Module flavio.physics.bdecays.bvll.observables_bs

Functions for exclusive $B_s\to V\ell^+\ell^-$ decays, taking into account the finite life-time difference between the $B_s$ mass eigenstates, see arXiv:1502.05509.

Functions

def FL_Bs(y, J, J_bar, J_h)

Expand source code

def FL_Bs(y, J, J_bar, J_h):
    r"""Longitudinal polarization fraction $F_L$"""
    return FL_num_Bs(y, J, J_bar, J_h)/SA_den_Bs(y, J, J_bar, J_h)

Longitudinal polarization fraction $F_L$

def FL_num_Bs(y, J, J_bar, J_h)

Expand source code

def FL_num_Bs(y, J, J_bar, J_h):
    return -S_theory_num_Bs(y, J, J_bar, J_h, '2c')

def SA_den_Bs(y, J, J_bar, J_h)

Expand source code

def SA_den_Bs(y, J, J_bar, J_h):
    return 2*dGdq2_ave_Bs(y, J, J_bar, J_h)

def S_experiment_Bs(y, J, J_bar, J_h, i)

Expand source code

def S_experiment_Bs(y, J, J_bar, J_h, i):
    r"""CP-averaged angular observable $S_i$ in the LHCb convention.

    See eq. (C.8) of arXiv:1506.03970v2.
    """
    return S_experiment_num_Bs(y, J, J_bar, J_h, i)/SA_den_Bs(y, J, J_bar, J_h)

CP-averaged angular observable $S_i$ in the LHCb convention.

See eq. (C.8) of arXiv:1506.03970v2.

def S_experiment_num_Bs(y, J, J_bar, J_h, i)

Expand source code

def S_experiment_num_Bs(y, J, J_bar, J_h, i):
    if i in [4, '6s', '6c', 7, 9]:
        return -S_theory_num_Bs(y, J, J_bar, J_h, i)
    return S_theory_num_Bs(y, J, J_bar, J_h, i)

def S_theory_num_Bs(y, J, J_bar, J_h, i)

Expand source code

def S_theory_num_Bs(y, J, J_bar, J_h, i):
    # (42) of 1502.05509
    flavio.citations.register("Descotes-Genon:2015hea")
    return 1/(1-y**2) * (J[i] + J_bar[i]) - y/(1-y**2) * J_h[i]

def bsvll_dbrdq2(q2, wc_obj, par, B, V, lep)

Expand source code

def bsvll_dbrdq2(q2, wc_obj, par, B, V, lep):
    tauB = par['tau_'+B]
    return tauB * bsvll_obs(dGdq2_ave_Bs, q2, wc_obj, par, B, V, lep)

def bsvll_dbrdq2_19_func(B, P, lep)

Expand source code

def bsvll_dbrdq2_19_func(B, P, lep):
    def fct(wc_obj, par):
        with warnings.catch_warnings():
            warnings.filterwarnings("ignore", message="The predictions in the region of narrow charmonium resonances are not meaningful.*")
            warnings.filterwarnings("ignore", message="The QCDF corrections should not be trusted*")

            q2max = 19
            q2min = 0.1
            return (1+par['delta_BsKstarmumu'])*bsvll_dbrdq2_int(q2min, q2max, wc_obj, par, B, P, lep)*(q2max-q2min)
    return fct

def bsvll_dbrdq2_func(B, V, lep)

Expand source code

def bsvll_dbrdq2_func(B, V, lep):
    def fct(wc_obj, par, q2):
        return bsvll_dbrdq2(q2, wc_obj, par, B, V, lep)
    return fct

def bsvll_dbrdq2_int(q2min, q2max, wc_obj, par, B, V, lep, epsrel=0.005)

Expand source code

def bsvll_dbrdq2_int(q2min, q2max, wc_obj, par, B, V, lep, epsrel=0.005):
    def obs(q2):
        return bsvll_dbrdq2(q2, wc_obj, par, B, V, lep)
    return flavio.physics.bdecays.bvll.observables.nintegrate_pole(obs, q2min, q2max, epsrel=epsrel)/(q2max-q2min)

def bsvll_dbrdq2_int_func(B, V, lep)

Expand source code

def bsvll_dbrdq2_int_func(B, V, lep):
    def fct(wc_obj, par, q2min, q2max):
        return bsvll_dbrdq2_int(q2min, q2max, wc_obj, par, B, V, lep)
    return fct

def bsvll_obs(function, q2, wc_obj, par, B, V, lep)

