Module flavio.physics.bdecays.wilsoncoefficients
Standard Model Wilson coefficients for $\Delta B=1$ transitions as well as tree-level $B$ decays
Functions
def CL_SM(par, scale)-
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def CL_SM(par, scale): r"""SM Wilson coefficient for $d_i\to d_j\nu\bar\nu$ transitions. This is implemented as an approximate formula as a function of the top mass.""" # # EW NLO corrections arXiv:1009.0947 # scale = 120. # <- result has very little sensitivity to high matching scale # mt = flavio.physics.running.running.get_mt(par, scale) # Xt0_165 = 1.50546 # LO result for mt=165, scale=120 # Xt0 = Xt0_165 * (1 + 1.14064 * (mt/165. - 1)) # LO # Xt1 = Xt0_165 * (-0.031435 - 0.139303 * (mt/165. - 1)) # QCD NLO # # (4.3), (4.4) of 1009.0947: NLO EW # flavio.citations.register("Brod:2010hi") # XtEW = Xt0 * (1 - 1.11508 + 1.12316*1.15338**(mt/165.)-0.179454*(mt/165)) - 1 # XtEW = XtEW * 0.00062392534457616328 # <- alpha_em/4pi at 120 GeV # Xt = Xt0 + Xt1 + XtEW s2w = par['s2w'] Xt = par['Xt_di->djnunu'] CL_SM = -Xt/s2w # CL_SM * alpha_e is scale invariant alpha_e_scale = flavio.physics.running.running.get_alpha(par, scale)['alpha_e'] alpha_e_mZ = flavio.physics.running.running.get_alpha(par, 91.1876)['alpha_e'] return CL_SM * alpha_e_mZ/alpha_e_scaleSM Wilson coefficient for $d_i\to d_j\nu\bar\nu$ transitions.
This is implemented as an approximate formula as a function of the top mass.
def get_C78eff(wc, qiqj)-
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def get_C78eff(wc, qiqj): r"""Return the effective Wilson coefficients $C_{7,8}^\text{eff}$ for sector `qiqj` (e.g. 'bs').""" yi = np.array([-1/3., -4/9., -20/3., -80/9.]) zi = np.array([1, -1/6., 20, -10/3.]) wceff = {} C36 = np.array([wc[k] for k in ['C3_'+qiqj, 'C4_'+qiqj, 'C5_'+qiqj, 'C6_'+qiqj]]) C36p = np.array([wc[k] for k in ['C3p_'+qiqj, 'C4p_'+qiqj, 'C5p_'+qiqj, 'C6p_'+qiqj]]) wceff['C7eff_' + qiqj] = wc['C7_' + qiqj] + np.dot(yi, C36) wceff['C8eff_' + qiqj] = wc['C8_' + qiqj] + np.dot(zi, C36) wceff['C7effp_' + qiqj] = wc['C7p_' + qiqj] + np.dot(yi, C36p) wceff['C8effp_' + qiqj] = wc['C8p_' + qiqj] + np.dot(zi, C36p) return wceffReturn the effective Wilson coefficients $C_{7,8}^\text{eff}$ for sector
qiqj(e.g. 'bs'). def get_CVLSM(par, scale, nf)-
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def get_CVLSM(par, scale, nf): r"""Get the Wilson coefficient of the operator $C_V$ in $d_i\to d_j\ell\nu$ in the SM including EW corrections.""" if nf >= 4: # for B and D physics alpha_e = running.get_alpha(par, scale)['alpha_e'] return 1 + alpha_e/pi * log(par['m_Z']/scale) else: # for K and pi physics # Marciano & Sirlin 1993 return sqrt(1.0232)Get the Wilson coefficient of the operator $C_V$ in $d_i\to d_j\ell\nu$ in the SM including EW corrections.
