def make_obs_br(M, l):
"""Make observable instances for branching ratios"""
_process_tex = _hadr[M]['tex'] + _tex[l] + r"^+" + _tex[l] + r"^-"
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _process_tex + r"$"
B = _hadr[M]['B']
V = _hadr[M]['V']
# binned branching ratio
_obs_name = "<dBR/dq2>(" + M + l + l + ")"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
_obs.set_description(r"Binned differential branching ratio of $" +
_process_tex + r"$")
_obs.tex = r"$\langle \frac{d\text{BR}}{dq^2} \rangle(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
func = lambda wc_obj, par, q2min, q2max: BVll_dBRdq2_int(
q2min, q2max, B, V, l, wc_obj, par)()
Prediction(_obs_name, func)
# differential branching ratio
_obs_name = "dBR/dq2(" + M + l + l + ")"
_obs = Observable(name=_obs_name, arguments=['q2'])
_obs.set_description(r"Differential branching ratio of $" + _process_tex +
r"$")
_obs.tex = r"$\frac{d\text{BR}}{dq^2}(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
func = lambda wc_obj, par, q2: BVll_dBRdq2(q2, B, V, l, wc_obj, par)()
Prediction(_obs_name, func)
def _define_obs_B_Mll(M, ll):
_process_tex = _hadr_lfv[M]['tex']+' '+_tex_lfv[''.join(ll)]
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to P\ell^+\ell^-$ :: $' + _process_tex + r"$"
_obs_name = "BR("+M+''.join(ll)+")"
_obs = Observable(_obs_name)
_obs.set_description(r"Total branching ratio of $"+_process_tex+r"$")
_obs.tex = r"$\text{BR}(" + _process_tex+r")$"
_obs.add_taxonomy(_process_taxonomy)
return _obs_name
def make_metadata_binned(M, l, obs, obsdict):
_process_tex = _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+r"^-"
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _process_tex + r"$"
B = _hadr[M]['B']
V = _hadr[M]['V']
_obs_name = "<" + obs + ">("+M+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
_obs.set_description('Binned ' + obsdict['desc'] + r" in $" + _process_tex + r"$")
_obs.tex = r"$\langle " + obsdict['tex'] + r"\rangle(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
return _obs
def make_metadata_differential(M, l, obs, obsdict):
_process_tex = _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+r"^-"
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _process_tex + r"$"
B = _hadr[M]['B']
V = _hadr[M]['V']
_obs_name = obs + "("+M+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2'])
_obs.set_description(obsdict['desc'][0].capitalize() + obsdict['desc'][1:] + r" in $" + _process_tex + r"$")
_obs.tex = r"$" + obsdict['tex'] + r"(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
return _obs
def make_metadata_binned(M, l, obs, obsdict):
_process_tex = _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+r"^-"
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _process_tex + r"$"
B = _hadr[M]['B']
V = _hadr[M]['V']
_obs_name = "<" + obs + ">("+M+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
_obs.set_description('Binned ' + obsdict['desc'] + r" in $" + _process_tex + r"$")
_obs.tex = r"$\langle " + obsdict['tex'] + r"\rangle(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
return _obs
def make_metadata_differential(M, l, obs, obsdict):
_process_tex = _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+r"^-"
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _process_tex + r"$"
B = _hadr[M]['B']
V = _hadr[M]['V']
_obs_name = obs + "("+M+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2'])
_obs.set_description(obsdict['desc'][0].capitalize() + obsdict['desc'][1:] + r" in $" + _process_tex + r"$")
_obs.tex = r"$" + obsdict['tex'] + r"(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
return _obs
def make_obs_neutron_corr(coeff, me_E=False):
_process_tex = r"n\to p^+ e^-\bar\nu_e"
_process_taxonomy = r'Process :: Nucleon decays :: Beta decays :: Neutron decay :: $' + _process_tex + r"$"
_obs_name = coeff + "_n"
if me_E:
_obs = Observable(_obs_name, arguments=['me_E'])
else:
_obs = Observable(_obs_name)
_obs.set_description(r"Correlation coefficient $" + tex + r"$ in neutron beta decay")
