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