def get_wceff(q2, wc, par, B, M, lep, scale)-
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def get_wceff(q2, wc, par, B, M, lep, scale): r"""Get a dictionary with the effective $\Delta F=1$ Wilson coefficients in the convention appropriate for the generalized angular distributions. """ xi_u = ckm.xi('u',meson_quark[(B,M)])(par) xi_t = ckm.xi('t',meson_quark[(B,M)])(par) qiqj=meson_quark[(B,M)] Yq2 = matrixelements.Y(q2, wc, par, scale, qiqj) + (xi_u/xi_t)*matrixelements.Yu(q2, wc, par, scale, qiqj) # b) NNLO Q1,2 delta_C7 = matrixelements.delta_C7(par=par, wc=wc, q2=q2, scale=scale, qiqj=qiqj) delta_C9 = matrixelements.delta_C9(par=par, wc=wc, q2=q2, scale=scale, qiqj=qiqj) mb = running.get_mb(par, scale) ll = lep + lep c = {} c['7'] = wc['C7eff_'+qiqj] + delta_C7 c['7p'] = wc['C7effp_'+qiqj] c['v'] = wc['C9_'+qiqj+ll] + delta_C9 + Yq2 c['vp'] = wc['C9p_'+qiqj+ll] c['a'] = wc['C10_'+qiqj+ll] c['ap'] = wc['C10p_'+qiqj+ll] c['s'] = mb * wc['CS_'+qiqj+ll] c['sp'] = mb * wc['CSp_'+qiqj+ll] c['p'] = mb * wc['CP_'+qiqj+ll] c['pp'] = mb * wc['CPp_'+qiqj+ll] c['t'] = 0 c['tp'] = 0 return cGet a dictionary with the effective $\Delta F=1$ Wilson coefficients in the convention appropriate for the generalized angular distributions.
def get_wceff_fccc(wc_obj, par, qiqj, lep, nu, mqi, scale, nf=5)-
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def get_wceff_fccc(wc_obj, par, qiqj, lep, nu, mqi, scale, nf=5): r"""Get a dictionary with the $d_i\to d_j$ Wilson coefficients in the convention appropriate for the generalized angular distributions. """ qqlnu = qiqj + lep + 'nu' + nu wc = wc_obj.get_wc(qqlnu, scale, par, nf_out=nf) if lep == nu: c_sm = get_CVLSM(par, scale, nf) else: c_sm = 0 # SM contribution only for neutrino flavor = lepton flavor c = {} c['7'] = 0 c['7p'] = 0 c['v'] = (c_sm + wc['CVL_'+qqlnu])/2. c['vp'] = wc['CVR_'+qqlnu]/2. c['a'] = -(c_sm + wc['CVL_'+qqlnu])/2. c['ap'] = -wc['CVR_'+qqlnu]/2. c['s'] = wc['CSR_'+qqlnu]/2. c['sp'] = wc['CSL_'+qqlnu]/2. c['p'] = -wc['CSR_'+qqlnu]/2. c['pp'] = -wc['CSL_'+qqlnu]/2. c['t'] = 0 c['tp'] = wc['CT_'+qqlnu] return cGet a dictionary with the $d_i\to d_j$ Wilson coefficients in the convention appropriate for the generalized angular distributions.
def get_wceff_fccc_std(wc_obj, par, qiqj, lep, nu, mqi, scale, nf=5)-
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def get_wceff_fccc_std(wc_obj, par, qiqj, lep, nu, mqi, scale, nf=5): r"""Get a dictionary with the $d_i\to d_j$ Wilson coefficients in the flavio default convention. """ qqlnu = qiqj + lep + 'nu' + nu wc = wc_obj.get_wc(qqlnu, scale, par, nf_out=nf) if lep == nu: c_sm = get_CVLSM(par, scale, nf) else: c_sm = 0 # SM contribution only for neutrino flavor = lepton flavor c = {} c['VL'] = c_sm + wc['CVL_'+qqlnu] c['VR'] = wc['CVR_'+qqlnu] c['SR'] = wc['CSR_'+qqlnu] c['SL'] = wc['CSL_'+qqlnu] c['T'] = wc['CT_'+qqlnu] return cGet a dictionary with the $d_i\to d_j$ Wilson coefficients in the flavio default convention.