_obs.tex = r"$" + tex + r"$"
_obs.add_taxonomy(_process_taxonomy)
if me_E:
func = lambda wc_obj, par, me_E: Neutron_corr(wc_obj, par, me_E, coeff)()
else:
func = lambda wc_obj, par: Neutron_corr(wc_obj, par, None, coeff)()
Prediction(_obs_name, func)
def make_obs_lfur(M, l):
"""Make observable instances for lepton flavour ratios"""
# binned ratio of BRs
_obs_name = "<R" + l[0] + l[1] + ">(" + M + "ll)"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
_obs.set_description(r"Ratio of partial branching ratios of $" +
_hadr[M]['tex'] + _tex[l[0]] + r"^+ " + _tex[l[0]] +
r"^-$" + " and " + r"$" + _hadr[M]['tex'] +
_tex[l[1]] + r"^+ " + _tex[l[1]] + "^-$")
_obs.tex = r"$\langle R_{" + _tex[l[0]] + ' ' + _tex[
l[1]] + r"} \rangle(" + _hadr[M]['tex'] + r"\ell^+\ell^-)$"
for li in l:
# add taxonomy for both processes (e.g. B->Vee and B->Vmumu)
_obs.add_taxonomy(
r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $'
+ _hadr[M]['tex'] + _tex[li] + r"^+" + _tex[li] + r"^-$")
Prediction(
_obs_name,
bvll_obs_int_ratio_leptonflavour(dGdq2_ave, _hadr[M]['B'],
_hadr[M]['V'], *l))
# differential ratio of BRs
_obs_name = "R" + l[0] + l[1] + "(" + M + "ll)"
_obs = Observable(name=_obs_name, arguments=['q2'])
_obs.set_description(r"Ratio of differential branching ratios of $" +
_hadr[M]['tex'] + _tex[l[0]] + r"^+ " + _tex[l[0]] +
r"^-$" + " and " + r"$" + _hadr[M]['tex'] +
_tex[l[1]] + r"^+ " + _tex[l[1]] + "^-$")
_obs.tex = r"$R_{" + _tex[l[0]] + ' ' + _tex[
l[1]] + r"} (" + _hadr[M]['tex'] + r"\ell^+\ell^-)$"
for li in l:
# add taxonomy for both processes (e.g. B->Vee and B->Vmumu)
_obs.add_taxonomy(
r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $'
+ _hadr[M]['tex'] + _tex[li] + r"^+" + _tex[li] + r"^-$")
func = lambda wc_obj, par, q2: BVll_dBRdq2(q2, B, V, l, wc_obj, par)()
Prediction(
_obs_name,
bvll_obs_ratio_leptonflavour(dGdq2_ave, _hadr[M]['B'], _hadr[M]['V'],
*l))
def make_obs_lfur(M, l):
"""Make observable instances for lepton flavour ratios"""
# binned ratio of BRs
_obs_name = "<R"+l[0]+l[1]+">("+M+"ll)"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
_obs.set_description(r"Ratio of partial branching ratios of $" + _hadr[M]['tex'] +_tex[l[0]]+r"^+ "+_tex[l[0]]+r"^-$" + " and " + r"$" + _hadr[M]['tex'] +_tex[l[1]]+r"^+ "+_tex[l[1]]+"^-$")
_obs.tex = r"$\langle R_{" + _tex[l[0]] + ' ' + _tex[l[1]] + r"} \rangle(" + _hadr[M]['tex'] + r"\ell^+\ell^-)$"
for li in l:
# add taxonomy for both processes (e.g. B->Vee and B->Vmumu)
_obs.add_taxonomy(r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _hadr[M]['tex'] +_tex[li]+r"^+"+_tex[li]+r"^-$")
Prediction(_obs_name, bvll_obs_int_ratio_leptonflavour(dGdq2_ave, _hadr[M]['B'], _hadr[M]['V'], *l))
# differential ratio of BRs
_obs_name = "R"+l[0]+l[1]+"("+M+"ll)"
_obs = Observable(name=_obs_name, arguments=['q2'])
_obs.set_description(r"Ratio of differential branching ratios of $" + _hadr[M]['tex'] +_tex[l[0]]+r"^+ "+_tex[l[0]]+r"^-$" + " and " + r"$" + _hadr[M]['tex'] +_tex[l[1]]+r"^+ "+_tex[l[1]]+"^-$")
_obs.tex = r"$R_{" + _tex[l[0]] + ' ' + _tex[l[1]] + r"} (" + _hadr[M]['tex'] + r"\ell^+\ell^-)$"
for li in l:
# add taxonomy for both processes (e.g. B->Vee and B->Vmumu)
_obs.add_taxonomy(r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _hadr[M]['tex'] +_tex[li]+r"^+"+_tex[li]+r"^-$")
func = lambda wc_obj, par, q2: BVll_dBRdq2(q2, B, V, l, wc_obj, par)()
Prediction(_obs_name, bvll_obs_ratio_leptonflavour(dGdq2_ave, _hadr[M]['B'], _hadr[M]['V'], *l))
def make_obs_br(M, l):
"""Make observable instances for branching ratios"""
_process_tex = _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+r"^-"
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _process_tex + r"$"
B = _hadr[M]['B']
V = _hadr[M]['V']
# binned branching ratio
_obs_name = "<dBR/dq2>("+M+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
_obs.set_description(r"Binned differential branching ratio of $" + _process_tex + r"$")
