form factor. + """ + T1, taup, tau1, tau2 = params + return T1, taup, tau1, tau2 + + def Fb( + self, + w: float, + ): + LambdaBar = self.LambdaBar + LambdaBarStar = self.LambdaBarStar + tau1 = self.tau1 + tau2 = self.tau2 + return LambdaBar + LambdaBarStar - (2 * w + 1) * tau1 - tau2 + + # Form factors for D1 + # The f form factors have to be multiplied by sqrt(6) + def fS( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarPrime = self.LambdaBarPrime + tau1 = self.tau1 + tau2 = self.tau2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + eta1 = self.eta1 + eta2 = self.eta2 + eta3 = self.eta3 + Fb = self.Fb(w) + CS = self.CS(w) + return -2 * (w + 1) * (1 + alphaS * CS) - 2 * epsilonB * (w - 1) * Fb - epsilonC * (4 * (w * LambdaBarPrime - LambdaBar) - 2 * (w - 1) * ((2 * w + 1) * tau1 + tau2) + 2 * (w + 1) * (6 * eta1 + 2 * (w - 1) * eta2 - eta3)) + + def fV1( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarPrime = self.LambdaBarPrime + tau1 = self.tau1 + tau2 = self.tau2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + eta1 = self.eta1 + eta3 = self.eta3 + Fb = self.Fb(w) + CV1 = self.CV1(w) + return (1 - w**2) * (1 + alphaS * CV1) - epsilonB * (w**2 - 1) * Fb - epsilonC * (4 * (w + 1) * (w * LambdaBarPrime - LambdaBar) - (w**2 - 1) * (3 * tau1 - 3 * tau2 + 2 * eta1 + 3 * eta3)) + + def fV2( + self, + w: float, + ): + alphaS = self.alphaS + tau1 = self.tau1 + tau2 = self.tau2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + eta1 = self.eta1 + eta2 = self.eta2 + eta3 = self.eta3 + Fb = self.Fb(w) + CV1 = self.CV1(w) + CV2 = self.CV2(w) + return -3 - alphaS * (3 * CV1 + 2 * (w + 1) * CV2) - 3 * epsilonB * Fb - epsilonC * ((4 * w - 1) * tau1 + 5 * tau2 + 10 * eta1 + 4 * (w - 1) * eta2 - 5 * eta3) + + def fV3( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarPrime = self.LambdaBarPrime + tau1 = self.tau1 + tau2 = self.tau2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + eta1 = self.eta1 + eta2 = self.eta2 + eta3 = self.eta3 + Fb = self.Fb(w) + CV1 = self.CV1(w) + CV3 = self.CV3(w) + return w - 2 - alphaS * ((2 - w) * CV1 + 2 * (w + 1) * CV3) + epsilonB * (w + 2) * Fb + epsilonC * (4 * (w * LambdaBarPrime - LambdaBar) + (w + 2)* tau1 + (2 + 3 * w) * tau2 - 2 * (w + 6) * eta1 - 4 * (w - 1) * eta2 - (3 * w - 2) * eta3) + + def fA( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarPrime = self.LambdaBarPrime + tau1 = self.tau1 + tau2 = self.tau2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + eta1 = self.eta1 + eta3 = self.eta3 + Fb = self.Fb(w) + CA1 = self.CA1(w) + return -(w + 1) * (1 + alphaS * CA1) - epsilonB * (w - 1) * Fb - epsilonC * (4 * (w * LambdaBarPrime - LambdaBar) - 3 * (w - 1) * (tau1 - tau2) - (w + 1) * (2 * eta1 + 3 * eta3)) + + def fT1( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarPrime = self.LambdaBarPrime + tau1 = self.tau1 + tau2 = self.tau2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + eta1 = self.eta1 + eta3 = self.eta3 + Fb = self.Fb(w) + CT1 = self.CT1(w) + CT2 = self.CT2(w) + return (w + 1) * (1 + alphaS * (CT1 + (w - 1) * CT2)) + epsilonB * (w - 1) * Fb - epsilonC * (4 * (w * LambdaBarPrime - LambdaBar) - 3 * (w - 1) * (tau1 - tau2) + (w + 1) * (2 * eta1 + 3 * eta3)) + + def fT2( + self, + w: float, + ): + alphaS = self.alphaS + LambdaBar = self.LambdaBar + LambdaBarPrime = self.LambdaBarPrime + tau1 = self.tau1 + tau2 = self.tau2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + eta1 = self.eta1 + eta2 = self.eta2 + eta3 = self.eta3 + Fb = self.Fb(w) + CT1 = self.CT1(w) + CT3 = self.CT3(w) + return -(w + 1) * (1 + alphaS * (CT1 - (w - 1) * CT3)) + epsilonB * (w - 1) * Fb - epsilonC * (4 * (w * LambdaBarPrime - LambdaBar) - 3 * (w - 1) * (tau1 - tau2) - (w + 1) * (2 * eta1 + 3 * eta3)) + + def fT3( + self, + w: float, + ): + alphaS = self.alphaS + tau1 = self.tau1 + tau2 = self.tau2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + eta1 = self.eta1 + eta2 = self.eta2 + eta3 = self.eta3 + Fb = self.Fb(w) + CT1 = self.CT1(w) + CT2 = self.CT2(w) + CT3 = self.CT3(w) + return 3 + alphaS * (3 * CT1 - (2 - w) * CT2 + 3 * CT3) + 3 * epsilonB * Fb - epsilonC * ((4 * w - 1) * tau1 + 5 * tau2 - 10 * eta1 - 4 * (w - 1) * eta2 + 5 * eta3) + + + # Form factors for D2* + def kP( + self, + w: float, + ): + alphaS = self.alphaS + tau1 = self.tau1 + tau2 = self.tau2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + eta1 = self.eta1 + eta2 = self.eta2 + eta3 = self.eta3 + Fb = self.Fb(w) + CP = self.CP(w) + return 1 + alphaS * CP + epsilonB * Fb + epsilonC * ((2 * w + 1) * tau1 + tau2 - 2 * eta1 - 2 * (w - 1) * eta2 + eta3) + + def kV( + self, + w: float, + ): + alphaS = self.alphaS + tau1 = self.tau1 + tau2 = self.tau2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + eta1 = self.eta1 + eta3 = self.eta3 + Fb = self.Fb(w) + CV1 = self.CV1(w) + return -1 - alphaS * CV1 - epsilonB * Fb - epsilonC * (tau1 - tau2 - 2 * eta1 + eta3) + + def kA1( + self, + w: float, + ): + alphaS = self.alphaS + tau1 = self.tau1 + tau2 = self.tau2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + eta1 = self.eta1 + eta3 = self.eta3 + Fb = self.Fb(w) + CA1 = self.CA1(w) + return -(w + 1) * (1 + alphaS * CA1) - epsilonB * (w - 1) * Fb - epsilonC * ((w - 1) * (tau1 - tau2) - (w + 1) * (2 * eta1 - eta3)) + + def kA2( + self, + w: float, + ): + alphaS = self.alphaS + tau1 = self.tau1 + epsilonC = 1 / (2 * self.m_c) + eta2 = self.eta2 + CA2 = self.CA2(w) + return alphaS * CA2 - 2 * epsilonC * (tau1 + eta2) + + def kA3( + self, + w: float, + ): + alphaS = self.alphaS + tau1 = self.tau1 + tau2 = self.tau2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + eta1 = self.eta1 + eta2 = self.eta2 + eta3 = self.eta3 + Fb = self.Fb(w) + CA1 = self.CA1(w) + CA3 = self.CA3(w) + return 1 + alphaS * (CA1 + CA3) + epsilonB * Fb - epsilonC * (tau1 + tau2 + 2 * eta1 - 2 * eta2 - eta3) + + def kT1( + self, + w: float, + ): + alphaS = self.alphaS + epsilonC = 1 / (2 * self.m_c) + eta1 = self.eta1 + eta3 = self.eta3 + CT1 = self.CT1(w) + CT2 = self.CT2(w) + CT3 = self.CT3(w) + return 1 + alphaS * (CT1 + 0.5 * (w - 1) * (CT2 - CT3)) - epsilonC * (2 * eta1 - eta3) + + def kT2( + self, + w: float, + ): + alphaS = self.alphaS + tau1 = self.tau1 + tau2 = self.tau2 + epsilonC = 1 / (2 * self.m_c) + epsilonB = 1 / (2 * self.m_b) + Fb = self.Fb(w) + CT2 = self.CT2(w) + CT3 = self.CT3(w) + return 0.5 * alphaS * (w + 1) * (CT2 + CT3) + epsilonB * Fb - epsilonC * (tau1 - tau2) + + def kT3( + self, + w: float, + ): + alphaS = self.alphaS + tau1 = self.tau1 + epsilonC = 1 / (2 * self.m_c) + eta2 = self.eta2 + CT2 = self.CT2(w) + return -alphaS * CT2 + 2 * epsilonC * (tau1 - eta2) + + +if __name__ == "__main__": + pass diff --git a/effort2/formfactors/DStStAlphaSCorrections.py b/effort2/formfactors/DStStAlphaSCorrections.py new file mode 100644 index 0000000..5ba75b9 --- /dev/null +++ b/effort2/formfactors/DStStAlphaSCorrections.py @@ -0,0 +1,154 @@ +import numpy as np +from effort2.math.functions import diLog + + +class DStStAlphaSCorrections: + """ + Class to compute the C functions used in the BLR model for B -> D** form factors. + Taken from Phys. Rev. D 95, 115008 Appendix A. + """ + + def __init__( + self, + m_c: float, + m_b: float, + ) -> None: + self.z = m_c / m_b + self.wz = 0.5 * (self.z + 1 / self.z) + + + def r( + self, + w: float, + ): + wp = w + np.sqrt(w**2 - 1) + return np.log(wp) / np.sqrt(w**2 - 1) + + + def Omega( + self, + w: float, + ): + z = self.z + r = self.r(w) + wp = w + np.sqrt(w**2 - 1) + wm = w - np.sqrt(w**2 - 1) + return w / (2 * np.sqrt(w**2 - 1)) * (2 * diLog(1 - wm * z) - 2 * diLog(1 - wp * z) + diLog(1 - wp**2) - diLog(1 - wm**2)) - w * r * np.log(z) + 1 + + + def CS( + self, + w: float, + ): + z = self.z + wz = self.wz + r = self.r(w) + Omega = self.Omega(w) + return 1 / (3 * z * (w - wz)) * (2 * z * (w - wz) * Omega - (w - 1) * (z + 1) * (z + 1) * r + (z**2 -1) * np.log(z)) + + + def CP( + self, + w: float, + ): + z = self.z + wz = self.wz + r = self.r(w) + Omega = self.Omega(w) + return 1 / (3 * z * (w - wz)) * (2 * z * (w - wz) * Omega - (w + 1) * (z - 1) * (z - 1) * r + (z**2 -1) * np.log(z)) + + + def CV1( + self, + w: float, + ): + z = self.z + wz = self.wz + r = self.r(w) + Omega = self.Omega(w) + return 1 / (6 * z * (w - wz)) * (2 * (w + 1) * ((3 * w - 1) * z - z**2 - 1) * r + (12 * z * (wz - w) - (z**2 - 1) * np.log(z)) + 4 * z * (w - wz) * Omega) + + def CV2( + self, + w: float, + ): + z = self.z + wz = self.wz + r = self.r(w) + return -1 / (6 * z**2 * (w - wz) * (w - wz)) * (((4 * w**2 + 2 * w) * z**2 - (2 * w**2 + 5 * w -1) * z - (w + 1) * z**3 + 2) * r + z * ( 2 * (z - 1) * (wz - w) + (z**2 - (4 * w - 2) * z + (3 - 2 * w)) * np.log(z))) + + + def CV3( + self, + w: float, + ): + z = self.z + wz = self.wz + r = self.r(w) + return 1 / (6 * z * (w - wz) * (w - wz)) * (((2 * w**2 + 5 * w - 1) * z**2 - (4 * w**2 + 2 * w) * z - 2 * z**3 + w + 1) * r + (2 * z * (z - 1) * (wz - w) + ((3 - 2 * w) * z**2 + (2 - 4 * w) * z + 1) * np.log(z))) + + + def CA1( + self, + w: float, + ): + z = self.z + wz = self.wz + r = self.r(w) + Omega = self.Omega(w) + return 1 / (6 * z * (w - wz)) * (2 * (w - 1) * ((3 * w + 1) * z - z**2 - 1) * r + (12 * z * (wz - w) - (z**2 - 1) * np.log(z)) + 4 * z * (w - wz) * Omega) + + + def CA2( + self, + w: float, + ): + z = self.z + wz = self.wz + r = self.r(w) + return -1 / (6 * z**2 * (w - wz) * (w - wz)) * (((4 * w**2 - 2 * w) * z**2 - (2 * w**2 - 5 * w -1) * z - (w - 1) * z**3 + 2) * r + z * ( 2 * (z + 1) * (wz - w) + (z**2 - (4 * w + 2) * z + (3 + 2 * w)) * np.log(z))) + + + def CA3( + self, + w: float, + ): + z = self.z + wz = self.wz + r = self.r(w) + return 1 / (6 * z * (w - wz) * (w - wz)) * ((2 * z**3 + (2 * w**2 - 5 * w -1) * z**2 + (4 * w**2 - 2 * w) * z - w + 1) * r + (2 * z * (z + 1) * (wz - w) - ((2 * w + 3) * z**2 - (4 * w + 2) * z + 1) * np.log(z))) + + + def CT1( + self, + w: float, + ): + z = self.z + wz = self.wz + r = self.r(w) + Omega = self.Omega(w) + return 1 / (3 * z * (w - wz)) * ((w - 1) * ((4 * w + 2) * z - z**2 - 1) * r + (6 * z * (wz - w) - (z**2 - 1) * np.log(z)) + 2 * z * (w - wz) * Omega) + + + def CT2( + self, + w: float, + ): + z = self.z + wz = self.wz + r = self.r(w) + return 2 / (3 * z * (w - wz)) * ((1 - w * z) * r + z * np.log(z)) + + + def CT3( + self, + w: float, + ): + z = self.z + wz = self.wz + r = self.r(w) + return 2 / (3 * (w - wz)) * ((w - z) * r + np.log(z)) + + +if __name__ == "__main__": + pass diff --git a/effort2/rates/BtoDStSt.py b/effort2/rates/BtoDStSt.py new file mode 100644 index 0000000..0cfdd44 --- /dev/null +++ b/effort2/rates/BtoDStSt.py @@ -0,0 +1,355 @@ +# dGamma/dw can be found in arxiv:1711.03110 +# dGamma/dwdcosTheta can be found in arxiv:1606:09300 + +import numpy as np +from effort2.formfactors.kinematics import Kinematics +from effort2.formfactors.BLR import BToDStarStarBroad, BToDStarStarNarrow +from effort2.math.integrate import quad + + +class BtoD0St(BToDStarStarBroad): + + def __init__( + self, + Vcb: float, + m_D: float, + m_B: float, + m_L:float=0, + G_F: float=1.1663787e-5, + m_c: float=1.31, + m_b: float=4.71, + params: tuple=(0.70, 0.2, 0.6), + alphaS: float=0.26, + LambdaBar: float=0.40, + LambdaBarPrime: float=0.80, + LambdaBarStar: float=0.76, + chi1: float=0, + chi2: float=0, + ) -> None: + + super().