def prefactor(q2, par, B, P, lep):
GF = par['GF']
ml = par['m_'+lep]
scale = config['renormalization scale']['bpll']
alphaem = running.get_alpha(par, scale)['alpha_e']
di_dj = meson_quark[(B,P)]
qi_qj = meson_quark[(B, P)]
if qi_qj == 'bu':
Vij = ckm.get_ckm(par)[0,2] # V_{ub} for b->u transitions
if qi_qj == 'bc':
Vij = ckm.get_ckm(par)[1,2] # V_{cb} for b->c transitions
if q2 <= ml**2:
return 0
return 4*GF/sqrt(2)*Vij
def prefactor(q2, par, B, P, lep):
GF = par['GF']
ml = par['m_' + lep]
scale = config['renormalization scale']['bpll']
alphaem = running.get_alpha(par, scale)['alpha_e']
di_dj = meson_quark[(B, P)]
qi_qj = meson_quark[(B, P)]
if qi_qj == 'bu':
Vij = ckm.get_ckm(par)[0, 2] # V_{ub} for b->u transitions
if qi_qj == 'bc':
Vij = ckm.get_ckm(par)[1, 2] # V_{cb} for b->c transitions
if q2 <= ml**2:
return 0
return 4 * GF / sqrt(2) * Vij
def prefactor(q2, par, B, V, lep):
GF = par['GF']
scale = config['renormalization scale']['bvll']
ml = par['m_' + lep]
mB = par['m_' + B]
mV = par['m_' + V]
tauB = par['tau_' + B]
laB = lambda_K(mB**2, mV**2, q2)
laGa = lambda_K(q2, ml**2, 0.)
qi_qj = meson_quark[(B, V)]
if qi_qj == 'bu':
Vij = ckm.get_ckm(par)[0, 2] # V_{ub} for b->u transitions
if qi_qj == 'bc':
Vij = ckm.get_ckm(par)[1, 2] # V_{cb} for b->c transitions
if q2 <= ml**2:
return 0
return 4 * GF / sqrt(2) * Vij
def prefactor(q2, par, B, V, lep):
GF = par['GF']
scale = config['renormalization scale']['bvll']
ml = par['m_'+lep]
mB = par['m_'+B]
mV = par['m_'+V]
tauB = par['tau_'+B]
laB = lambda_K(mB**2, mV**2, q2)
laGa = lambda_K(q2, ml**2, 0.)
qi_qj = meson_quark[(B, V)]
if qi_qj == 'bu':
Vij = ckm.get_ckm(par)[0,2] # V_{ub} for b->u transitions
if qi_qj == 'bc':
Vij = ckm.get_ckm(par)[1,2] # V_{cb} for b->c transitions
if q2 <= ml**2:
return 0
return 4*GF/sqrt(2)*Vij
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 wilsoncoefficients_sm_sl(par, scale):
r"""Return the $\Delta S=1$ Wilson coefficients of semi-leptonic operators
in the SM at the scale `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)
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
wc_dict['C10_c'] = -Pc / par['s2w'] * Vus**4
return wc_dict
def wilsoncoefficients_sm_sl(par, scale):
r"""Return the $\Delta S=1$ Wilson coefficients of semi-leptonic operators
in the SM at the scale `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)
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
wc_dict['C10_c'] = -Pc / par['s2w'] * Vus**4
return wc_dict
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