_obs.tex = r"$\langle \frac{d\text{BR}}{dq^2} \rangle(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
func = lambda wc_obj, par, q2min, q2max: BVll_dBRdq2_int(q2min, q2max, B, V, l, wc_obj, par)()
Prediction(_obs_name, func)
# differential branching ratio
_obs_name = "dBR/dq2("+M+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2'])
_obs.set_description(r"Differential branching ratio of $" + _process_tex + r"$")
_obs.tex = r"$\frac{d\text{BR}}{dq^2}(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
func = lambda wc_obj, par, q2: BVll_dBRdq2(q2, B, V, l, wc_obj, par)()
Prediction(_obs_name, func)
wc_s = flavio.physics.bdecays.wilsoncoefficients.wctot_dict(wc_obj, "bsee", scale, par, nf_out=5)
br_d = abs(xi_t_d) ** 2 * PE0_BR_BXgamma(wc_d, par, "d", E0)
br_s = abs(xi_t_s) ** 2 * PE0_BR_BXgamma(wc_s, par, "s", E0)
as_d = abs(xi_t_d) ** 2 * PE0_ACP_BXgamma(wc_d, par, "d", E0)
as_s = abs(xi_t_s) ** 2 * PE0_ACP_BXgamma(wc_s, par, "s", E0)
# return (as_s)/(br_s + br_d)
return (as_s + as_d) / (br_s + br_d)
_process_taxonomy = r"Process :: $b$ hadron decays :: FCNC decays :: $B\to X\gamma$ :: "
_obs_name = "BR(B->Xsgamma)"
_obs = Observable(_obs_name)
_obs.set_description(r"CP-averaged branching ratio of $B\to X_s\gamma$ for $E_\gamma>1.6$ GeV")
_obs.tex = r"$\text{BR}(B\to X_s\gamma)$"
_obs.add_taxonomy(_process_taxonomy + r"$B\to X_s\gamma$")
Prediction(_obs_name, lambda wc_obj, par: BRBXgamma(wc_obj, par, "s", 1.6))
_obs_name = "BR(B->Xdgamma)"
_obs = Observable(_obs_name)
_obs.set_description(r"CP-averaged branching ratio of $B\to X_d\gamma$ for $E_\gamma>1.6$ GeV")
_obs.tex = r"$\text{BR}(B\to X_d\gamma)$"
_obs.add_taxonomy(_process_taxonomy + r"$B\to X_d\gamma$")
Prediction(_obs_name, lambda wc_obj, par: BRBXgamma(wc_obj, par, "d", 1.6))
_obs_name = "ACP(B->Xgamma)"
_obs = Observable(_obs_name)
_obs.set_description(r"Direct CP asymmetry in $B\to X_{s+d}\gamma$ for $E_\gamma>1.6$ GeV")
_obs.tex = r"$A_\text{CP}(B\to X_{s+d}\gamma)$"
_obs.add_taxonomy(_process_taxonomy + r"$B\to X_{s+d}\gamma$")
Prediction(_obs_name, lambda wc_obj, par: ACPBXgamma(wc_obj, par, 1.6))
br_d = abs(xi_t_d)**2 * PE0_BR_BXgamma(wc_d, par, 'd', E0)
br_s = abs(xi_t_s)**2 * PE0_BR_BXgamma(wc_s, par, 's', E0)
as_d = abs(xi_t_d)**2 * PE0_ACP_BXgamma(wc_d, par, 'd', E0)
as_s = abs(xi_t_s)**2 * PE0_ACP_BXgamma(wc_s, par, 's', E0)
# return (as_s)/(br_s + br_d)
return (as_s + as_d) / (br_s + br_d)
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to X\gamma$ :: '
_obs_name = "BR(B->Xsgamma)"
_obs = Observable(_obs_name)
_obs.set_description(
r"CP-averaged branching ratio of $B\to X_s\gamma$ for $E_\gamma>1.6$ GeV")
_obs.tex = r"$\text{BR}(B\to X_s\gamma)$"
_obs.add_taxonomy(_process_taxonomy + r"$B\to X_s\gamma$")
Prediction(_obs_name, lambda wc_obj, par: BRBXgamma(wc_obj, par, 's', 1.6))
_obs_name = "BR(B->Xdgamma)"
_obs = Observable(_obs_name)
_obs.set_description(
r"CP-averaged branching ratio of $B\to X_d\gamma$ for $E_\gamma>1.6$ GeV")
_obs.tex = r"$\text{BR}(B\to X_d\gamma)$"
_obs.add_taxonomy(_process_taxonomy + r"$B\to X_d\gamma$")
Prediction(_obs_name, lambda wc_obj, par: BRBXgamma(wc_obj, par, 'd', 1.6))
_obs_name = "ACP(B->Xgamma)"
_obs = Observable(_obs_name)
_obs.set_description(
r"Direct CP asymmetry in $B\to X_{s+d}\gamma$ for $E_\gamma>1.6$ GeV")
_obs.tex = r"$A_\text{CP}(B\to X_{s+d}\gamma)$"
return (-par['omega+'] / (sqrt(2) * par['eps_K'])
* (ImA0 / ReA0 * (1 - par['Omegahat_eff'])
- 1 / a * ImA2 / ReA2).real)
def epsprime_NP(wc_obj, par):
r"""Compute the NP contribution to $\epsilon'/\epsilon$."""
# Neglecting isospin breaking corrections!
A = Kpipi_amplitudes_NP(wc_obj, par)
ImA0 = A[0].imag
ImA2 = A[2].imag
ReA0 = par['ReA0(K->pipi)']
ReA2 = par['ReA2(K->pipi)']
a = par['epsp a'] # eq. (16)
# dividing by a to remove the isospin brk corr in omega+, cf. (16) in 1507.06345
return (-par['omega+'] / a / (sqrt(2) * par['eps_K'])
* (ImA0 / ReA0 - ImA2 / ReA2).real)
def epsprime(wc_obj, par):
r"""Compute $\epsilon'/\epsilon$, parametrizing direct CPV in
$K\to\pi\pi$."""
