def ff(process, q2, par, scale):
r"""Central value of $B\to P$ form factors in the lattice convention
CLN parametrization.
See arXiv:hep-ph/9712417 and arXiv:1703.05330.
"""
pd = process_dict[process]
mB = par['m_' + pd['B']]
mP = par['m_' + pd['P']]
w = max((mB**2 + mP**2 - q2) / (2 * mB * mP), 1)
phqet = hqet.get_hqet_parameters(par, scale)
ash = phqet['ash']
epsc = phqet['epsc']
epsb = phqet['epsb']
zc = phqet['zc']
CV1 = hqet.CV1(w, zc)
CV2 = hqet.CV2(w, zc)
CV3 = hqet.CV3(w, zc)
CT1 = hqet.CT1(w, zc)
CT2 = hqet.CT2(w, zc)
CT3 = hqet.CT3(w, zc)
L = hqet.L(par, w)
# leading, universal Isgur-Wise function
rho2 = par['CLN rho2_xi']
c = par['CLN c_xi']
z = common.z(mB, mP, q2, t0='tm')
xi = 1 - 8 * rho2 * z + (64 * c - 16 * rho2) * z**2
h = {}
h['h+'] = xi * (1 + ash * (CV1 + (w + 1) / 2 * (CV2 + CV3)) +
(epsc + epsb) * L[1] + epsc**2 * par['B->D CLN deltac_h+'])
h['h-'] = xi * (ash * (w + 1) / 2 * (CV2 - CV3) + (epsc - epsb) * L[4])
h['hT'] = xi * (1 + ash * (CT1 - CT2 + CT3) + (epsc + epsb) *
(L[1] - L[4]))
return h_to_f(mB, mP, h, q2)
def ff(process, q2, par, scale, order_z=3, order_z_slp=2, order_z_sslp=1):
r"""Central value of $B\to V$ form factors in the lattice convention
CLN parametrization.
See arXiv:1703.05330.
"""
pd = process_dict[process]
mB = par['m_' + pd['B']]
mV = par['m_' + pd['V']]
w = max((mB**2 + mV**2 - q2) / (2 * mB * mV), 1)
phqet = hqet.get_hqet_parameters(par)
ash = phqet['ash']
epsc = phqet['epsc']
epsb = phqet['epsb']
zc = phqet['zc']
# eq. (22) of arXiv:0809.0222
CV1 = hqet.CV1(w, zc)
CV2 = hqet.CV2(w, zc)
CV3 = hqet.CV3(w, zc)
CA1 = hqet.CA1(w, zc)
CA2 = hqet.CA2(w, zc)
CA3 = hqet.CA3(w, zc)
CT1 = hqet.CT1(w, zc)
CT2 = hqet.CT2(w, zc)
CT3 = hqet.CT3(w, zc)
z = common.z(mB, mV, q2, t0='tm')
rho2 = par['CLN rho2_xi']
c = par['CLN c_xi']
xi3 = par['CLN xi3']
xi = hqet.xi(z, rho2, c, xi3, order_z=order_z)
L = hqet.Lz(par, w, z, order_z=order_z_slp)
ell = hqet.ell(par, z, order_z=order_z_sslp)
h = {}
h['V'] = xi * (1 + ash * CV1 + epsc * (L[2] - L[5]) + epsb *
(L[1] - L[4]) + epsc**2 * (ell[2] - ell[5]))
h['A1'] = xi * (1 + ash * CA1 + epsc * (L[2] - L[5] * (w - 1) /
(w + 1)) + epsb *
(L[1] - L[4] * (w - 1) / (w + 1)) + epsc**2 *
(ell[2] - ell[5] * (w - 1) / (w + 1)))
h['A2'] = xi * (ash * CA2 + epsc * (L[3] + L[6]))
h['A3'] = xi * (1 + ash * (CA1 + CA3) + epsc *
(L[2] - L[3] + L[6] - L[5]) + epsb *
(L[1] - L[4]) + epsc**2 *
(ell[2] - ell[3] + ell[6] - ell[5]))
h['T1'] = xi * (1 + ash * (CT1 + (w - 1) / 2 * (CT2 - CT3)) + epsc * L[2] +
epsb * L[1] + epsc**2 * ell[2])
h['T2'] = xi * (ash * (w + 1) / 2 *
(CT2 + CT3) + epsc * L[5] - epsb * L[4] + epsc * ell[5])
h['T3'] = xi * (ash * CT2 + epsc * (L[6] - L[3]) + epsc *
(ell[6] - ell[3]))
return h_to_A(mB, mV, h, q2)
def ff(process, q2, par, scale):
r"""Central value of $B\to V$ form factors in the lattice convention
CLN parametrization.
