def FFV4_3(F1, F2, COUP, M3, W3):
OM3 = 0.0
if (M3): OM3 = 1.0 / M3**2
V3 = wavefunctions.WaveFunction(size=6)
V3[0] = F1[0] + F2[0]
V3[1] = F1[1] + F2[1]
P3 = [
-complex(V3[0]).real, -complex(V3[1]).real, -complex(V3[1]).imag,
-complex(V3[0]).imag
]
TMP4 = (F1[4] * (F2[2] * (P3[0] - P3[3]) - F2[3] * (P3[1] + 1j *
(P3[2]))) + F1[5] *
(F2[2] * (+1j * (P3[2]) - P3[1]) + F2[3] * (P3[0] + P3[3])))
TMP1 = (F1[2] * (F2[4] * (P3[0] + P3[3]) + F2[5] * (P3[1] + 1j *
(P3[2]))) + F1[3] *
(F2[4] * (P3[1] - 1j * (P3[2])) + F2[5] * (P3[0] - P3[3])))
denom = COUP / (P3[0]**2 - P3[1]**2 - P3[2]**2 - P3[3]**2 - M3 *
(M3 - 1j * W3))
V3[2] = denom * (-2j) * (
OM3 * -1 / 2 * P3[0] * (TMP1 + 2 * (TMP4)) +
(+1 / 2 *
(F1[2] * F2[4] + F1[3] * F2[5]) + F1[4] * F2[2] + F1[5] * F2[3]))
V3[3] = denom * (-2j) * (
OM3 * -1 / 2 * P3[1] * (TMP1 + 2 * (TMP4)) +
(-1 / 2 *
(F1[2] * F2[5] + F1[3] * F2[4]) + F1[4] * F2[3] + F1[5] * F2[2]))
V3[4] = denom * 2j * (OM3 * 1 / 2 * P3[2] * (TMP1 + 2 * (TMP4)) +
(+1j / 2 * (F1[2] * F2[5]) - 1j / 2 *
(F1[3] * F2[4]) - 1j * (F1[4] * F2[3]) + 1j *
(F1[5] * F2[2])))
V3[5] = denom * 2j * (OM3 * 1 / 2 * P3[3] * (TMP1 + 2 * (TMP4)) +
(+1 / 2 * (F1[2] * F2[4]) - 1 / 2 *
(F1[3] * F2[5]) - F1[4] * F2[2] + F1[5] * F2[3]))
return V3
def sxxxxx(p, nss):
"""initialize a scalar wavefunction"""
sc = WaveFunction(1)
sc[2] = complex(1., 0.)
sc[0] = complex(p[0] * nss, p[3] * nss)
sc[1] = complex(p[1] * nss, p[2] * nss)
return sc
def FFV1P0_3(F1, F2, COUP, M3, W3):
V3 = wavefunctions.WaveFunction(size=6)
V3[0] = F1[0] + F2[0]
V3[1] = F1[1] + F2[1]
P3 = [
-complex(V3[0]).real, -complex(V3[1]).real, -complex(V3[1]).imag,
-complex(V3[0]).imag
]
denom = COUP / (P3[0]**2 - P3[1]**2 - P3[2]**2 - P3[3]**2 - M3 *
(M3 - 1j * W3))
V3[2] = denom * (-1j) * (F1[2] * F2[4] + F1[3] * F2[5] + F1[4] * F2[2] +
F1[5] * F2[3])
V3[3] = denom * (-1j) * (F1[4] * F2[3] + F1[5] * F2[2] - F1[2] * F2[5] -
F1[3] * F2[4])
V3[4] = denom * (-1j) * (-1j * (F1[2] * F2[5] + F1[5] * F2[2]) + 1j *
(F1[3] * F2[4] + F1[4] * F2[3]))
V3[5] = denom * (-1j) * (F1[3] * F2[5] + F1[4] * F2[2] - F1[2] * F2[4] -
F1[5] * F2[3])
return V3
def FFV2_3(F1, F2, COUP, M3, W3):
OM3 = 0.0
if (M3): OM3 = 1.0 / M3**2
V3 = wavefunctions.WaveFunction(size=6)
V3[0] = F1[0] + F2[0]
V3[1] = F1[1] + F2[1]
P3 = [