return epsprime_SM(par) + epsprime_NP(wc_obj, par)
# Observable and Prediction instances
o = Observable('epsp/eps')
o.tex = r"$\epsilon^\prime/\epsilon$"
Prediction('epsp/eps', epsprime)
o.set_description(r"Direct CP violation parameter")
o.add_taxonomy(r'Process :: $s$ hadron decays :: Non-leptonic decays :: $K\to \pi\pi$')
'Bs->phi': {'tex': r"B_s\to \phi ", 'B': 'Bs', 'V': 'phi', },
}
for l in ['e', 'mu', 'tau']:
for M in _hadr.keys():
_process_tex = _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+r"^-"
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to V\ell^+\ell^-$ :: $' + _process_tex + r"$"
for obs in sorted(_observables.keys()):
# binned angular observables
_obs_name = "<" + obs + ">("+M+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
_obs.set_description('Binned ' + _observables[obs]['desc'] + r" in $" + _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+"^-$")
_obs.tex = r"$\langle " + _observables[obs]['tex'] + r"\rangle(" + _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+"^-)$"
_obs.add_taxonomy(_process_taxonomy)
Prediction(_obs_name, bsvll_obs_int_ratio_func(_observables[obs]['func_num'], SA_den_Bs, _hadr[M]['B'], _hadr[M]['V'], l))
# differential angular observables
_obs_name = obs + "("+M+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2'])
_obs.set_description(_observables[obs]['desc'][0].capitalize() + _observables[obs]['desc'][1:] + r" in $" + _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+"^-$")
_obs.tex = r"$" + _observables[obs]['tex'] + r"(" + _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+"^-)$"
_obs.add_taxonomy(_process_taxonomy)
Prediction(_obs_name, bsvll_obs_ratio_func(_observables[obs]['func_num'], SA_den_Bs, _hadr[M]['B'], _hadr[M]['V'], l))
# binned branching ratio
_obs_name = "<dBR/dq2>("+M+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
_obs.set_description(r"Binned time-integrated differential branching ratio of $" + _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+"^-$")
_obs.tex = r"$\langle \frac{d\overline{\text{BR}}}{dq^2} \rangle(" + _hadr[M]['tex'] +_tex[l]+r"^+"+_tex[l]+"^-)$"
def BR_tot_leptonflavour_function(lnum, lden):
return lambda wc_obj, par: BR_tot_leptonflavour(wc_obj, par, lnum, lden)
_process_taxonomy = r'Process :: $b$ hadron decays :: Semi-leptonic tree-level decays :: $B\to X\ell\nu$ :: $'
_lep = {'e': 'e', 'mu': r'\mu', 'tau': r'\tau', 'l': r'\ell'}
for l in _lep:
_obs_name = "BR(B->Xc" + l + "nu)"
_process_tex = r"B\to X_c" + _lep[l] + r"^+\nu_" + _lep[l]
_obs = Observable(_obs_name)
_obs.set_description(r"Total branching ratio of $" + _process_tex + r"$")
_obs.tex = r"$\text{BR}(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy + _process_tex + r"$")
Prediction(_obs_name, BR_tot_function(l))
# Lepton flavour ratios
for l in [('mu', 'e'), ('tau', 'mu'), ('tau', 'l')]:
_obs_name = "R" + l[0] + l[1] + "(B->Xclnu)"
_obs = Observable(name=_obs_name)
_process_1 = r"B\to X_c" + _lep[l[0]] + r"^+\nu_" + _lep[l[0]]
_process_2 = r"B\to X_c" + _lep[l[1]] + r"^+\nu_" + _lep[l[1]]
_obs.set_description(r"Ratio of total branching ratios of $" + _process_1 +
r"$" + " and " + r"$" + _process_2 + r"$")
_obs.tex = r"$R_{" + _lep[l[0]] + ' ' + _lep[
l[1]] + r"}(B\to X_c\ell^+\nu)$"
# add taxonomy for both processes (e.g. B->Xcenu and B->Xcmunu)
_obs.add_taxonomy(_process_taxonomy + _process_1 + r"$")
_obs.add_taxonomy(_process_taxonomy + _process_2 + r"$")
(1 - par['Omegahat_eff']) - 1 / a * ImA2 / ReA2).real)
def epsprime_NP(wc_obj, par):
r"""Compute the NP contribution to $\epsilon'/\epsilon$."""
# Neglecting isospin breaking corrections!
A = Kpipi_amplitudes_NP(wc_obj, par)
ImA0 = A[0].imag
ImA2 = A[2].imag
ReA0 = par['ReA0(K->pipi)']
ReA2 = par['ReA2(K->pipi)']
a = par['epsp a'] # eq. (16)
# dividing by a to remove the isospin brk corr in omega+, cf. (16) in 1507.06345
return (-par['omega+'] / a / (sqrt(2) * par['eps_K']) *
(ImA0 / ReA0 - ImA2 / ReA2).real)
def epsprime(wc_obj, par):
r"""Compute $\epsilon'/\epsilon$, parametrizing direct CPV in
$K\to\pi\pi$."""
return epsprime_SM(par) + epsprime_NP(wc_obj, par)
# Observable and Prediction instances
o = Observable('epsp/eps')
o.tex = r"$\epsilon^\prime/\epsilon$"
Prediction('epsp/eps', epsprime)
o.set_description(r"Direct CP violation parameter")
o.add_taxonomy(
r'Process :: $s$ hadron decays :: Non-leptonic decays :: $K\to \pi\pi$')
# Observable and Prediction instances
_tex = {'e': 'e', 'mu': '\mu', 'tau': r'\tau'}
for l in ['e', 'mu', 'tau']:
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to\ell^+\ell^-$ :: $'
# For the Bs decay, we take the time-integrated branching ratio
_obs_name = "BR(Bs->" + l + l + ")"
_obs = Observable(_obs_name)
_process_tex = r"B_s\to " + _tex[l] + r"^+" + _tex[l] + r"^-"
_obs.set_description(r"Time-integrated branching ratio of $" +
_process_tex + r"$.")
_obs.tex = r"$\overline{\text{BR}}(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy + _process_tex + r"$")
Prediction(_obs_name, bqll_obs_function(br_timeint, 'Bs', l, l))
# Add the effective lifetimes for Bs
_obs_name = 'tau_' + l + l
_obs = Observable(_obs_name)
_obs.set_description(r"Effective lifetime for $" + _process_tex + r"$.")