__init__( + m_c, + m_b, + params, + alphaS, + LambdaBar, + LambdaBarPrime, + LambdaBarStar, + chi1, + chi2, + ) + self.m_c = m_c + self.m_b = m_b + self.alphaS = alphaS / np.pi + self.LambdaBar = LambdaBar + self.LambdaBarPrime = LambdaBarPrime + self.LambdaBarStar = LambdaBarStar + self.chi1 = chi1 + self.chi2 = chi2 + + self.Z1, self.zetap, self.zeta1 = self.set_model_parameters(params) + + self.rm = m_D / m_B + self.rho = (m_L / m_B)**2 + + self.Gamma0 = (G_F**2 * Vcb**2 * m_B**5) / (192 * np.pi**3) + + self.kinematics = Kinematics(m_B, m_D, m_L) + self.w_min, self.w_max = self.kinematics.w_range_numerical_stable + + + def q2( + self, + w: float, + ): + rm = self.rm + return 1 + rm**2 - 2 * rm * w + + def dGamma_dw( + self, + w: float, + ) -> float: + Gamma0 = self.Gamma0 + rho = self.rho + rm = self.rm + q2 = self.q2(w) + zeta = self.Z1 * (1 + self.zetap * (w - 1)) # LO expansion of IW functions: Equation (36) in arxiv:1711.03110 + gminus = self.gminus(w) * zeta + gplus = self.gplus(w) * zeta + return 4 * Gamma0 * rm**3 * np.sqrt(w**2 - 1) * (q2 - rho)**2 / q2**3 * (gminus**2 * (w - 1) * (rho *((1 + rm**2) * (2 * w - 1) + 2 * rm * (w - 2)) + (1 - rm)**2 * (w + 1) * q2) + gplus**2 * (w + 1) * (rho * ((1 + rm**2) * (2 * w + 1) - 2 * rm * (w + 2)) + (1 + rm)**2 * (w - 1) * q2) - 2 * gminus * gplus * (1 - rm**2) * (w**2 - 1) * (q2 + 2 * rho)) + + def Gamma( + self, + wmin: float=None, + wmax: float=None, + ) -> float: + wmin = self.w_min if wmin is None else wmin + wmax = self.w_max if wmax is None else wmax + assert self.w_min <= wmin < wmax <= self.w_max, f"{wmin}, {wmax}" + + return quad(lambda w: self.dGamma_dw(w), wmin, wmax)[0] + + +class BtoD1St(BToDStarStarBroad): + + def __init__( + self, + Vcb: float, + m_D: float, + m_B: float, + m_L:float=0, + G_F: float=1.1663787e-5, + m_c: float=1.31, + m_b: float=4.71, + params: tuple=(0.70, 0.2, 0.6), + alphaS: float=0.26, + LambdaBar: float=0.40, + LambdaBarPrime: float=0.80, + LambdaBarStar: float=0.76, + chi1: float=0, + chi2: float=0, + ) -> None: + + super().__init__( + m_c, + m_b, + params, + alphaS, + LambdaBar, + LambdaBarPrime, + LambdaBarStar, + chi1, + chi2, + ) + self.m_c = m_c + self.m_b = m_b + self.alphaS = alphaS / np.pi + self.LambdaBar = LambdaBar + self.LambdaBarPrime = LambdaBarPrime + self.LambdaBarStar = LambdaBarStar + self.chi1 = chi1 + self.chi2 = chi2 + + self.Z1, self.zetap, self.zeta1 = self.set_model_parameters(params) + + self.rm = m_D / m_B + self.rho = (m_L / m_B)**2 + + self.Gamma0 = (G_F**2 * Vcb**2 * m_B**5) / (192 * np.pi**3) + + self.kinematics = Kinematics(m_B, m_D, m_L) + self.w_min, self.w_max = self.kinematics.w_range_numerical_stable + + + def q2( + self, + w: float, + ): + rm = self.rm + return 1 + rm**2 - 2 * rm * w + + def dGamma_dw( + self, + w: float, + ) -> float: + Gamma0 = self.Gamma0 + rho = self.rho + rm = self.rm + q2 = self.q2(w) + zeta = self.Z1 * (1 + self.zetap * (w - 1)) # LO expansion of IW functions: Equation (36) in