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   "source": [
    "# Strong Coupling"
   ]
  },
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   "id": "b01c5ee6-2afa-49a5-9fb4-3812db491b1a",
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    "`eko` can be used to compute the value of the strong coupling at a given scale, \n",
    "in this tutorial we show how to do it.\n",
    "\n",
    "In `eko` the running of $\\alpha_s$ is managed by an independent class `eko.couplings.Couplings`.\n",
    "\n",
    "To instantiate this object you need to specify at least the boundary conditions on $\\alpha_s(\\mu_{R,0})$ (`alphas`,`scale`), the masses of the heavy quarks with the relative thresholds ratios (`heavy_quark_masses`, `thresholds_ratios`), and the (QCD,QED) perturbative order (`order`).\n",
    "\n",
    "See [here](https://eko.readthedocs.io/en/latest/modules/eko/eko.html#eko.couplings.Couplings)\n",
    "for detailed API."
   ]
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   "source": [
    "import numpy as np\n",
    "\n",
    "from eko.couplings import Couplings\n",
    "from eko.quantities.couplings import CouplingEvolutionMethod, CouplingsInfo\n",
    "from eko.quantities.heavy_quarks import QuarkMassScheme\n",
    "\n",
    "# set the (alpha_s, alpha_em) reference values\n",
    "couplings_ref = CouplingsInfo(alphas=0.118, alphaem=0.007496252, ref=(91.0, 5))\n",
    "\n",
    "# set heavy quark masses and their threshold ratios\n",
    "heavy_quark_masses = np.power([1.51, 4.92, 172.0], 2)\n",
    "thresholds_ratios = np.array([1.0, 1.0, 1.0])\n",
    "\n",
    "# set (QCD,QED) perturbative order\n",
    "order = (3, 1)\n",
    "\n",
    "sc = Couplings(\n",
    "    couplings_ref,\n",
    "    order,\n",
    "    CouplingEvolutionMethod.EXACT,\n",
    "    heavy_quark_masses,\n",
    "    QuarkMassScheme.POLE,\n",
    "    thresholds_ratios,\n",
    ")"
   ]
  },
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   "source": [
    "Now evaluating $\\alpha_s$ at different scale it's rather simple, \n",
    "as you just need to call the method `eko.couplings.Couplings.a_s`.\n",
    "\n",
    "**Warning**: this will return the value of $a_s$, but the class takes $\\alpha_s$ as input! "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8b908bb3-cbcc-4d7f-b631-27f1f37464f8",
   "metadata": {
    "tags": []
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   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "The value of alpha_s at Q^2=100 GeV^2 is:  0.17804304498411003\n"
     ]
    }
   ],
   "source": [
    "target_scale = 10.0**2\n",
    "a_s = sc.a_s(target_scale)\n",
    "print(\"The value of alpha_s at Q^2=100 GeV^2 is: \", 4.0 * np.pi * a_s)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "39977ebc",
   "metadata": {},
   "source": [
    "You can read more about the strong coupling running in the relative [documentation](https://eko.readthedocs.io/en/latest/theory/pQCD.html#strong-coupling)\n",
    "\n",
    "To see how the flavor path are sorted, you can read [this page](https://eko.readthedocs.io/en/latest/code/Utilities.html)"
   ]
  }
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