def get_wceff_lfv(q2, wc, par, B, M, l1, l2, scale)-
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def get_wceff_lfv(q2, wc, par, B, M, l1, l2, scale): r"""Get a dictionary with the effective $\Delta F=1$ Wilson coefficients with lepton flavour violation in the convention appropriate for the generalized angular distributions. """ mb = running.get_mb(par, scale) qiqj=meson_quark[(B,M)] c = {} c['7'] = 0 c['7p'] = 0 c['v'] = wc['C9_'+qiqj+l1+l2] c['vp'] = wc['C9p_'+qiqj+l1+l2] c['a'] = wc['C10_'+qiqj+l1+l2] c['ap'] = wc['C10p_'+qiqj+l1+l2] c['s'] = mb * wc['CS_'+qiqj+l1+l2] c['sp'] = mb * wc['CSp_'+qiqj+l1+l2] c['p'] = mb * wc['CP_'+qiqj+l1+l2] c['pp'] = mb * wc['CPp_'+qiqj+l1+l2] c['t'] = 0 c['tp'] = 0 return cGet a dictionary with the effective $\Delta F=1$ Wilson coefficients with lepton flavour violation in the convention appropriate for the generalized angular distributions.
def get_wceff_nunu(q2, wc, par, B, M, nu1, nu2, scale)-
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def get_wceff_nunu(q2, wc, par, B, M, nu1, nu2, scale): r"""Get a dictionary with the effective $\Delta F=1$ Wilson coefficients with neutrinos in the final state in the convention appropriate for the generalized angular distributions. """ qiqj=meson_quark[(B,M)] c = {} c['7'] = 0 c['7p'] = 0 c['v'] = wc['CL_'+qiqj+nu1+nu2] c['vp'] = wc['CR_'+qiqj+nu1+nu2] c['a'] = -wc['CL_'+qiqj+nu1+nu2] c['ap'] = -wc['CR_'+qiqj+nu1+nu2] c['s'] = 0 c['sp'] = 0 c['p'] = 0 c['pp'] = 0 c['t'] = 0 c['tp'] = 0 return cGet a dictionary with the effective $\Delta F=1$ Wilson coefficients with neutrinos in the final state in the convention appropriate for the generalized angular distributions.
def wctot_dict(wc_obj, sector, scale, par, nf_out=5)-
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def wctot_dict(wc_obj, sector, scale, par, nf_out=5): r"""Get a dictionary with the total (SM + new physics) values of the $\Delta F=1$ Wilson coefficients at a given scale, given a WilsonCoefficients instance.""" wc_np_dict = wc_obj.get_wc(sector, scale, par, nf_out=nf_out) if nf_out == 5: wc_sm = wcsm_nf5(scale) else: raise NotImplementedError("DeltaF=1 Wilson coefficients only implemented for B physics") # fold in approximate m_t-dependence of C_10 (see eq. 4 of arXiv:1311.0903) flavio.citations.register("Bobeth:2013uxa") wc_sm[9] = wc_sm[9] * (par['m_t']/173.1)**1.53 # go from the effective to the "non-effective" WCs for C7 and C8 yi = np.array([0, 0, -1/3., -4/9., -20/3., -80/9.]) zi = np.array([0, 0, 1, -1/6., 20, -10/3.]) wc_sm[6] = wc_sm[6] - np.dot(yi, wc_sm[:6]) # c7 (not effective!) wc_sm[7] = wc_sm[7] - np.dot(zi, wc_sm[:6]) # c8 (not effective!) wc_labels = fcnclabels[sector] wc_sm_dict = dict(zip(wc_labels, wc_sm)) # now here comes an ugly fix. If we have b->s transitions, we should take # into account the fact that C7' = C7*ms/mb, and the same for C8, which is # not completely negligible. To find out whether we have b->s, we look at # the "sector" string. if sector[:2] == 'bs': eps_s = running.get_ms(par, scale)/running.get_mb(par, scale) wc_sm_dict['C7p_bs'] = eps_s * wc_sm_dict['C7_bs'] wc_sm_dict['C8p_bs'] = eps_s * wc_sm_dict['C8_bs'] tot_dict = add_dict((wc_np_dict, wc_sm_dict)) # add C7eff(p) and C8eff(p) tot_dict.update(get_C78eff(tot_dict, sector[:2])) return tot_dictGet a dictionary with the total (SM + new physics) values of the $\Delta F=1$ Wilson coefficients at a given scale, given a WilsonCoefficients instance.