arxiv:1711.03110 + gV1 = self.gV1(w) * zeta + gV2 = self.gV2(w) * zeta + gV3 = self.gV3(w) * zeta + gA = self.gA(w) * zeta + return 2 * Gamma0 * rm**3 * np.sqrt(w**2 - 1) * (q2 - rho)**2 / q2**3 * (gV1**2 * (2 * q2 * ((w - rm)**2 + 2 * q2) + rho * (4 * (w - rm)**2 - q2)) + (w**2 - 1) * (gV2**2 * (2 * rm**2 * q2 * (w**2 - 1) + rho * (3 * q2 + 4 * rm**2 * (w**2 - 1))) + gV3**2 * (2 * q2 * (w**2 - 1) + rho * (4 * (w - rm)**2 - q2)) + 2 * gA**2 * q2 * (2 * q2 + rho) + 2 * gV1 * gV2 * (2 * rm * q2 * (w - rm) + rho * (3 - rm**2 - 2 * rm * w)) + 4 * gV1 * gV3 * (w - rm) * (q2 + 2 * rho) + 2 * gV2 * gV3 * (2 * rm * q2 * (w**2 - 1) + rho * (3 * w * q2 + 4 * rm * (w**2 - 1))))) + + def Gamma( + self, + wmin: float=None, + wmax: float=None, + ) -> float: + wmin = self.w_min if wmin is None else wmin + wmax = self.w_max if wmax is None else wmax + assert self.w_min <= wmin < wmax <= self.w_max, f"{wmin}, {wmax}" + + return quad(lambda w: self.dGamma_dw(w), wmin, wmax)[0] + + +class BtoD1(BToDStarStarNarrow): + + def __init__( + self, + Vcb: float, + m_D: float, + m_B: float, + m_L:float=0, + G_F: float=1.1663787e-5, + m_c: float=1.31, + m_b: float=4.71, + params: tuple=(0.70, -1.6, -0.5, 2.9), + alphaS: float=0.26, + LambdaBar: float=0.40, + LambdaBarPrime: float=0.80, + LambdaBarStar: float=0.76, + eta1: float=0, + eta2: float=0, + eta3: float=0, + ) -> None: + + super().__init__( + m_c, + m_b, + params, + alphaS, + LambdaBar, + LambdaBarPrime, + LambdaBarStar, + eta1, + eta2, + eta3, + ) + self.m_c = m_c + self.m_b = m_b + self.alphaS = alphaS / np.pi + self.LambdaBar = LambdaBar + self.LambdaBarPrime = LambdaBarPrime + self.LambdaBarStar = LambdaBarStar + self.eta1 = eta1 + self.eta2 = eta2 + self.eta3 = eta3 + + self.T1, self.taup, self.tau1, self.tau2 = self.set_model_parameters(params) + + self.rm = m_D / m_B + self.rho = (m_L / m_B)**2 + + self.Gamma0 = (G_F**2 * Vcb**2 * m_B**5) / (192 * np.pi**3) + + self.kinematics = Kinematics(m_B, m_D, m_L) + self.w_min, self.w_max = self.kinematics.w_range_numerical_stable + + + def q2( + self, + w: float, + ): + rm = self.rm + return 1 + rm**2 - 2 * rm * w + + def dGamma_dw( + self, + w: float, + ) -> float: + Gamma0 = self.Gamma0 + rho = self.rho + rm = self.rm + q2 = self.q2(w) + tau = self.T1 * (1 + self.taup * (w - 1)) # LO expansion of IW functions: Equation (36) in arxiv:1711.03110 + fV1 = self.fV1(w) * tau + fV2 = self.fV2(w) * tau + fV3 = self.fV3(w) * tau + fA = self.fA(w) * tau + return 2 * Gamma0 * rm**3 * np.sqrt(w**2 - 1) * (q2 - rho)**2 / q2**3 * (fV1**2 * (2 * q2 * ((w - rm)**2 + 2 * q2) + rho * (4 * (w - rm)**2 - q2)) + (w**2 - 1) * (fV2**2 * (2 * rm**2 * q2 * (w**2 - 1) + rho * (3 * q2 + 4 * rm**2 * (w**2 - 1))) + fV3**2 * (2 * q2 * (w**2 - 1) + rho * (4 * (w - rm)**2 - q2)) + 2 * fA**2 * q2 * (2 * q2 + rho) + 2 * fV1 * fV2 * (2 * rm * q2 * (w - rm) + rho * (3 - rm**2 - 2 * rm * w)) + 4 * fV1 * fV3 * (w - rm) * (q2 + 2 * rho) + 2 * fV2 * fV3 * (2 * rm * q2 * (w**2 - 1) + rho * (3 * w * q2 + 4 * rm * (w**2 - 1))))) + + def Gamma( + self, + wmin: float=None, + wmax: float=None, + ) -> float: + wmin = self.w_min if wmin is None else wmin + wmax = self.w_max if wmax is None else wmax + assert self.w_min <= wmin < wmax <= self.w_max, f"{wmin}, {wmax}" + + return quad(lambda w: self.dGamma_dw(w), wmin, wmax)[0] + + +class BtoD2St(BToDStarStarNarrow): + + def __init__( + self, + Vcb: float, + m_D: float, + m_B: float, + m_L:float=0, + G_F: float=1.1663787e-5, + m_c: float=1.31, + m_b: float=4.71, + params: tuple=(0.70, -1.6, -0.5, 2.9), + alphaS: float=0.26, + LambdaBar: float=0.40, + LambdaBarPrime: float=0.80, + LambdaBarStar: float=0.76, + eta1: float=0, + eta2: float=0, + eta3: float=0, + ) -> None: + + super().__init__( + m_c, + m_b, + params, + alphaS, + LambdaBar, + LambdaBarPrime, + LambdaBarStar, + eta1, + eta2, + eta3, + ) + self.m_c = m_c + self.m_b = m_b + self.alphaS = alphaS / np.pi + self.LambdaBar = LambdaBar + self.LambdaBarPrime = LambdaBarPrime + self.LambdaBarStar = LambdaBarStar + self.eta1 = eta1 + self.eta2 = eta2 + self.eta3 = eta3 + + self.T1, self.taup, self.tau1, self.tau2 = self.set_model_parameters(params) + + self.rm = m_D / m_B + self.rho = (m_L / m_B)**2 + + self.Gamma0 = (G_F**2 * Vcb**2 * m_B**5) / (192 * np.pi**3) + + self.kinematics = Kinematics(m_B, m_D, m_L) + self.w_min, self.w_max = self.kinematics.w_range_numerical_stable + + + def q2( + self, + w: float, + ): + rm = self.rm + return 1 + rm**2 - 2 * rm * w + + def dGamma_dw( + self, + w: float, + ) -> float: + Gamma0 = self.Gamma0 + rho = self.rho + rm = self.rm + q2 = self.q2(w) + tau = self.T1 * (1 + self.taup * (w - 1)) # LO expansion of IW functions: Equation (36) in arxiv:1711.03110 + kA1 = self.kA1(w) * tau + kA2 = self.kA2(w) * tau + kA3 = self.kA3(w) * tau + kV = self.kV(w) * tau + return (2/3) * Gamma0 * rm**3 * (w**2 - 1)**(3/2) * (q2 - rho)**2 / q2**3 * (kA1**2 * (2 * q2 * (2 * (w - rm)**2 + 3 * q2) + rho * (8 * (w - rm)**2 - 3 * q2)) + 2 * (w**2 - 1) * (kA2**2 * (2 * rm**2 * q2 * (w**2 - 1) + rho * (3 * q2 + 4 * rm**2 * (w**2 - 1))) + kA3**2 * (2 * q2 * (w**2 - 1) + rho * (4 * (w - rm)**2 - q2)) + 3 * kV**2 * q2 * (q2 + rho/2) + 2 * kA1 * kA2 * (2 * rm * q2 * (w - rm) + rho * (3 - rm**2 - 2 * rm * w)) + 4 * kA1 * kA3 * (w - rm) * (q2 + 2 * rho) + 2 * kA2 * kA3 * (2 * rm * q2 * (w**2 - 1) + rho * (3 * w * q2 + 4 * rm * (w**2 - 1))))) + + def Gamma( + self, + wmin: float=None, + wmax: float=None, + ) -> float: + wmin = self.w_min if wmin is None else wmin + wmax = self.w_max if wmax is None else wmax + assert self.w_min <= wmin < wmax <= self.w_max, f"{wmin}, {wmax}" + + return quad(lambda w: self.dGamma_dw(w), wmin, wmax)[0] + + +if __name__ == "__main__": + pass