-complex(V3[0]).real, -complex(V3[1]).real, -complex(V3[1]).imag,
-complex(V3[0]).imag
]
TMP1 = (F1[2] * (F2[4] * (P3[0] + P3[3]) + F2[5] * (P3[1] + 1j *
(P3[2]))) + F1[3] *
(F2[4] * (P3[1] - 1j * (P3[2])) + F2[5] * (P3[0] - P3[3])))
denom = COUP / (P3[0]**2 - P3[1]**2 - P3[2]**2 - P3[3]**2 - M3 *
(M3 - 1j * W3))
V3[2] = denom * (-1j) * (F1[2] * F2[4] + F1[3] * F2[5] -
P3[0] * OM3 * TMP1)
V3[3] = denom * (-1j) * (-F1[2] * F2[5] - F1[3] * F2[4] -
P3[1] * OM3 * TMP1)
V3[4] = denom * (-1j) * (-1j * (F1[2] * F2[5]) + 1j *
(F1[3] * F2[4]) - P3[2] * OM3 * TMP1)
V3[5] = denom * (-1j) * (F1[3] * F2[5] - F1[2] * F2[4] -
P3[3] * OM3 * TMP1)
return V3
def __init__(self, param_card=None):
""" Instantiates using default value or the path of a SLHA param card."""
# Param card accessor
slha = ParamCard(param_card)
self.ZERO = 0.
# Computing independent parameters
mdl_WH = slha.get_block_entry("decay", 25, 6.382339e-03);
mdl_WT = slha.get_block_entry("decay", 6, 1.491500e+00);
mdl_WW = slha.get_block_entry("decay", 24, 2.047600e+00);
mdl_WZ = slha.get_block_entry("decay", 23, 2.441404e+00);
mdl_MTA = slha.get_block_entry("mass", 15, 1.777000e+00);
mdl_MH = slha.get_block_entry("mass", 25, 1.250000e+02);
mdl_MB = slha.get_block_entry("mass", 5, 4.700000e+00);
mdl_MT = slha.get_block_entry("mass", 6, 1.730000e+02);
mdl_MZ = slha.get_block_entry("mass", 23, 9.118800e+01);
mdl_ymtau = slha.get_block_entry("yukawa", 15, 1.777000e+00);
mdl_ymt = slha.get_block_entry("yukawa", 6, 1.730000e+02);
mdl_ymb = slha.get_block_entry("yukawa", 5, 4.700000e+00);
aS = slha.get_block_entry("sminputs", 3, 1.180000e-01);
mdl_Gf = slha.get_block_entry("sminputs", 2, 1.166390e-05);
aEWM1 = slha.get_block_entry("sminputs", 1, 1.325070e+02);
mdl_conjg__CKM3x3 = 1.0
mdl_CKM3x3 = 1.0
mdl_conjg__CKM1x1 = 1.0
mdl_complexi = complex(0,1)
mdl_MZ__exp__2 = mdl_MZ**2
mdl_MZ__exp__4 = mdl_MZ**4
mdl_sqrt__2 = cmath.sqrt(2)
mdl_MH__exp__2 = mdl_MH**2
mdl_aEW = 1/aEWM1
mdl_MW = cmath.sqrt(mdl_MZ__exp__2/2. + cmath.sqrt(mdl_MZ__exp__4/4. - (mdl_aEW*cmath.pi*mdl_MZ__exp__2)/(mdl_Gf*mdl_sqrt__2)))
mdl_sqrt__aEW = cmath.sqrt(mdl_aEW)
mdl_ee = 2*mdl_sqrt__aEW*cmath.sqrt(cmath.pi)
mdl_MW__exp__2 = mdl_MW**2
mdl_sw2 = 1 - mdl_MW__exp__2/mdl_MZ__exp__2
mdl_cw = cmath.sqrt(1 - mdl_sw2)
mdl_sqrt__sw2 = cmath.sqrt(mdl_sw2)
mdl_sw = mdl_sqrt__sw2
