def _br_taupnu(wc_obj, par, P, lep):
r"""Branching ratio of $\tau^+\to P^+\bar\nu_\ell$."""
# CKM element
scale = flavio.config['renormalization scale']['taudecays']
if P == 'pi+':
Vij = flavio.physics.ckm.get_ckm(par)[0, 0] # Vud
qqlnu = 'dutaunu' + lep
mq1 = flavio.physics.running.running.get_md(par, scale)
mq2 = flavio.physics.running.running.get_mu(par, scale)
elif P == 'K+':
Vij = flavio.physics.ckm.get_ckm(par)[0, 1] # Vus
qqlnu = 'sutaunu' + lep
mq1 = flavio.physics.running.running.get_ms(par, scale)
mq2 = flavio.physics.running.running.get_mu(par, scale)
# Wilson coefficients
wc = wc_obj.get_wc(qqlnu, scale, par, nf_out=4)
# add SM contribution to Wilson coefficient
if lep == 'tau':
# for the SM contribution, need the Fermi constant with possible
# NP effects in mu->enunu subtracted, not the measured one
r_GF = GFeff(wc_obj, par) / par['GF']
wc['CVL_' + qqlnu] += get_CVLSM(par, scale, nf=4) * r_GF
mtau = par['m_tau']
mP = par['m_' + P]
rWC = ((wc['CVL_' + qqlnu] - wc['CVR_' + qqlnu]) + mP**2 / mtau /
(mq1 + mq2) * (wc['CSR_' + qqlnu] - wc['CSL_' + qqlnu]))
gR = -sqrt(2) * par['GF'] * Vij * rWC * par['f_' + P] * par['m_tau']
return par['tau_tau'] * common.GammaFsf(mtau, mP, 0, 0, gR)
def _br_plnu(wc_obj, par, P, lep, nu):
# CKM element
if P == 'K+':
Vij = flavio.physics.ckm.get_ckm(par)[0, 1]
qiqj = 'su'
elif P == 'pi+':
Vij = flavio.physics.ckm.get_ckm(par)[0, 0]
qiqj = 'du'
# renormalization scale is m_rho
scale = par['m_rho0']
# Wilson coefficients
wc = wc_obj.get_wc(qiqj + lep + 'nu' + nu, scale, par, nf_out=3)
# add SM contribution to Wilson coefficient
if lep == nu:
# for the SM contribution, need the Fermi constant with possible
# NP effects in mu->enunu subtracted, not the measured one
r_GF = GFeff(wc_obj, par) / par['GF']
wc['CVL_' + qiqj + lep + 'nu' +
nu] += flavio.physics.bdecays.wilsoncoefficients.get_CVLSM(
par, scale, nf=3) * r_GF
if P == 'K+':
mq = flavio.physics.running.running.get_ms(par, scale)
elif P == 'pi+':
mq = flavio.physics.running.running.get_md(par, scale)
mu = flavio.physics.running.running.get_mu(par, scale)
return br_plnu_general(wc,
par,
Vij,
P,
qiqj,
lep,
nu,
mq,
mu,
delta=delta_Plnu(par, P, lep))
def __call__(self):
Vud = get_ckm(self.par)[0, 0]
GF = GFeff(self.wc_obj, self.par)
pre = GF / sqrt(2) * Vud
ft = K(self.par) / self.xi() * 1 / (1 + self.b() * self.me_E) / abs(pre)**2
fn = self.par['f_n']
Rp = self.par['deltaRp_n']
return ft / log(2) / fn / (1 + Rp)
def Ft_superallowed(par, wc_obj, A):
r"""Corrected $\mathcal{F}t$ value of the beta decay of isotope `A`."""
MF = sqrt(2)
MGT = 0
Z = nuclei_superallowed[A]['Z']
scale = config['renormalization scale']['betadecay']
C = wc_eff(par, wc_obj, scale, nu='e')
Xi = xi(C, MF, MGT)
B = b(C, MF, MGT, par['alpha_e'], Z, s=-1) # s=-1 for beta+ decay
me_E = nuclei_superallowed[A]['<me/E>']
Vud = get_ckm(par)[0, 0]
GF = GFeff(wc_obj, par)
pre = GF / sqrt(2) * Vud
ddRp = par['delta_deltaRp_Z2'] * Z**2 # relative uncertainty on \delta R' (universal)
return (1 + ddRp) * K(par) / Xi * 1 / (1 + B * me_E) / abs(pre)**2