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couplings.py
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couplings.py
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"""
Helper functions to track QCD axion parameter space and model-dependent things.
"""
from .constants import *
from .fmath import *
# DFSZ and KSVZ parameter relations from 2003.01100:
# "The landscape of QCD axion models", Di Luzio, Giannotti, Nardi, Visinelli
############ UNIVERSAL RELATIONS ############
def f_a(ma):
# ma in eV, returns f_a in GeV
return 5.691e6 / ma
############ D F S Z A X I O N S ############
# Fermion couplings
def Cae(ma, tanbeta, dfsz_type):
# ma in eV
# electron coupling coefficient for DFSZ models
fa = f_a(ma)
if dfsz_type == "DFSZI":
EbyN = 8/3
return -(1/3)*sin(arctan(tanbeta))**2 + (3*ALPHA**2)/(4*pi**2) * (EbyN * log(fa/(M_E*1e-3)) - 1.92 * log(1/(M_E*1e-3)))
if dfsz_type == "DFSZII":
EbyN = 2/3
return (1/3)*cos(arctan(tanbeta))**2 + (3*ALPHA**2)/(4*pi**2) * (EbyN * log(fa/(M_E*1e-3)) - 1.92 * log(1/(M_E*1e-3)))
def Camu(ma, tanbeta, dfsz_type):
# ma in eV
# muon coupling coefficient for DFSZ models
fa = f_a(ma)
if dfsz_type == "DFSZI":
EbyN = 8/3
return -(1/3)*sin(arctan(tanbeta))**2 + (3*ALPHA**2)/(4*pi**2) * (EbyN * log(fa/(M_MU*1e-3)) - 1.92 * log(1/(M_MU*1e-3)))
if dfsz_type == "DFSZII":
EbyN = 2/3
return (1/3)*cos(arctan(tanbeta))**2 + (3*ALPHA**2)/(4*pi**2) * (EbyN * log(fa/(M_MU*1e-3)) - 1.92 * log(1/(M_MU*1e-3)))
def Catau(ma, tanbeta, dfsz_type):
# ma in eV
# tau coupling coefficient for DFSZ models
fa = f_a(ma)
if dfsz_type == "DFSZI":
EbyN = 8/3
return -(1/3)*sin(arctan(tanbeta))**2 + (3*ALPHA**2)/(4*pi**2) * (EbyN * log(fa/(M_TAU*1e-3)) - 1.92 * log(1/(M_TAU*1e-3)))
if dfsz_type == "DFSZII":
EbyN = 2/3
return (1/3)*cos(arctan(tanbeta))**2 + (3*ALPHA**2)/(4*pi**2) * (EbyN * log(fa/(M_TAU*1e-3)) - 1.92 * log(1/(M_TAU*1e-3)))
def Can(tanbeta):
# neutron coupling coefficient for DFSZ models
cu0 = -cos(arctan(tanbeta))**2 / 3
cd0 = -sin(arctan(tanbeta))**2 / 3
csea = 0.038*cd0 + 0.012*cu0 + 0.009*cd0 + 0.0035*cu0
return -0.023 + 0.88*cd0 - 0.39*cu0 - csea
def Cap(tanbeta):
# proton coupling coefficient for DFSZ models
cu0 = -cos(arctan(tanbeta))**2 / 3
cd0 = -sin(arctan(tanbeta))**2 / 3
csea = 0.038*cd0 + 0.012*cu0 + 0.009*cd0 + 0.0035*cu0
return -0.47 + 0.88*cu0 - 0.39*cd0 - csea
def Capi0(tanbeta):
# pion coupling for DFSZ models
cu0 = -cos(arctan(tanbeta))**2 / 3
cd0 = -sin(arctan(tanbeta))**2 / 3
