def prop_trace(prop_list, aq, sin=True):
"Trace of qslash*inv(prop)*(1/12q^2). Supports two forms of q."
N = len(prop_list)
prop_inv = inv(sum(prop_list)/N)
qslash = dw.slash(aq)
qslash_sin = dw.slash(np.sin(aq))
qsquared = dw.inner(aq)
qsquared_sin = dw.inner(np.sin(aq))
if sin:
return (1./12)*trace(dot(qslash_sin, prop_inv)).imag/qsquared_sin
else:
return (1./12)*trace(dot(qslash, prop_inv)).imag/qsquared
def bilinear_Lambdas(Data):
# type check? data loaded?
amputated = amputate_bilinears(Data.inprop_list,
Data.outprop_list,
Data.bilinear_array)
# Include Tr[qslash*inv(prop)]
# Are you matching momenta to the prop correctly?
Data.prop_trace_in = prop_trace(Data.inprop_list, Data.ap, sin=True)*Data.V
#Data.prop_trace_out = prop_trace(Data.outprop_list, Data.ap2, sin=True)*Data.V
Data.prop_trace_in2 = prop_trace(Data.inprop_list, Data.ap, sin=False)*Data.V
#Data.prop_trace_out2 = prop_trace(Data.outprop_list, Data.ap2, sin=False)*Data.V
norm = Data.V/12.
Lambda = lambda x, y: (trace(dot(dw.hc(x), y)).real)*norm
Data.Lambda = map(Lambda, Gc, amputated)
# For the (X, g) schemes.
Data.Lambda_V = (Data.Lambda[1] + Data.Lambda[2] + Data.Lambda[4] +
Data.Lambda[8])*(1./4)
Data.Lambda_A = (Data.Lambda[14] + Data.Lambda[13] + Data.Lambda[11] +
Data.Lambda[7])*(1./4)
Data.Lambda_VpA = (Data.Lambda[1] + Data.Lambda[2] + Data.Lambda[4] +
Data.Lambda[8] + Data.Lambda[14] + Data.Lambda[13] +
Data.Lambda[11] + Data.Lambda[7])*(1./8)
Data.Lambda_VmA = 2*(Data.Lambda_V - Data.Lambda_A)/\
(Data.Lambda_V + Data.Lambda_A)
Data.Lambda_PmS = 2*(Data.Lambda[15] - Data.Lambda[0])/\
(Data.Lambda[15] + Data.Lambda[0])
Data.Lambda_T = (Data.Lambda[3] + Data.Lambda[5] + Data.Lambda[6] +
Data.Lambda[9] + Data.Lambda[10] + Data.Lambda[12])/6.
# For the (X, q) schemes.
aq = Data.aq
Gmu = (amputated[1], amputated[2], amputated[4], amputated[8])
qmuGmu = sum([aq[i]*Gmu[i] for i in range(4)])
Data.Vq = (trace(dot(qmuGmu, dw.slash(aq))).real)*norm/Data.apSq
Gmu5 = (amputated[14], -amputated[13], amputated[11], -amputated[7])
qmuGmu5 = sum([aq[i]*Gmu5[i] for i in range(4)])
tmp = reduce(dot, [qmuGmu5, Gc[15], dw.slash(aq)]).real
Data.Vq5 = trace(tmp*norm)/Data.apSq
Data.Vq_ = Data.Vq
Data.Vq = (Data.Vq + Data.Vq5)/2
# Z-factors.
Data.Z_S = dict(g=None, q=None)
Data.Z_T = dict(g=None, q=None)
Data.Z_S['g'] = Data.Lambda_VpA/Data.Lambda[0]
Data.Z_S['q'] = Data.Vq/Data.Lambda[0]
Data.Z_T['g'] = Data.Lambda_VpA/Data.Lambda_T
Data.Z_T['q'] = Data.Vq/Data.Lambda_T
def proj_q5(amputated, aq):
"Contract amputated fourquark correlator w/ qslash5 x qslash5 projector."
qslash5 = dot(dw.slash(aq), Gc[15])
tmp = tensordot(qslash5, amputated, ([0,1], [1,0]))
return tensordot(qslash5, tmp, ([0,1], [1,0]))
def proj_q(amputated, aq):
"Contract amputated fourquark correlator w/ qslash x qslash projector."
qslash = dw.slash(aq)
tmp = tensordot(qslash, amputated, ([0,1], [1,0]))
return tensordot(qslash, tmp, ([0,1], [1,0]))
def Vq5(amputated):
Gmu5 = (amputated[14], -amputated[13], amputated[11], -amputated[7])
qmuGmu5 = sum([aq[i]*Gmu5[i] for i in range(4)])
tmp = reduce(dot, [qmuGmu5, Gc[15], dw.slash(aq)]).real
return trace(tmp*norm)/Data.apSq
def Vq(amputated):
Gmu = (amputated[1], amputated[2], amputated[4], amputated[8])
qmuGmu = sum([aq[i]*Gmu[i] for i in range(4)])
return (trace(dot(qmuGmu, dw.slash(aq))).real)*norm/apSq
