import sympy
from equation_database.util.doc import bib, equation
[docs]
@bib()
def bibtex():
bibtex: str = r"""
@article{Fiaschi:2022odp,
author = "Fiaschi, Juri and Fuks, Benjamin and Klasen, Michael and Neuwirth, Alexander",
title = "{Soft gluon resummation for associated squark-electroweakino production at the LHC}",
eprint = "2202.13416",
archivePrefix = "arXiv",
primaryClass = "hep-ph",
reportNumber = "MS-TP-22-05, LTH 1299",
doi = "10.1007/JHEP06(2022)130",
journal = "JHEP",
volume = "06",
pages = "130",
year = "2022"
}
"""
return bibtex
[docs]
@equation()
def equation_2_4(
M_s=sympy.Symbol("M_s"),
g_s=sympy.Symbol("g_s"),
C_A=sympy.Symbol("C_A"),
C_F=sympy.Symbol("C_F"),
B=sympy.Symbol("B"),
s=sympy.Symbol("s"),
m_X=sympy.Symbol("m_X"),
t=sympy.Symbol("t"),
):
"""
Args:
M_s: Matrix element for the s channel
g_s: strong coupling constant
C_A: Casimir operator for the adjoint representation of SU(3)
C_F: Casimir operator for the fundamental representation of SU(3)
B: squared eletroweakino-squark coupling
s: Mandelstam variable s
m_X: Mass of the electroweakino
t: Mandelstam variable t
"""
return sympy.Eq(sympy.Abs(M_s) ** 2, g_s**2 * C_A * C_F * B / s * 2 * (m_X**2 - t))
[docs]
@equation()
def equation_2_5(
M_u=sympy.Symbol("M_u"),
g_s=sympy.Symbol("g_s"),
C_A=sympy.Symbol("C_A"),
C_F=sympy.Symbol("C_F"),
B=sympy.Symbol("B"),
u=sympy.Symbol("u"),
m_X=sympy.Symbol("m_X"),
m_sq=sympy.Symbol("m_sq"),
):
"""
Args:
M_u: Matrix element for the u channel
g_s: strong coupling constant
C_A: Casimir operator for the adjoint representation of SU(3)
C_F: Casimir operator for the fundamental representation of SU(3)
B: squared eletroweakino-squark coupling
u: Mandelstam variable u
m_X: Mass of the electroweakino
m_sq: Mass of the squark
"""
return sympy.Eq(
sympy.Abs(M_u) ** 2,
g_s**2 * C_A * C_F * B / (u - m_sq**2) ** 2 * 2 * (m_X**2 - u) * (m_sq**2 + u),
)
[docs]
@equation()
def equation_2_6(
M_s=sympy.Symbol("M_s"),
M_u=sympy.Symbol("M_u"),
g_s=sympy.Symbol("g_s"),
C_A=sympy.Symbol("C_A"),
C_F=sympy.Symbol("C_F"),
B=sympy.Symbol("B"),
s=sympy.Symbol("s"),
u=sympy.Symbol("u"),
m_X=sympy.Symbol("m_X"),
m_sq=sympy.Symbol("m_sq"),
):
"""
Args:
M_s: Matrix element for the s channel
M_u: Matrix element for the u channel
g_s: strong coupling constant
C_A: Casimir operator for the adjoint representation of SU(3)
C_F: Casimir operator for the fundamental representation of SU(3)
B: squared eletroweakino-squark coupling
s: Mandelstam variable s
u: Mandelstam variable u
m_X: Mass of the electroweakino
m_sq: Mass of the squark
"""
return sympy.Eq(
2 * sympy.re(M_s * sympy.conjugate(M_u)),
g_s**2
* C_A
* C_F
* B
/ (s * (u - m_sq**2))
* (
2 * (m_X**4 - m_sq**4)
+ m_sq**2 * (2 * u - 3 * s)
- 2 * m_X**2 * (2 * m_sq**2 + u)
- s * u
),
)
[docs]
@equation()
def equation_2_8(
M=sympy.Symbol("M"),
M_s=sympy.Symbol("M_s"),
M_u=sympy.Symbol("M_u"),
):
"""
total spin- and colour-averaged squared amplitude
Args:
M: Matrix element for the process
M_s: Matrix element for the s channel
M_u: Matrix element for the u channel
"""
return sympy.Eq(
sympy.Abs(M) ** 2,
(
sympy.Abs(M_s) ** 2
+ sympy.Abs(M_u) ** 2
+ 2 * sympy.re(M_s * sympy.conjugate(M_u))
)
/ 96,
)