return 0.12 + (cd0 - cu0)/3
def gae_DFSZ(ma, tanbeta, dfsz_type):
# ma in eV
# return g_ae as a function of m_a, \tan\beta, and the DFSZ model (I or II)
return abs((M_E*1e-3) * Cae(ma, tanbeta, dfsz_type) / f_a(ma))
def gamu_DFSZ(ma, tanbeta, dfsz_type):
# ma in eV
# return g_amu as a function of m_a, \tan\beta, and the DFSZ model (I or II)
return abs((M_MU*1e-3) * Camu(ma, tanbeta, dfsz_type) / f_a(ma))
def gatau_DFSZ(ma, tanbeta, dfsz_type):
# ma in eV
# return g_atau as a function of m_a, \tan\beta, and the DFSZ model (I or II)
return abs((M_TAU*1e-3) * Catau(ma, tanbeta, dfsz_type) / f_a(ma))
def gan1_DFSZ(ma, tanbeta):
cu0 = -cos(arctan(tanbeta))**2 / 3
cd0 = -sin(arctan(tanbeta))**2 / 3
csea = 0.038*cd0 + 0.012*cu0 + 0.009*cd0 + 0.0035*cu0
can = -0.023 + 0.88*cd0 - 0.39*cu0 - csea
cap = -0.47 + 0.88*cu0 - 0.39*cd0 - csea
caN = abs((cap - can)/2)
return caN*(M_P*1e6)*ma / 5.691e15
def gan0_DFSZ(ma, tanbeta):
cu0 = -cos(arctan(tanbeta))**2 / 3
cd0 = -sin(arctan(tanbeta))**2 / 3
csea = 0.038*cd0 + 0.012*cu0 + 0.009*cd0 + 0.0035*cu0
can = -0.023 + 0.88*cd0 - 0.39*cu0 - csea
cap = -0.47 + 0.88*cu0 - 0.39*cd0 - csea
caN = abs((cap + can)/2)
return caN*(M_P*1e6)*ma / 5.691e15
def gagamma_DFSZI(ma):
# ma in eV
return (0.203*8/3 - 0.39)*ma*1e-9
def gagamma_DFSZII(ma):
# ma in eV
return (0.203*2/3 - 0.39)*ma*1e-9
def gangae_DFSZ(ma, tanbeta, dfsz_type="DFSZI"):
# Combined product of couplings gan * gae
cu0 = -cos(arctan(tanbeta))**2 / 3
cd0 = -sin(arctan(tanbeta))**2 / 3
csea = 0.038*cd0 + 0.012*cu0 + 0.009*cd0 + 0.0035*cu0
cae = Cae(ma, tanbeta, dfsz_type)
can = -0.023 + 0.88*cd0 - 0.39*cu0 - csea
cap = -0.47 + 0.88*cu0 - 0.39*cd0 - csea
caN = (cap - can)/2
return abs(caN*cae*(M_P*1e6)*(M_E*1e6)*ma**2 / power(5.691e15,2))
def gangagamma_DFSZ(ma, tanbeta, dfsz_type="DFSZI"):
# Combined product of couplings gan * gagamma
if dfsz_type == "DFSZII":
EbyN = 2/3
if dfsz_type == "DFSZI":
EbyN = 8/3
return gan1_DFSZ(ma, tanbeta) * gagamma_KSVZ(ma, EbyN)
############ K S V Z A X I O N S ############
def gagamma_KSVZ(ma, eByN):
# return g_{a\gamma} as a function of m_a and E/N for the KSVZ models
# ma in eV
return abs(0.203*eByN - 0.39)*ma*1e-9
# Generic couplings at loop level
def gamma_loop(gf, mf, ma):
tau = 4*power(mf/ma, 2)
bf = 1 - tau*power(arcsin(1/sqrt(tau)), 2) if tau >= 1 \
else 1 - tau*(pi/2 + 1j*log((1+sqrt(1-tau))/(1-sqrt(1-tau))))*(pi/2 - 1j*log((1+sqrt(1-tau))/(1-sqrt(1-tau))))
return abs(ALPHA * (2*gf/mf) * bf / pi)