_obs.tex = r"$\tau_{B_s \to " + _tex[l] + _tex[l] + "}$"
_obs.add_taxonomy(_process_taxonomy + _process_tex + r"$")
if l == 'e':
Prediction(_obs_name,
lambda wc_obj, par: tau_ll_func(wc_obj, par, 'Bs', 'e'))
if l == 'mu':
Prediction(_obs_name,
lambda wc_obj, par: tau_ll_func(wc_obj, par, 'Bs', 'mu'))
if l == 'tau':
def CR_mueAl(wc_obj, par):
r"""Conversion rate for $\phantom k^{27}_{13} \mathrm{Al}$"""
return CR_mue(wc_obj, par, 'Al')
def CR_mueTi(wc_obj, par):
r"""Conversion rate for $\phantom k^{48}_{22} \mathrm{Ti}$"""
return CR_mue(wc_obj, par, 'Ti')
CRAu = Observable('CR(mu->e, Au)')
Prediction('CR(mu->e, Au)', CR_mueAu)
CRAu.tex = r"$CR(\mu - e)$ in $\phantom k^{197}_{79} \mathrm{Au}$"
CRAu.description = r"Coherent conversion rate of $\mu^-$ to $e^-$ in $\phantom k^{197}_{79} \mathrm{Au}$"
CRAu.add_taxonomy(
r'Process :: muon decays :: LFV decays :: $\mu N \to e N$ :: ' + CRAu.tex)
CRAl = Observable('CR(mu->e, Al)')
Prediction('CR(mu->e, Al)', CR_mueAl)
CRAl.tex = r"$CR(\mu - e)$ in $\phantom k^{27}_{13} \mathrm{Al}$"
CRAl.description = r"Coherent conversion rate of $\mu^-$ to $e^-$ in $\phantom k^{27}_{13} \mathrm{Al}$"
CRAl.add_taxonomy(
r'Process :: muon decays :: LFV decays :: $\mu N \to e N$ :: ' + CRAl.tex)
CRTi = Observable('CR(mu->e, Ti)')
Prediction('CR(mu->e, Ti)', CR_mueTi)
CRTi.tex = r"$CR(\mu - e)$ in $\phantom k^{48}_{22} \mathrm{Ti}$"
CRTi.description = r"Coherent conversion rate of $\mu^-$ to $e^-$ in $\phantom k^{48}_{22} \mathrm{Ti}$"
CRTi.add_taxonomy(
r'Process :: muon decays :: LFV decays :: $\mu N \to e N$ :: ' + CRTi.tex)
'FL': {'func_num': FL_num, 'tex': r'F_L', 'desc': 'longitudinal polarization fraction'},
'AFBl': {'func_num': AFBl_num, 'tex': r'A_\text{FB}^\ell', 'desc': 'leptonic forward-backward asymmetry'},
'AFBh': {'func_num': AFBh_num, 'tex': r'A_\text{FB}^h', 'desc': 'hadronic forward-backward asymmetry'},
'AFBlh': {'func_num': AFBlh_num, 'tex': r'A_\text{FB}^{\ell h}', 'desc': 'lepton-hadron forward-backward asymmetry'},
}
for l in ['e', 'mu', ]: # tau requires lepton mass dependence!
_process_tex = r"\Lambda_b\to\Lambda " +_tex[l]+r"^+"+_tex[l]+r"^-"
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $\Lambda_b\to \Lambda\ell^+\ell^-$ :: $' + _process_tex + r"$"
# binned branching ratio
_obs_name = "<dBR/dq2>(Lambdab->Lambda"+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
_obs.set_description(r"Binned differential branching ratio of $" + _process_tex + r"$")
_obs.tex = r"$\langle \frac{d\text{BR}}{dq^2} \rangle(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
Prediction(_obs_name, dbrdq2_int_func(l))
# differential branching ratio
_obs_name = "dBR/dq2(Lambdab->Lambda"+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2'])
_obs.set_description(r"Differential branching ratio of $" + _process_tex + r"$")
_obs.tex = r"$\frac{d\text{BR}}{dq^2}(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
Prediction(_obs_name, dbrdq2_func(l))
for obs in _observables:
# binned angular observables
_obs_name = "<" + obs + ">(Lambdab->Lambda"+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
_obs.set_description("Binned " + _observables[obs]['desc'] + r" in $" + _process_tex + r"$")
# Observable instances
_tex = {'e': 'e', 'mu': '\mu', 'tau': r'\tau', 'l': r'\ell'}
for l in ['e', 'mu', 'tau', 'l']:
for q in ['s', 'd']:
_process_tex = r"B\to X_" + q +_tex[l]+r"^+"+_tex[l]+r"^-"
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to X\ell^+\ell^-$ :: $' + _process_tex + r"$"
# binned branching ratio
_obs_name = "<BR>(B->X"+q+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
_obs.set_description(r"Binned branching ratio of $" + _process_tex + r"$")
_obs.tex = r"$\langle \text{BR} \rangle(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
Prediction(_obs_name, bxll_br_int_func(q, l))
# differential branching ratio
_obs_name = "dBR/dq2(B->X"+q+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2'])
_obs.set_description(r"Differential branching ratio of $" + _process_tex + r"$")
