mirror of
https://github.com/vale981/bachelor_thesis
synced 2025-03-10 04:46:40 -04:00
75 lines
2 KiB
Python
75 lines
2 KiB
Python
"""
|
|
Implementation of the analytical cross section for q q_bar ->
|
|
gamma gamma
|
|
|
|
Author: Valentin Boettcher <hiro@protagon.space>
|
|
"""
|
|
|
|
import numpy as np
|
|
from scipy.constants import alpha
|
|
|
|
# NOTE: a more elegant solution would be a decorator
|
|
def energy_factor(charge, esp):
|
|
"""
|
|
Calculates the factor common to all other values in this module
|
|
|
|
Arguments:
|
|
esp -- center of momentum energy in GeV
|
|
charge -- charge of the particle in units of the elementary charge
|
|
"""
|
|
|
|
return charge**4*(alpha/esp)**2/6
|
|
|
|
|
|
def diff_xs(θ, charge, esp):
|
|
"""
|
|
Calculates the differential cross section as a function of the
|
|
azimuth angle θ in units of 1/GeV².
|
|
|
|
Arguments:
|
|
θ -- azimuth angle
|
|
esp -- center of momentum energy in GeV
|
|
charge -- charge of the particle in units of the elementary charge
|
|
"""
|
|
|
|
f = energy_factor(charge, esp)
|
|
return f*((np.cos(θ)**+1)/np.sin(θ)**2)
|
|
|
|
def diff_xs_eta(η, charge, esp):
|
|
"""
|
|
Calculates the differential cross section as a function of the
|
|
pseudo rapidity of the photons in units of 1/GeV^2.
|
|
|
|
Arguments:
|
|
η -- pseudo rapidity
|
|
esp -- center of momentum energy in GeV
|
|
charge -- charge of the particle in units of the elementary charge
|
|
"""
|
|
|
|
f = energy_factor(charge, esp)
|
|
return f*(2*np.cosh(η)**2 - 1)
|
|
|
|
def total_xs_eta(η, charge, esp):
|
|
"""
|
|
Calculates the total cross section as a function of the pseudo
|
|
rapidity of the photons in units of 1/GeV^2. If the rapditiy is
|
|
specified as a tuple, it is interpreted as an interval. Otherwise
|
|
the interval [-η, η] will be used.
|
|
|
|
Arguments:
|
|
η -- pseudo rapidity (tuple or number)
|
|
esp -- center of momentum energy in GeV
|
|
charge -- charge of the particle in units of the elementar charge
|
|
"""
|
|
|
|
f = energy_factor(charge, esp)
|
|
if not isinstance(η, tuple):
|
|
η = (-η, η)
|
|
|
|
if len(η) != 2:
|
|
raise ValueError('Invalid η cut.')
|
|
|
|
def F(x):
|
|
return np.tanh(x) - 2*x
|
|
|
|
return 2*np.pi*f*(F(η[0]) - F(η[1]))
|