fpi-fK new.ipynb

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  {
   "cell_type": "markdown",
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   "source": [
    "# $f_\\pi$-$f_K$\n",
    "\n",
    "The idea is to use $f_\\pi$ from FLAG without using data and then the $f_\\pi/f_K$ average to determine the $f_\\pi$-$f_K$ correlation\n",
    "\n",
    "FLAG 19:\n",
    "\n",
    "$$f_\\pi^\\pm=130.2(0.8)$$\n",
    "$$f_K^\\pm/f_\\pi^\\pm=1.1932(19)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([130.1994679 , 155.35374008]),\n",
       " array([0.800003  , 0.98593355]),\n",
       " 0.9680247482084436)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "N = 10000000\n",
    "\n",
    "fpi = np.random.normal(130.2, 0.8, N)\n",
    "rpiK = np.random.normal(1.1932, 0.0019, N)\n",
    "fK = fpi * rpiK\n",
    "\n",
    "mn = np.mean([fpi, fK], axis=1)\n",
    "cov = np.cov([fpi, fK])\n",
    "err = np.sqrt(np.diag(cov))\n",
    "corr = cov[0, 1] / err[0] / err[1]\n",
    "\n",
    "mn, err, corr"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([[1.        , 0.96802475],\n",
       "       [0.96802475, 1.        ]])"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cov / np.outer(err, err)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "r_check = np.random.multivariate_normal(mn, cov, N)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([130.19955211, 155.35393757]), array([0.80014574, 0.98598111]))"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean(r_check, axis=0), np.std(r_check, axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.1931987232851002, 0.0019000841634458055)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "_x = r_check[:, 1] / r_check[:, 0]\n",
    "np.mean(_x), np.std(_x)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Check in flavio"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "import flavio\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "par_r = flavio.default_parameters.get_random_all(size=100000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.1935458482977104, 0.0019292902546725911)"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = par_r['f_K+'] / par_r['f_pi+']\n",
    "np.mean(r), np.std(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1.1935424579239557, 0.0019221587127443874)"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "r = par_r['f_K0'] / par_r['f_pi0']\n",
    "np.mean(r), np.std(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.1935483870967742"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "0.1554/0.1302"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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