mdl_g1 = mdl_ee/mdl_cw
mdl_gw = mdl_ee/mdl_sw
mdl_vev = (2*mdl_MW*mdl_sw)/mdl_ee
mdl_vev__exp__2 = mdl_vev**2
mdl_lam = mdl_MH__exp__2/(2.*mdl_vev__exp__2)
mdl_yb = (mdl_ymb*mdl_sqrt__2)/mdl_vev
mdl_yt = (mdl_ymt*mdl_sqrt__2)/mdl_vev
mdl_ytau = (mdl_ymtau*mdl_sqrt__2)/mdl_vev
mdl_muH = cmath.sqrt(mdl_lam*mdl_vev__exp__2)
mdl_I1x33 = mdl_yb*mdl_conjg__CKM3x3
mdl_I2x33 = mdl_yt*mdl_conjg__CKM3x3
mdl_I3x33 = mdl_CKM3x3*mdl_yt
mdl_I4x33 = mdl_CKM3x3*mdl_yb
mdl_ee__exp__2 = mdl_ee**2
mdl_sw__exp__2 = mdl_sw**2
mdl_cw__exp__2 = mdl_cw**2
# Computing independent couplings
GC_3 = -(mdl_ee*mdl_complexi)
GC_51 = (mdl_cw*mdl_ee*mdl_complexi)/(2.*mdl_sw)
GC_59 = (mdl_ee*mdl_complexi*mdl_sw)/(2.*mdl_cw)
# Computing dependent parameters
mdl_sqrt__aS = cmath.sqrt(aS)
G = 2*mdl_sqrt__aS*cmath.sqrt(cmath.pi)
mdl_G__exp__2 = G**2
# Computing independent parameters
# Setting independent parameters
# Model parameters independent of aS
self.mdl_WH = float(mdl_WH.real)
self.mdl_WT = float(mdl_WT.real)
self.mdl_WW = float(mdl_WW.real)
self.mdl_WZ = float(mdl_WZ.real)
self.mdl_MTA = float(mdl_MTA.real)
self.mdl_MH = float(mdl_MH.real)
self.mdl_MB = float(mdl_MB.real)
self.mdl_MT = float(mdl_MT.real)
self.mdl_MZ = float(mdl_MZ.real)
self.mdl_ymtau = float(mdl_ymtau.real)
self.mdl_ymt = float(mdl_ymt.real)
self.mdl_ymb = float(mdl_ymb.real)
self.aS = float(aS.real)
self.mdl_Gf = float(mdl_Gf.real)
self.aEWM1 = float(aEWM1.real)
self.mdl_conjg__CKM3x3 = float(mdl_conjg__CKM3x3.real)
self.mdl_CKM3x3 = float(mdl_CKM3x3.real)
self.mdl_conjg__CKM1x1 = float(mdl_conjg__CKM1x1.real)
self.mdl_complexi = complex(mdl_complexi)
self.mdl_MZ__exp__2 = float(mdl_MZ__exp__2.real)
self.mdl_MZ__exp__4 = float(mdl_MZ__exp__4.real)
self.mdl_sqrt__2 = float(mdl_sqrt__2.real)
self.mdl_MH__exp__2 = float(mdl_MH__exp__2.real)
self.mdl_aEW = float(mdl_aEW.real)
self.mdl_MW = float(mdl_MW.real)
self.mdl_sqrt__aEW = float(mdl_sqrt__aEW.real)
self.mdl_ee = float(mdl_ee.real)
self.mdl_MW__exp__2 = float(mdl_MW__exp__2.real)
self.mdl_sw2 = float(mdl_sw2.real)
self.mdl_cw = float(mdl_cw.real)
self.mdl_sqrt__sw2 = float(mdl_sqrt__sw2.real)
self.mdl_sw = float(mdl_sw.real)
self.mdl_g1 = float(mdl_g1.real)
self.mdl_gw = float(mdl_gw.real)
self.mdl_vev = float(mdl_vev.real)
self.mdl_vev__exp__2 = float(mdl_vev__exp__2.real)
