mirror of
https://github.com/vale981/bachelor_thesis
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68 lines
2 KiB
Python
68 lines
2 KiB
Python
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"""
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Implementation of the analytical cross section for q q_bar ->
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γγ in the lab frame.
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Author: Valentin Boettcher <hiro@protagon.space>
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"""
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import numpy as np
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def energy_factor(e_proton, charge, x_1, x_2):
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"""Calculates the factor common to all other values in this module.
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:param e_proton: proton energy per beam
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:param charge: charge of the quark
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:param x_1: momentum fraction of the first quark
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:param x_2: momentum fraction of the second quark
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"""
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return charge ** 4 / (137.036 * e_proton) ** 2 / (24 * x_1 * x_2)
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def momenta(e_proton, x_1, x_2, cosθ):
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"""Given the Energy of the incoming protons `e_proton` and the
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momentum fractions `x_1` and `x_2` as well as the cosine of the
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azimuth angle of the first photon the 4-momenta of all particles
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are calculated.
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"""
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q_1 = e_proton * x_1 * np.array([1, 0, 0, 1])
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q_2 = e_proton * x_2 * np.array([1, 0, 0, -1])
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g_3 = (
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e_proton
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* x_1
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* x_2
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/ (2 * x_2 + (x_1 - x_2) * (1 - cosθ))
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* np.array([1, cosθ, 0, sinθ])
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)
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g_4 = q_1 + q_2 - g_3
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return q_1, q_2, g_3, g_4
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def diff_xs(e_proton, charge, cosθ, x_1, x_2):
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"""Calculates the differential cross section as a function of the
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cosine of the azimuth angle θ of one photon in units of 1/GeV².
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Here dΩ=d(cosθ)dφ
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:param e_proton: proton energy per beam [GeV]
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:param charge: charge of the quark
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:param x_1: momentum fraction of the first quark
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:param x_2: momentum fraction of the second quark
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:param cosθ: the angle
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:return: the differential cross section [GeV^{-2}]
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"""
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f = energy_factor(e_proton, charge, x_1, x_2)
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return (x_1 ** 2 * (1 - cosθ) ** 2 + x_2 ** 2 * (1 + cosθ) ** 2) / (
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(1 - cosθ ** 2) * (x_1 * (1 - cosθ) + x_2 * (1 + cosθ))
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)
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def t_channel_q2(e_proton, cosθ, x_1, x_2):
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p, _, p_tag, _ = momenta(e_proton, x_1, x_2, cosθ)
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q = (p - p_tag)
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return -minkowski_product(q, q)
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