import sympy
from equation_database.util.doc import bib, equation
# x_1 = sympy.Symbol('x_1')
# """quark momentum fraction"""
# x_2 = sympy.Symbol('x_2')
# """antiquark momentum fraction"""
#
# alpha_C = sympy.Symbol('alpha_C')
# """Colour charge"""
# alpha = sympy.Symbol('alpha')
# """Fine structure constant"""
# Q = sympy.Symbol('Q')
# """Mass of the electron pair (virtual photon)"""
#
# sum_e_q_squared = sympy.Symbol('sum_e_q_squared')
# """Sum of electric charges of quarks squared"""
#
# sigma_pt = sympy.Symbol('sigma_pt')
# """Parton cross section"""
#
# sigma = sympy.Symbol('sigma')
# """Cross section"""
[docs]
@equation()
def equation_2_8(
sigma_pt=sympy.Symbol("sigma_pt"),
alpha=sympy.Symbol("alpha"),
Q=sympy.Symbol("Q"),
sum_e_q_squared=sympy.Symbol("sum_e_q_squared"),
):
"""
Args:
sigma_pt: Parton cross section
alpha: Fine structure constant
Q: Mass of the electron pair (virtual photon)
sum_e_q_squared: Sum of electric charges of quarks squared
"""
return sympy.Eq(sigma_pt, 4 * sympy.pi * alpha**2 / Q**2 * sum_e_q_squared)
[docs]
@equation()
def equation_2_9(
sigma=sympy.Symbol("sigma"),
sigma_pt=sympy.Symbol("sigma_pt"),
x_1=sympy.Symbol("x_1"),
x_2=sympy.Symbol("x_2"),
alpha_C=sympy.Symbol("alpha_C"),
):
"""
Args:
sigma: Cross section
sigma_pt: Parton cross section
x_1: Quark momentum fraction
x_2: Antiquark momentum fraction
alpha_C: Colour charge
"""
return sympy.Eq(
sympy.Derivative(sigma, x_1, x_2) / sigma_pt,
2 * alpha_C / 3 / sympy.pi * (x_1**2 + x_2**2) / ((1 - x_1) * (1 - x_2)),
)
[docs]
@bib()
def bibtex():
bibtex: str = r"""
@article{DeGrand:1977sy,
author = "DeGrand, Thomas A. and Ng, Yee Jack and Tye, S. H. H.",
title = "{Jet Structure in e+ e- Annihilation as a Test of QCD and the Quark-Confining String}",
reportNumber = "SLAC-PUB-1950",
doi = "10.1103/PhysRevD.16.3251",
journal = "Phys. Rev. D",
volume = "16",
pages = "3251",
year = "1977"
}
"""
return bibtex