self.mdl_lam = float(mdl_lam.real)
self.mdl_yb = float(mdl_yb.real)
self.mdl_yt = float(mdl_yt.real)
self.mdl_ytau = float(mdl_ytau.real)
self.mdl_muH = float(mdl_muH.real)
self.mdl_I1x33 = complex(mdl_I1x33)
self.mdl_I2x33 = complex(mdl_I2x33)
self.mdl_I3x33 = complex(mdl_I3x33)
self.mdl_I4x33 = complex(mdl_I4x33)
self.mdl_ee__exp__2 = float(mdl_ee__exp__2.real)
self.mdl_sw__exp__2 = float(mdl_sw__exp__2.real)
self.mdl_cw__exp__2 = float(mdl_cw__exp__2.real)
# Setting independent couplings
# Model parameters dependent on aS
self.mdl_sqrt__aS = float(mdl_sqrt__aS.real)
self.G = float(G.real)
self.mdl_G__exp__2 = float(mdl_G__exp__2.real)
# Setting dependent parameters
# Model couplings independent of aS
self.GC_3 = complex(GC_3)
self.GC_51 = complex(GC_51)
self.GC_59 = complex(GC_59)
def oxxxxx(p, fmass, nhel, nsf):
""" initialize an outgoing fermion"""
fo = WaveFunction(2)
fo[0] = complex(p[0] * nsf, p[3] * nsf)
fo[1] = complex(p[1] * nsf, p[2] * nsf)
nh = nhel * nsf
if (fmass != 0.):
pp = min(p[0], sqrt(p[1]**2 + p[2]**2 + p[3]**2))
if (pp == 0.):
sqm = [sqrt(abs(fmass))]
sqm.append(sign(sqm[0], fmass))
ip = int(-((1 - nh) // 2) * nhel)
im = int((1 + nh) // 2 * nhel)
fo[2] = im * sqm[abs(im)]
fo[3] = ip * nsf * sqm[abs(im)]
fo[4] = im * nsf * sqm[abs(ip)]
fo[5] = ip * sqm[abs(ip)]
else:
sf = [(1 + nsf + (1 - nsf) * nh) * 0.5,
(1 + nsf - (1 - nsf) * nh) * 0.5]
omega = [sqrt(p[0] + pp), fmass / (sqrt(p[0] + pp))]
ip = (1 + nh) // 2
im = (1 - nh) // 2
sfomeg = [sf[0] * omega[ip], sf[1] * omega[im]]
pp3 = max(pp + p[3], 0.)
if (pp3 == 0.):
chi1 = complex(-nh, 0.)
else:
chi1 = complex(nh*p[1]/sqrt(2.*pp*pp3),\
-p[2]/sqrt(2.*pp*pp3))
chi = [complex(sqrt(pp3 * 0.5 / pp)), chi1]
fo[2] = sfomeg[1] * chi[im]
fo[3] = sfomeg[1] * chi[ip]
fo[4] = sfomeg[0] * chi[im]
fo[5] = sfomeg[0] * chi[ip]
else:
sqp0p3 = sqrt(max(p[0] + p[3], 0.)) * nsf
if (sqp0p3 == 0.):
chi1 = complex(-nhel * sqrt(2. * p[0]), 0.)
else:
chi1 = complex(nh * p[1] / sqp0p3, -p[2] / sqp0p3)
chi = [complex(sqp0p3, 0.), chi1]
if (nh == 1):
fo[2] = chi[0]
fo[3] = chi[1]
fo[4] = complex(0., 0.)
fo[5] = complex(0., 0.)
else:
fo[2] = complex(0., 0.)
fo[3] = complex(0., 0.)
fo[4] = chi[1]
fo[5] = chi[0]
return fo
def orxxxx(p, mass, nhel, nsr):
""" initialize a incoming spin 3/2 wavefunction."""