Expand source code

def bsvll_obs(function, q2, wc_obj, par, B, V, lep):
    ml = par['m_'+lep]
    mB = par['m_'+B]
    mV = par['m_'+V]
    y = par['DeltaGamma/Gamma_'+B]/2.
    if q2 < 4*ml**2 or q2 > (mB-mV)**2:
        return 0
    scale = flavio.config['renormalization scale']['bvll']
    mb = flavio.physics.running.running.get_mb(par, scale)
    ff = flavio.physics.bdecays.bvll.amplitudes.get_ff(q2, par, B, V)
    h = flavio.physics.bdecays.bvll.amplitudes.helicity_amps(q2, ff, wc_obj, par, B, V, lep)
    h_bar = flavio.physics.bdecays.bvll.amplitudes.helicity_amps_bar(q2, ff, wc_obj, par, B, V, lep)
    J = flavio.physics.bdecays.angular.angularcoeffs_general_v(h, q2, mB, mV, mb, 0, ml, ml)
    J_bar = flavio.physics.bdecays.angular.angularcoeffs_general_v(h_bar, q2, mB, mV, mb, 0, ml, ml)
    h_tilde = h_bar.copy()
    h_tilde[('pl', 'V')] = h_bar[('mi', 'V')]
    h_tilde[('pl', 'A')] = h_bar[('mi', 'A')]
    h_tilde[('mi', 'V')] = h_bar[('pl', 'V')]
    h_tilde[('mi', 'A')] = h_bar[('pl', 'A')]
    h_tilde['S'] = -h_bar['S']
    q_over_p = flavio.physics.mesonmixing.observables.q_over_p(wc_obj, par, B)
    phi = cmath.phase(-q_over_p) # the phase of -q/p
    J_h = flavio.physics.bdecays.angular.angularcoeffs_h_v(phi, h, h_tilde, q2, mB, mV, mb, 0, ml, ml)
    return function(y, J, J_bar, J_h)

def bsvll_obs_int(function, q2min, q2max, wc_obj, par, B, V, lep, epsrel=0.005)

Expand source code

def bsvll_obs_int(function, q2min, q2max, wc_obj, par, B, V, lep, epsrel=0.005):
    def obs(q2):
        return bsvll_obs(function, q2, wc_obj, par, B, V, lep)
    return flavio.physics.bdecays.bvll.observables.nintegrate_pole(obs, q2min, q2max, epsrel=epsrel)

def bsvll_obs_int_ratio_func(func_num, func_den, B, V, lep)

Expand source code

def bsvll_obs_int_ratio_func(func_num, func_den, B, V, lep):
    def fct(wc_obj, par, q2min, q2max):
        num = bsvll_obs_int(func_num, q2min, q2max, wc_obj, par, B, V, lep)
        if num == 0:
            return 0
        denom = bsvll_obs_int(func_den, q2min, q2max, wc_obj, par, B, V, lep)
        return num/denom
    return fct

def bsvll_obs_int_ratio_leptonflavour(func, B, V, l1, l2)

Expand source code

def bsvll_obs_int_ratio_leptonflavour(func, B, V, l1, l2):
    def fct(wc_obj, par, q2min, q2max):
        num = bsvll_obs_int(func, q2min, q2max, wc_obj, par, B, V, l1, epsrel=0.0005)
        if num == 0:
            return 0
        denom = bsvll_obs_int(func, q2min, q2max, wc_obj, par, B, V, l2, epsrel=0.0005)
        return num/denom
    return fct

def bsvll_obs_ratio_func(func_num, func_den, B, V, lep)

Expand source code

def bsvll_obs_ratio_func(func_num, func_den, B, V, lep):
    def fct(wc_obj, par, q2):
        num = bsvll_obs(func_num, q2, wc_obj, par, B, V, lep)
        if num == 0:
            return 0
        denom = bsvll_obs(func_den, q2, wc_obj, par, B, V, lep)
        return num/denom
    return fct

def dGdq2_ave_Bs(y, J, J_bar, J_h)

Expand source code

def dGdq2_ave_Bs(y, J, J_bar, J_h):
    # (48) of 1502.05509
    flavio.citations.register("Descotes-Genon:2015hea")
    return (1/(1-y**2) * (observables.dGdq2(J) + observables.dGdq2(J_bar))
            - y/(1-y**2) * observables.dGdq2(J_h))/2.