Exemplo n.º 1
0
def wctot_dict(wc_obj, sector, scale, par, nf_out=None):
    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)
    wcsm_120 = _wcsm_120.copy()
    wc_sm = running.get_wilson(par, wcsm_120, wc_obj.rge_derivative[sector], 120., scale, nf_out=nf_out)
    # 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':
        # go from the effective to the "non-effective" WCs
        yi = np.array([0, 0, -1/3., -4/9., -20/3., -80/9.])
        zi = np.array([0, 0, 1, -1/6., 20, -10/3.])
        c7 = wc_sm[6] - np.dot(yi, wc_sm[:6]) # c7 (not effective!)
        c8 = wc_sm[7] - np.dot(zi, wc_sm[:6]) # c8 (not effective!)
        eps_s = running.get_ms(par, scale)/running.get_mb(par, scale)
        c7p = eps_s * c7
        c8p = eps_s * c8
        # go back to the effective WCs
        wc_sm[21] = c7p + np.dot(yi, wc_sm[15:21]) # c7p_eff
        wc_sm[22] = c7p + np.dot(zi, wc_sm[15:21]) # c8p_eff
    wc_labels = wc_obj.coefficients[sector]
    wc_sm_dict =  dict(zip(wc_labels, wc_sm))
    return add_dict((wc_np_dict, wc_sm_dict))
Exemplo n.º 2
0
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_dict
Exemplo n.º 3
0
def wctot_dict(wc_obj, sector, scale, par, nf_out=None):
    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)
    wcsm_120 = _wcsm_120.copy()
    # fold in approximate m_t-dependence of C_10 (see eq. 4 of arXiv:1311.0903)
    wcsm_120[9] = wcsm_120[9] * (par['m_t'] / 173.1)**1.53
    wc_sm = running.get_wilson(par,
                               wcsm_120,
                               wc_obj.rge_derivative[sector],
                               120.,
                               scale,
                               nf_out=nf_out)
    # 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':
        # go from the effective to the "non-effective" WCs
        yi = np.array([0, 0, -1 / 3., -4 / 9., -20 / 3., -80 / 9.])
        zi = np.array([0, 0, 1, -1 / 6., 20, -10 / 3.])
        c7 = wc_sm[6] - np.dot(yi, wc_sm[:6])  # c7 (not effective!)
        c8 = wc_sm[7] - np.dot(zi, wc_sm[:6])  # c8 (not effective!)
        eps_s = running.get_ms(par, scale) / running.get_mb(par, scale)
        c7p = eps_s * c7
        c8p = eps_s * c8
        # go back to the effective WCs
        wc_sm[21] = c7p + np.dot(yi, wc_sm[15:21])  # c7p_eff
        wc_sm[22] = c8p + np.dot(zi, wc_sm[15:21])  # c8p_eff
    wc_labels = wc_obj.coefficients[sector]
    wc_sm_dict = dict(zip(wc_labels, wc_sm))
    return add_dict((wc_np_dict, wc_sm_dict))
Exemplo n.º 4
0
def amplitudes(par, wc, B, l1, l2):
    r"""Amplitudes P and S entering the $B_q\to\ell_1^+\ell_2^-$ observables.

    Parameters
    ----------

    - `par`: parameter dictionary
    - `B`: should be `'Bs'` or `'B0'`
    - `l1` and `l2`: should be `'e'`, `'mu'`, or `'tau'`

    Returns
    -------

    `(P, S)` where for the special case `l1 == l2` one has

    - $P = \frac{2m_\ell}{m_{B_q}} (C_{10}-C_{10}') + m_{B_q} (C_P-C_P')$
    - $S = m_{B_q} (C_S-C_S')$
    """
    scale = config['renormalization scale']['bll']
    # masses
    ml1 = par['m_' + l1]
    ml2 = par['m_' + l2]
    mB = par['m_' + B]
    mb = running.get_mb(par, scale, nf_out=5)
    #   get the mass of the spectator quark
    if B == 'Bs':
        mspec = running.get_ms(par, scale, nf_out=5)
    elif B == 'B0':
        mspec = running.get_md(par, scale, nf_out=5)
    # Wilson coefficients
    qqll = meson_quark[B] + l1 + l2
    # For LFV expressions see arXiv:1602.00881 eq. (5)
    C9m = wc['C9_' + qqll] - wc['C9p_' + qqll]  # only relevant for l1 != l2!
    C10m = wc['C10_' + qqll] - wc['C10p_' + qqll]
    CPm = wc['CP_' + qqll] - wc['CPp_' + qqll]
    CSm = wc['CS_' + qqll] - wc['CSp_' + qqll]
    beta_m = sqrt(1 - (ml1 - ml2)**2 / mB**2)
    beta_p = sqrt(1 - (ml1 + ml2)**2 / mB**2)
    P = beta_m * ((ml2 + ml1) / mB * C10m + mB * mb / (mb + mspec) * CPm)
    S = beta_p * ((ml2 - ml1) / mB * C9m + mB * mb / (mb + mspec) * CSm)
    return P, S
Exemplo n.º 5
0
def amplitudes(par, wc, B, l1, l2):
    r"""Amplitudes P and S entering the $B_q\to\ell_1^+\ell_2^-$ observables.

    Parameters
    ----------

    - `par`: parameter dictionary
    - `B`: should be `'Bs'` or `'B0'`
    - `l1` and `l2`: should be `'e'`, `'mu'`, or `'tau'`

    Returns
    -------

    `(P, S)` where for the special case `l1 == l2` one has

    - $P = \frac{2m_\ell}{m_{B_q}} (C_{10}-C_{10}') + m_{B_q} (C_P-C_P')$
    - $S = m_{B_q} (C_S-C_S')$
    """
    scale = config['renormalization scale']['bll']
    # masses
    ml1 = par['m_'+l1]
    ml2 = par['m_'+l2]
    mB = par['m_'+B]
    mb = running.get_mb(par, scale, nf_out=5)
    #   get the mass of the spectator quark
    if B=='Bs':
        mspec = running.get_ms(par, scale, nf_out=5)
    elif B=='B0':
        mspec = running.get_md(par, scale, nf_out=5)
    # Wilson coefficients
    qqll = meson_quark[B] + l1 + l2
    # For LFV expressions see arXiv:1602.00881 eq. (5)
    C9m = wc['C9_'+qqll] - wc['C9p_'+qqll] # only relevant for l1 != l2!
    C10m = wc['C10_'+qqll] - wc['C10p_'+qqll]
    CPm = wc['CP_'+qqll] - wc['CPp_'+qqll]
    CSm = wc['CS_'+qqll] - wc['CSp_'+qqll]
    P = (ml2 + ml1)/mB * C10m + mB * mb/(mb + mspec) * CPm
    S = (ml2 - ml1)/mB * C9m  + mB * mb/(mb + mspec) * CSm
    return P, S