_obs.tex = r"$\frac{d\text{BR}}{dq^2}(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
Prediction(_obs_name, bxll_dbrdq2_func(q, l))
if l != 'tau': # AFB not yet implemented for tau! (ml=0)
# binned AFB
_obs_name = "<AFB>(B->X"+q+l+l+")"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
for l in ['e', 'mu', 'tau', 'l']:
for br in ['dBR/dq2', 'BR', '<BR>',
'dBR_L/dq2', 'BR_L', '<BR_L>',
'dBR_T/dq2', 'BR_T', '<BR_T>',
'<BR>/<cl>', '<BR>/<cV>', '<BR>/<phi>',
'dBR/dcl', 'dBR/dcV', 'dBR/dphi',
'<FL>', 'FL', 'FLtot']:
for M in _hadr.keys():
_process_tex = _hadr[M]['tex']+_tex[l]+r"^+\nu_"+_tex[l]
_obs_name = br + "("+M+l+"nu)"
_obs = Observable(_obs_name)
_obs.set_description(_desc[br] + r" branching ratio of $" + _process_tex + "$")
_obs.tex = r'$' + _tex_br[br] + r"(" +_process_tex + ")$"
_obs.arguments = _args[br]
_obs.add_taxonomy(_process_taxonomy + _process_tex + r'$')
if br in _A:
# for dBR/dq2, need to distinguish between total, L, and T
Prediction(_obs_name, _func[br](_hadr[M]['B'], _hadr[M]['V'], l, A=_A[br]))
else:
# for other observables not
Prediction(_obs_name, _func[br](_hadr[M]['B'], _hadr[M]['V'], l))
# Lepton flavour ratios
for l in [('mu','e'), ('tau','mu'), ('tau', 'l')]:
for M in _hadr_l.keys():
# binned ratio of BRs
_obs_name = "<R"+l[0]+l[1]+">("+M+"lnu)"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
xi = etaCP * qp * A / A_bar
return -2*xi.imag / ( 1 + abs(xi)**2 )
def S_BJpsiK(wc_obj, par):
return S(wc_obj, par, 'B0', amplitude_BJpsiK, etaCP=-1)
def S_Bspsiphi(wc_obj, par):
return S(wc_obj, par, 'Bs', amplitude_Bspsiphi, etaCP=+1)
# Observable and Prediction instances
o = Observable('DeltaM_s')
o.set_description(r"Mass difference in the $B_s$-$\bar B_s$ system")
o.tex = r"$\Delta M_s$"
o.add_taxonomy(r'Process :: Meson-antimeson mixing :: $B_s$-$\bar B_s$ mixing')
Prediction('DeltaM_s', lambda wc_obj, par: DeltaM(wc_obj, par, 'Bs'))
o = Observable('DeltaM_d')
o.set_description(r"Mass difference in the $B^0$-$\bar B^0$ system")
o.tex = r"$\Delta M_d$"
o.add_taxonomy(r'Process :: Meson-antimeson mixing :: $B^0$-$\bar B^0$ mixing')
Prediction('DeltaM_d', lambda wc_obj, par: DeltaM(wc_obj, par, 'B0'))
o = Observable('a_fs_s')
o.set_description(r"CP asymmetry in flavour-specific $B_s$ decays")
o.tex = r"$a_\text{fs}^s$"
o.add_taxonomy(r'Process :: Meson-antimeson mixing :: $B_s$-$\bar B_s$ mixing')
Prediction('a_fs_s', lambda wc_obj, par: a_fs(wc_obj, par, 'Bs'))
o = Observable('a_fs_d')
# Observable instances
_tex = {'e': 'e', 'mu': '\mu', 'tau': r'\tau', 'l': r'\ell'}
for l in ['e', 'mu', 'tau', 'l']:
for q in ['s', 'd']:
_process_tex = r"B\to X_" + q + _tex[l] + r"^+" + _tex[l] + r"^-"
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to X\ell^+\ell^-$ :: $' + _process_tex + r"$"
# binned branching ratio
_obs_name = "<BR>(B->X" + q + l + l + ")"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
_obs.set_description(r"Binned branching ratio of $" + _process_tex +
r"$")
_obs.tex = r"$\langle \text{BR} \rangle(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
Prediction(_obs_name, bxll_br_int_func(q, l))
# differential branching ratio
_obs_name = "dBR/dq2(B->X" + q + l + l + ")"
_obs = Observable(name=_obs_name, arguments=['q2'])
_obs.set_description(r"Differential branching ratio of $" +
_process_tex + r"$")
_obs.tex = r"$\frac{d\text{BR}}{dq^2}(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
Prediction(_obs_name, bxll_dbrdq2_func(q, l))
if l != 'tau': # AFB not yet implemented for tau! (ml=0)
# binned AFB
_obs_name = "<AFB>(B->X" + q + l + l + ")"
xi = etaCP * qp * A / A_bar
return -2*xi.imag / ( 1 + abs(xi)**2 )
def S_BJpsiK(wc_obj, par):
return S(wc_obj, par, 'B0', amplitude_BJpsiK, etaCP=-1)
def S_Bspsiphi(wc_obj, par):
return S(wc_obj, par, 'Bs', amplitude_Bspsiphi, etaCP=+1)
# Observable and Prediction instances
o = Observable('DeltaM_s')
o.set_description(r"Mass difference in the $B_s$-$\bar B_s$ system")
o.tex = r"$\Delta M_s$"
o.add_taxonomy(r'Process :: Meson-antimeson mixing :: $B_s$-$\bar B_s$ mixing')
