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smeftew.py
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smeftew.py
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r"""Shift of electroweak parameters and $Z$ couplings due to dimension-6
operators in SMEFT.
Taken from Appendix A.1 in arXiv:1706.08945."""
from math import sqrt, pi
import flavio
# fermion quantum numbers
_QN = {}
_QN['e'] = _QN['mu'] = _QN['tau'] = {'T3L': -1 / 2, 'Q': -1, 'Nc': 1}
_QN['nue'] = _QN['numu'] = _QN['nutau'] = {'T3L': 1 / 2, 'Q': 0, 'Nc': 1}
_QN['u'] = _QN['c'] = {'T3L': 1 / 2, 'Q': 2 / 3, 'Nc': 3}
_QN['d'] = _QN['s'] = _QN['b'] = {'T3L': -1 / 2, 'Q': -1 / 3, 'Nc': 3}
_sectors = {'l': {'e': 1, 'mu': 2, 'tau': 3},
'nu': {'nue': 1, 'numu': 2, 'nutau': 3},
'u': {'u': 1, 'c': 2,},
'd': {'d': 1, 's': 2, 'b': 3}}
def d_GF(par, C):
flavio.citations.register("Brivio:2017vri")
return 1 / (sqrt(2) * par['GF']) * sqrt(2) / 2 * (C['phil3_22'] + C['phil3_11'] - C['ll_1221'] / 2)
def _sinthetahat2(par):
r"""$sin^2(\hat\theta)$"""
flavio.citations.register("Brivio:2017vri")
return 1 / 2 * (1 - sqrt(1 - (4 * pi * par['alpha_e']) / (sqrt(2) * par['GF'] * par['m_Z']**2)))
def d_sh2(par, C):
flavio.citations.register("Brivio:2017vri")
sh2 = _sinthetahat2(par)
sh = sqrt(sh2)
ch2 = 1 - sh2
ch = sqrt(ch2)
s2h = 2 * ch * sh # sin(2 * thetahat)
c2h = ch**2 - sh**2 # cos(2 * thetahat)
dC = s2h * (C['phiD'] + 2 * (C['phil3_22'] + C['phil3_11'] - C['ll_1221'] / 2)) + 4 * C['phiWB']
return s2h / (8 * c2h * sqrt(2) * par['GF']) * dC
def d_mZ2(par, C):
flavio.citations.register("Brivio:2017vri")
return (1 / (2 * sqrt(2)) * par['m_Z']**2 / par['GF'] * C['phiD']
+ (2**(1 / 4) * sqrt(pi * par['alpha_e']) * par['m_Z'])
/ par['GF']**(3 / 2) * C['phiWB'])
def d_gZb(par, C):
flavio.citations.register("Brivio:2017vri")
sh2 = _sinthetahat2(par)
sh = sqrt(sh2)
ch = sqrt(1 - sh2)
return (-d_GF(par, C) / sqrt(2)
- d_mZ2(par, C) / (2 * par['m_Z']**2)
+ sh * ch / (sqrt(2) * par['GF']) * C['phiWB'])
def gV_SM(f, par):
T3L = _QN[f]['T3L']
Q = _QN[f]['Q']
if f == 'b':
s2w_eff = par['s2w'] * 1.0065
else:
s2w_eff = par['s2w'] * 1.0010
return T3L / 2 - Q * s2w_eff
def gA_SM(f, par):
T3L = _QN[f]['T3L']
return T3L / 2
def d_gVl(f1, f2, par, C):
flavio.citations.register("Brivio:2017vri")
i, j = sorted((_sectors['l'][f1], _sectors['l'][f2]))
d_g = -(C['phie_{}{}'.format(i, j)] + C['phil1_{}{}'.format(i, j)] + C['phil3_{}{}'.format(i, j)]) / (4 * sqrt(2) * par['GF'])
if i > j:
d_g = d_g.conjugate()
if f1 == f2:
d_g += d_gZb(par, C) * gV_SM(f1, par) + d_sh2(par, C)
return d_g
def d_gVnu(f1, f2, par, C):
flavio.citations.register("Brivio:2017vri")
i, j = sorted((_sectors['nu'][f1], _sectors['nu'][f2]))
d_g = -(C['phil1_{}{}'.format(i, j)] - C['phil3_{}{}'.format(i, j)]) / (4 * sqrt(2) * par['GF'])
if i > j:
d_g = d_g.conjugate()
if f1 == f2:
d_g += d_gZb(par, C) * gV_SM(f1, par)
return d_g
def d_gVu(f1, f2, par, C):
flavio.citations.register("Brivio:2017vri")
i, j = sorted((_sectors['u'][f1], _sectors['u'][f2]))
