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))
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
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))
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
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