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Citations for K decays
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MJKirk committed Dec 1, 2020
1 parent 5e34790 commit 11d8670
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5 changes: 5 additions & 0 deletions flavio/physics/kdecays/formfactors.py
@@ -1,5 +1,6 @@
r"""Functions for $K\to pi$ hadronic form factors."""

import flavio
from flavio.classes import AuxiliaryQuantity, Implementation
from flavio.config import config
from math import exp
Expand All @@ -19,13 +20,17 @@ def fp0_dispersive(q2, par):
H1 = par['K->pi H1']
H2 = par['K->pi H2']
# (A.1) of 0903.1654
flavio.citations.register("Bernard:2009zm")
x = q2/t0
G = x*D + (1-x)*d + x*(1-x)*k
# (A.3) of 0903.1654
flavio.citations.register("Bernard:2009zm")
H = H1*x + H2*x**2
# (33) of 1005.2323
flavio.citations.register("Antonelli:2010yf")
f0_bar = exp(q2/DeltaKpi * (lnC - G))
# (37) of 1005.2323
flavio.citations.register("Antonelli:2010yf")
fp_bar = exp(q2/mpi**2 * (Lp + H))
ff = {}
ff['f+'] = fp_0 * fp_bar
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1 change: 1 addition & 0 deletions flavio/physics/kdecays/kll.py
Expand Up @@ -44,6 +44,7 @@ def amplitudes_LD(par, K, l):
s2w = par['s2w']
pre = 2 * ml / mK / s2w
# numbers extracted from arXiv:1711.11030
flavio.citations.register("Chobanova:2017rkj")
ASgaga = 2.49e-4 * (-2.821 + 1.216j)
ALgaga = 2.02e-4 * (par['chi_disp(KL->gammagamma)'] - 5.21j)
S = pre * ASgaga
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1 change: 1 addition & 0 deletions flavio/physics/kdecays/klnu.py
Expand Up @@ -39,6 +39,7 @@ def _br_plnu(wc_obj, par, P, lep, nu):
def r_plnu(wc_obj, par, P):
# resumming logs according to (111) of 0707.4464
# (this is negligibly small for the individual rates)
flavio.citations.register("Cirigliano:2007ga")
rg_corr = 1.00055
return rg_corr*br_plnu(wc_obj, par, P, 'e')/br_plnu(wc_obj, par, P, 'mu')

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1 change: 1 addition & 0 deletions flavio/physics/kdecays/kpinunu.py
Expand Up @@ -32,6 +32,7 @@ def kpinunu_charm(par):
mc = par['m_c']
alpha_s = par['alpha_s']
# approximate formula for NNLO perturbative result: (14) of hep-ph/0603079
flavio.citations.register("Buras:2006gb")
return 0.379 * (mc/1.3)**2.155 * (alpha_s/0.1187)**(-1.417)

def br_kplus_pinunu(wc_obj, par, nu1, nu2):
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2 changes: 2 additions & 0 deletions flavio/physics/kdecays/kpipi.py
Expand Up @@ -150,6 +150,7 @@ def epsprime_SM(par):
ReA0 = par['ReA0(K->pipi)']
ReA2 = par['ReA2(K->pipi)']
# eq. (19) of arXiv:1507.06345
flavio.citations.register("Buras:2015yba")
return (-par['omega+'] / (sqrt(2) * par['eps_K'])
* (ImA0 / ReA0 * (1 - par['Omegahat_eff'])
- 1 / a * ImA2 / ReA2).real)
Expand All @@ -165,6 +166,7 @@ def epsprime_NP(wc_obj, par):
ReA2 = par['ReA2(K->pipi)']
a = par['epsp a'] # eq. (16)
# dividing by a to remove the isospin brk corr in omega+, cf. (16) in 1507.06345
flavio.citations.register("Buras:2015yba")
return (-par['omega+'] / a / (sqrt(2) * par['eps_K'])
* (ImA0 / ReA0 - ImA2 / ReA2).real)

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4 changes: 4 additions & 0 deletions flavio/physics/kdecays/wilsoncoefficients.py
@@ -1,6 +1,7 @@
r"""Functions for SM Wilson coefficients in kaon decays."""

import scipy.interpolate
import flavio
from flavio.physics import ckm


Expand Down Expand Up @@ -28,6 +29,7 @@ def wilsoncoefficients_sm_fourquark(par, scale):
Currently only implemented for `scale=1.3`."""
if scale != 1.3:
raise ValueError("Wilson coefficients only implemented for scale=1.3")
flavio.citations.register("Buras:2015yba")
wcarr = wcsm(par['alpha_s'])
wc_dict = dict(zip(["z1", "z2", "y3", "y4", "y5", "y6",
"y7/al", "y8/al", "y9/al", "y10/al",], wcarr))
Expand All @@ -43,8 +45,10 @@ def wilsoncoefficients_sm_sl(par, scale):
Currently only $C_{10}$ (top and charm contributions) is implemented."""
wc_dict = {}
# fold in approximate m_t-dependence of C_10 (see eq. 4 of arXiv:1311.0903)
flavio.citations.register("Bobeth:2013uxa")
wc_dict['C10_t'] = -4.10 * (par['m_t']/173.1)**1.53
Vus = abs(ckm.get_ckm(par)[0, 1])
Pc = 0.115 # +-0.011, arXiv:hep-ph/0605203
flavio.citations.register("Gorbahn:2006bm")
wc_dict['C10_c'] = -Pc / par['s2w'] * Vus**4
return wc_dict

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