d_g = (-C['phiu_{}{}'.format(i, j)] - C['phiq1_{}{}'.format(i, j)] + C['phiq3_{}{}'.format(i, j)]) / (4 * sqrt(2) * par['GF'])
if i > j:
d_g = d_g.conjugate()
if f1 == f2:
d_g += d_gZb(par, C) * gV_SM(f1, par) - 2 / 3 * d_sh2(par, C)
return d_g
def d_gVd(f1, f2, par, C):
flavio.citations.register("Brivio:2017vri")
i, j = sorted((_sectors['d'][f1], _sectors['d'][f2]))
d_g = -(C['phid_{}{}'.format(i, j)] + C['phiq1_{}{}'.format(i, j)] + C['phiq3_{}{}'.format(i, j)]) / (4 * sqrt(2) * par['GF'])
if i > j:
d_g = d_g.conjugate()
if f1 == f2:
d_g += d_gZb(par, C) * gV_SM(f1, par) + 1 / 3 * d_sh2(par, C)
return d_g
def d_gAl(f1, f2, par, C):
flavio.citations.register("Brivio:2017vri")
i, j = sorted((_sectors['l'][f1], _sectors['l'][f2]))
d_g = (C['phie_{}{}'.format(i, j)] - C['phil1_{}{}'.format(i, j)] - C['phil3_{}{}'.format(i, j)]) / (4 * sqrt(2) * par['GF'])
if i > j:
d_g = d_g.conjugate()
if f1 == f2:
d_g += d_gZb(par, C) * gA_SM(f1, par)
return d_g
def d_gAnu(f1, f2, par, C):
return d_gVnu(f1, f2, par, C) # V == A for neutrinos
def d_gAu(f1, f2, par, C):
flavio.citations.register("Brivio:2017vri")
i, j = sorted((_sectors['u'][f1], _sectors['u'][f2]))
d_g = -(-C['phiu_{}{}'.format(i, j)] + C['phiq1_{}{}'.format(i, j)] - C['phiq3_{}{}'.format(i, j)]) / (4 * sqrt(2) * par['GF'])
if i > j:
d_g = d_g.conjugate()
if f1 == f2:
d_g += d_gZb(par, C) * gA_SM(f1, par)
return d_g
def d_gAd(f1, f2, par, C):
flavio.citations.register("Brivio:2017vri")
i, j = sorted((_sectors['d'][f1], _sectors['d'][f2]))
d_g = (C['phid_{}{}'.format(i, j)] - C['phiq1_{}{}'.format(i, j)] - C['phiq3_{}{}'.format(i, j)]) / (4 * sqrt(2) * par['GF'])
if i > j:
d_g = d_g.conjugate()
if f1 == f2:
d_g += d_gZb(par, C) * gA_SM(f1, par)
return d_g
def d_gV(f1, f2, par, C):
if f1 in _sectors['l']:
return d_gVl(f1, f2, par, C)
if f1 in _sectors['nu']:
return d_gVnu(f1, f2, par, C)
if f1 in _sectors['u']:
return d_gVu(f1, f2, par, C)
if f1 in _sectors['d']:
return d_gVd(f1, f2, par, C)
def d_gA(f1, f2, par, C):
if f1 in _sectors['l']:
return d_gAl(f1, f2, par, C)
if f1 in _sectors['nu']:
return d_gAnu(f1, f2, par, C)
if f1 in _sectors['u']:
return d_gAu(f1, f2, par, C)
if f1 in _sectors['d']:
return d_gAd(f1, f2, par, C)
def d_gWl(f1, f2, par, C):
flavio.citations.register("Brivio:2017vri")
i, j = sorted((_sectors['l'][f1], _sectors['l'][f2]))
sh2 = _sinthetahat2(par)
sh = sqrt(sh2)
ch = sqrt(1 - sh2)
d_g = (C['phil3_{}{}'.format(i, j)] + 1 / 2 * ch / sh * C['phiWB']) / (2 * sqrt(2) * par['GF']) - 1 / 4 * d_sh2(par, C) / sh**2
return d_g
def d_gWq(f1, f2, par, C):
flavio.citations.register("Brivio:2017vri")
i, j = sorted((_sectors['u'][f1], _sectors['d'][f2]))
sh2 = _sinthetahat2(par)
sh = sqrt(sh2)
ch = sqrt(1 - sh2)
d_g = (C['phiq3_{}{}'.format(i, j)] + 1 / 2 * ch / sh * C['phiWB']) / (2 * sqrt(2) * par['GF']) - 1 / 4 * d_sh2(par, C) / sh**2
return d_g
def d_gW(f1, f2, par, C):
if f1 in _sectors['l']:
return d_gWl(f1, f2, par, C)
if f1 in _sectors['u']:
return d_gWq(f1, f2, par, C)