Prediction('DeltaM_s', lambda wc_obj, par: DeltaM_positive(wc_obj, par, 'Bs'))
o = Observable('DeltaM_d')
o.set_description(r"Mass difference in the $B^0$-$\bar B^0$ system")
o.tex = r"$\Delta M_d$"
o.add_taxonomy(r'Process :: Meson-antimeson mixing :: $B^0$-$\bar B^0$ mixing')
Prediction('DeltaM_d', lambda wc_obj, par: DeltaM_positive(wc_obj, par, 'B0'))
o = Observable('DeltaM_d/DeltaM_s')
o.set_description(r"Ratio of Mass differences in the $B^0$-$\bar B^0$ and $B_s$-$\bar B_s$ systems")
o.tex = r"$\Delta M_d/\Delta M_s$"
o.add_taxonomy(r'Process :: Meson-antimeson mixing :: $B^0$-$\bar B^0$ mixing')
o.add_taxonomy(r'Process :: Meson-antimeson mixing :: $B_s$-$\bar B_s$ mixing')
Prediction('DeltaM_d/DeltaM_s', lambda wc_obj, par: DeltaM_positive(wc_obj, par, 'B0')
/ DeltaM_positive(wc_obj, par, 'Bs'))
return num/den
def BR_tot_leptonflavour_function(lnum, lden):
return lambda wc_obj, par: BR_tot_leptonflavour(wc_obj, par, lnum, lden)
_process_taxonomy = r'Process :: $b$ hadron decays :: Semi-leptonic tree-level decays :: $B\to X\ell\nu$ :: $'
_lep = {'e': 'e', 'mu': r'\mu', 'tau': r'\tau', 'l': r'\ell'}
for l in _lep:
_obs_name = "BR(B->Xc"+l+"nu)"
_process_tex = r"B\to X_c"+_lep[l]+r"^+\nu_"+_lep[l]
_obs = Observable(_obs_name)
_obs.set_description(r"Total branching ratio of $" + _process_tex + r"$")
_obs.tex = r"$\text{BR}(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy + _process_tex + r"$")
Prediction(_obs_name, BR_tot_function(l))
# Lepton flavour ratios
for l in [('mu','e'), ('tau','mu'), ('tau', 'l')]:
_obs_name = "R"+l[0]+l[1]+"(B->Xclnu)"
_obs = Observable(name=_obs_name)
_process_1 = r"B\to X_c"+_lep[l[0]]+r"^+\nu_"+_lep[l[0]]
_process_2 = r"B\to X_c"+_lep[l[1]]+r"^+\nu_"+_lep[l[1]]
_obs.set_description(r"Ratio of total branching ratios of $" + _process_1 + r"$" + " and " + r"$" + _process_2 +r"$")
_obs.tex = r"$R_{" + _lep[l[0]] + ' ' + _lep[l[1]] + r"}(B\to X_c\ell^+\nu)$"
# add taxonomy for both processes (e.g. B->Xcenu and B->Xcmunu)
_obs.add_taxonomy(_process_taxonomy + _process_1 + r"$")
_obs.add_taxonomy(_process_taxonomy + _process_2 + r"$")
Prediction(_obs_name, BR_tot_leptonflavour_function(l[0], l[1]))
def BR_tot_function(B, V, lep):
return lambda wc_obj, par: BR_tot(wc_obj, par, B, V, lep)
# Observable and Prediction instances
_tex = {'e': 'e', 'mu': '\mu', 'tau': r'\tau', 'l': r'\ell'}
_func = {'dBR/dq2': dBRdq2_function, 'BR': BR_tot_function, '<BR>': BR_binned_function}
_desc = {'dBR/dq2': 'Differential', 'BR': 'Total', '<BR>': 'Binned'}
_tex_br = {'dBR/dq2': r'\frac{d\text{BR}}{dq^2}', 'BR': r'\text{BR}', '<BR>': r'\langle\text{BR}\rangle'}
_args = {'dBR/dq2': ['q2'], 'BR': None, '<BR>': ['q2min', 'q2max']}
_hadr = {
'B0->D*': {'tex': r"B^0\to D^{\ast -}", 'B': 'B0', 'V': 'D*+', },
'B+->D*': {'tex': r"B^+\to D^{\ast 0}", 'B': 'B+', 'V': 'D*0', },
'B0->rho': {'tex': r"B^0\to \rho^-", 'B': 'B0', 'V': 'rho+', },
'B+->rho': {'tex': r"B^+\to \rho^0", 'B': 'B+', 'V': 'rho0', },
'B+->omega': {'tex': r"B^+\to \omega ", 'B': 'B+', 'V': 'omega', },
'Bs->K*': {'tex': r"B_s\to K^{* -} ", 'B': 'Bs', 'V': 'K*+', },
}
for l in ['e', 'mu', 'tau', 'l']:
for br in ['dBR/dq2', 'BR', '<BR>']:
for M in _hadr.keys():
_process_tex = _hadr[M]['tex']+_tex[l]+r"^+\nu_"+_tex[l]
_obs_name = br + "("+M+l+"nu)"
_obs = Observable(_obs_name)
_obs.set_description(_desc[br] + r" branching ratio of $" + _process_tex + "$")
_obs.tex = r'$' + _tex_br[br] + r"(" +_process_tex + ")$"
_obs.arguments = _args[br]
_obs.add_taxonomy(r'Process :: $b$ hadron decays :: Semi-leptonic tree-level decays :: $B\to V\ell\nu$ :: $' + _process_tex + r'$')
Prediction(_obs_name, _func[br](_hadr[M]['B'], _hadr[M]['V'], l))
},
}
_process_taxonomy = r'Process :: $b$ hadron decays :: Semi-leptonic tree-level decays :: $B\to V\ell\nu$ :: $'
for l in ['e', 'mu', 'tau', 'l']:
for br in ['dBR/dq2', 'BR', '<BR>']:
for M in _hadr.keys():
_process_tex = _hadr[M]['tex'] + _tex[l] + r"^+\nu_" + _tex[l]
_obs_name = br + "(" + M + l + "nu)"