See arXiv:1703.05330.
"""
pd = process_dict[process]
mB = par['m_' + pd['B']]
mV = par['m_' + pd['V']]
w = max((mB**2 + mV**2 - q2) / (2 * mB * mV), 1)
phqet = hqet.get_hqet_parameters(par, scale)
ash = phqet['ash']
epsc = phqet['epsc']
epsb = phqet['epsb']
zc = phqet['zc']
# eq. (22) of arXiv:0809.0222
CV1 = hqet.CV1(w, zc)
CV2 = hqet.CV2(w, zc)
CV3 = hqet.CV3(w, zc)
CA1 = hqet.CA1(w, zc)
CA2 = hqet.CA2(w, zc)
CA3 = hqet.CA3(w, zc)
CT1 = hqet.CT1(w, zc)
CT2 = hqet.CT2(w, zc)
CT3 = hqet.CT3(w, zc)
L = hqet.L(par, w)
# leading, universal Isgur-Wise function
rho2 = par['CLN rho2_xi']
c = par['CLN c_xi']
z = common.z(mB, mV, q2, t0='tm')
xi = 1 - 8 * rho2 * z + (64 * c - 16 * rho2) * z**2
h = {}
h['V'] = xi * (1 + ash * CV1 + epsc * (L[2] - L[5]) + epsb * (L[1] - L[4]))
h['A1'] = xi * (1 + ash * CA1 + epsc * (L[2] - L[5] * (w - 1) /
(w + 1)) + epsb *
(L[1] - L[4] * (w - 1) /
(w + 1)) + epsc**2 * par['B->D* CLN deltac_hA1'])
h['A2'] = xi * (ash * CA2 + epsc * (L[3] + L[6]))
h['A3'] = xi * (1 + ash * (CA1 + CA3) + epsc *
(L[2] - L[3] + L[6] - L[5]) + epsb * (L[1] - L[4]))
h['T1'] = xi * (1 + ash * (CT1 + (w - 1) / 2 * (CT2 - CT3)) + epsc * L[2] +
epsb * L[1] + epsc**2 * par['B->D* CLN deltac_hT1'])
h['T2'] = xi * (ash * (w + 1) / 2 *
(CT2 + CT3) + epsc * L[5] - epsb * L[4])
h['T3'] = xi * (ash * CT2 + epsc * (L[6] - L[3]))
return h_to_A(mB, mV, h, q2)
def ff(process, q2, par, scale, order_z=3, order_z_slp=2, order_z_sslp=1):
r"""Central value of $B\to P$ form factors in the lattice convention
CLN parametrization.
See arXiv:hep-ph/9712417 and arXiv:1703.05330.
"""
pd = process_dict[process]
mB = par['m_' + pd['B']]
mP = par['m_' + pd['P']]
w = max((mB**2 + mP**2 - q2) / (2 * mB * mP), 1)
phqet = hqet.get_hqet_parameters(par)
ash = phqet['ash']
epsc = phqet['epsc']
epsb = phqet['epsb']
zc = phqet['zc']
CV1 = hqet.CV1(w, zc)
CV2 = hqet.CV2(w, zc)
CV3 = hqet.CV3(w, zc)
CT1 = hqet.CT1(w, zc)
CT2 = hqet.CT2(w, zc)
CT3 = hqet.CT3(w, zc)
z = common.z(mB, mP, q2, t0='tm')
rho2 = par['CLN rho2_xi']
c = par['CLN c_xi']
xi3 = par['CLN xi3']
xi = hqet.xi(z, rho2, c, xi3, order_z=order_z)
L = hqet.Lz(par, w, z, order_z=order_z_slp)
ell = hqet.ell(par, z, order_z=order_z_sslp)
h = {}
h['h+'] = xi * (1 + ash * (CV1 + (w + 1) / 2 * (CV2 + CV3))
+ (epsc + epsb) * L[1]
+ epsc**2 * ell[1])
h['h-'] = xi * (ash * (w + 1) / 2 * (CV2 - CV3)
+ (epsc - epsb) * L[4]
+ epsc**2 * ell[4])
h['hT'] = xi * (1 + ash * (CT1 - CT2 + CT3)
+ (epsc + epsb) * (L[1] - L[4])
+ epsc**2 * (ell[1] - ell[4]))
return h_to_f(mB, mP, h, q2)