_obs = Observable(_obs_name)
_obs.set_description(_desc[br] + r" branching ratio of $" +
_process_tex + "$")
_obs.tex = r'$' + _tex_br[br] + r"(" + _process_tex + ")$"
_obs.arguments = _args[br]
_obs.add_taxonomy(_process_taxonomy + _process_tex + r'$')
Prediction(_obs_name, _func[br](_hadr[M]['B'], _hadr[M]['V'], l))
# Lepton flavour ratios
for l in [('mu', 'e'), ('tau', 'mu'), ('tau', 'l')]:
for M in _hadr_l.keys():
# binned ratio of BRs
_obs_name = "<R" + l[0] + l[1] + ">(" + M + "lnu)"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
_obs.set_description(r"Ratio of partial branching ratios of $" +
_hadr_l[M]['tex'] + _tex[l[0]] + r"^+ \nu_" +
_tex[l[0]] + r"$" + " and " + r"$" +
_hadr_l[M]['tex'] + _tex[l[1]] + r"^+ \nu_" +
_tex[l[1]] + r"$")
_obs.tex = r"$\langle R_{" + _tex[l[0]] + ' ' + _tex[
}
for l in ['e', 'mu', 'tau']:
for M in _hadr.keys():
_process_tex = _hadr[M]['tex'] + _tex[l] + r"^+" + _tex[l] + r"^-"
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to P\ell^+\ell^-$ :: $' + _process_tex + r"$"
for obs in sorted(_observables.keys()):
_obs_name = "<" + obs + ">(" + M + l + l + ")"
_obs = Observable(name=_obs_name, arguments=['q2min', 'q2max'])
_obs.set_description('Binned ' + _observables[obs]['desc'] +
r" in $" + _process_tex + r"$")
_obs.tex = r"$\langle " + _observables[obs][
'tex'] + r"\rangle(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
Prediction(
_obs_name,
bpll_obs_int_ratio_func(_observables[obs]['func_num'],
dGdq2_cpaverage, _hadr[M]['B'],
_hadr[M]['P'], l))
_obs_name = obs + "(" + M + l + l + ")"
_obs = Observable(name=_obs_name, arguments=['q2'])
_obs.set_description(_observables[obs]['desc'][0].capitalize() +
_observables[obs]['desc'][1:] + r" in $" +
_process_tex + r"$")
_obs.tex = r"$" + _observables[obs][
'tex'] + r"(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
Prediction(
'dBR/dq2': r'\frac{d\text{BR}}{dq^2}',
'BR': r'\text{BR}',
'<BR>': r'\langle\text{BR}\rangle'
}
_args = {'dBR/dq2': ['q2'], 'BR': None, '<BR>': ['q2min', 'q2max']}
_hadr = {
'KL->pi': {
'tex': r"K_L\to \pi^+",
'K': 'KL',
'P': 'pi+',
},
'K+->pi': {
'tex': r"K^+\to \pi^0",
'K': 'K+',
'P': 'pi0',
},
}
for l in ['e', 'mu', 'l']:
for M in _hadr.keys():
_process_tex = _hadr[M]['tex'] + _tex[l] + r"^+\nu_" + _tex[l]
_process_taxonomy = r'Process :: $s$ hadron decays :: Semi-leptonic tree-level decays :: $K\to P\ell\nu$ :: $' + _process_tex + r"$"
_obs_name = "BR(" + M + l + "nu)"
_obs = Observable(_obs_name)
_obs.set_description(r"Total branching ratio of $" + _process_tex +
r"$")
_obs.tex = r"$\text{BR}(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy)
Prediction(_obs_name, BR_tot_function(_hadr[M]['K'], _hadr[M]['P'], l))
wc = wctot_dict(wc_obj, label, scale, par)
return ADeltaGamma(par, wc, B, lep)
return ADG_func
# Observable and Prediction instances
_tex = {'e': 'e', 'mu': '\mu', 'tau': r'\tau'}
for l in ['e', 'mu', 'tau']:
_process_taxonomy = r'Process :: $b$ hadron decays :: FCNC decays :: $B\to\ell^+\ell^-$ :: $'
# For the B^0 decay, we take the time-integrated branching ratio
_obs_name = "BR(Bs->"+l+l+")"
_obs = Observable(_obs_name)
_process_tex = r"B_s\to "+_tex[l]+r"^+"+_tex[l]+r"^-"
_obs.set_description(r"Time-integrated branching ratio of $" + _process_tex + r"$.")
_obs.tex = r"$\overline{\text{BR}}(" + _process_tex + r")$"
_obs.add_taxonomy(_process_taxonomy + _process_tex + r"$")
Prediction(_obs_name, bqll_obs_function(br_timeint, 'Bs', l, l))
# Add the effective lifetimes for Bs
_obs_name = 'tau_'+l+l
_obs = Observable(_obs_name)
_obs.set_description(r"Effective lifetime for $"+ _process_tex + r"$.")
_obs.tex = r"$\tau_{B_s \to " +_tex[l] +_tex[l] + "}$"
_obs.add_taxonomy(_process_taxonomy + _process_tex + r"$")
if l=='e':
Prediction(_obs_name, lambda wc_obj, par: tau_ll_func(wc_obj, par, 'Bs', 'e'))
if l=='mu':
Prediction(_obs_name, lambda wc_obj, par: tau_ll_func(wc_obj, par, 'Bs', 'mu'))
if l=='tau':
Prediction(_obs_name, lambda wc_obj, par: tau_ll_func(wc_obj, par, 'Bs', 'tau'))