# This routines is a python translation of a routine written by
# K.Mawatari in fortran dated from the 2008/02/26
ro = WaveFunction(spin=4)
sqh = sqrt(0.5)
sq2 = sqrt(2)
sq3 = sqrt(3)
pt2 = p[1]**2 + p[2]**2
pp = min([p[0], sqrt(pt2 + p[3]**2)])
pt = min([pp, sqrt(pt2)])
rc = {}
rc[(4, 0)] = complex(p[0], p[3]) * nsr
rc[(5, 0)] = complex(p[1], p[2]) * nsr
nsv = nsr # nsv=+1 for final, -1 for initial
# Construct eps+
if nhel > 0:
ep = [0] * 4
if pp:
#ep[0] = 0
ep[3] = pt / pp * sqh
if pt:
pzpt = p[3] / (pp * pt) * sqh
ep[1] = complex(-p[1] * pzpt, -nsv * p[2] / pt * sqh)
ep[2] = complex(-p[2] * pzpt, nsv * p[1] / pt * sqh)
else:
ep[1] = -sqh
ep[2] = complex(0, nsv * sign(sqh, p[3]))
else:
#ep[0] = 0d0
ep[1] = -sqh
ep[2] = complex(0, nsv * sqh)
#ep[3] = 0d0
if (nhel < 0):
#construct eps-
em = [0] * 4
if (pp == 0):
#em[0] = 0
em[1] = sqh
em[2] = complex(0, nsv * sqh)
#em[3] = 0
else:
#em[0] = 0
em[3] = -pt / pp * sqh
if pt:
pzpt = -p[3] / (pp * pt) * sqh
em[1] = complex(-p[1] * pzpt, -nsv * p[2] / pt * sqh)
em[2] = complex(-p[2] * pzpt, nsv * p[1] / pt * sqh)
else:
em[1] = sqh
em[2] = complex(0, nsv * sign(sqh, p[3]))
if (abs(nhel) <= 1):
#construct eps0
e0 = [0] * 4
if (pp == 0):
#e0[0] = complex( rZero )
#e0[1] = complex( rZero )
#e0[2] = complex( rZero )
e0[3] = 1
else:
emp = p[0] / (mass * pp)
e0[0] = pp / mass
e0[3] = p[3] * emp
if pt:
e0[1] = p[1] * emp
e0[2] = p[2] * emp
#else:
# e0[1] = complex( rZero )
# e0[2] = complex( rZero )
if nhel >= -1:
#constract spinor+
nh = nsr
sqm, fop, omega, sf, sfomeg = [0] * 2, [0] * 4, [0] * 2, [0] * 2, [
0
] * 2
chi = [0] * 2
if mass:
pp = min([p[0], sqrt(p[1]**2 + p[2]**2 + p[3]**2)])
if (pp == 0):
sqm[0] = sqrt(
abs(mass)) # possibility of negative fermion masses
sqm[1] = sign(sqm[0],
mass) # possibility of negative fermion masses
ip = -((1 + nh) / 2)
im = (1 - nh) / 2
fop[0] = im * sqm[im]
fop[1] = ip * nsr * sqm[im]
fop[2] = im * nsr * sqm[-ip]
fop[3] = ip * sqm[-ip]
else:
pp = min(p[0], sqrt(p[1]**2 + p[2]**2 + p[3]**2))
sf[0] = (1 + nsr + (1 - nsr) * nh) * 0.5
sf[1] = (1 + nsr - (1 - nsr) * nh) * 0.5
omega[0] = sqrt(p[0] + pp)
omega[1] = mass / omega[0]
ip = (3 + nh) // 2 - 1 # -1 since this is index
im = (3 - nh) // 2 - 1 # -1 since this is index
sfomeg[0] = sf[0] * omega[ip]
sfomeg[1] = sf[1] * omega[im]
pp3 = max([pp + p[3], 0])
chi[0] = sqrt(pp3 * 0.5 / pp)
if pp3 == 0:
chi[1] = -nh
else:
chi[1] = complex(nh * p[1], -p[2]) / sqrt(2 * pp * pp3)
fop[0] = sfomeg[1] * chi[im]
fop[1] = sfomeg[1] * chi[ip]
fop[2] = sfomeg[0] * chi[im]
fop[3] = sfomeg[0] * chi[ip]
else:
if (p[1] == 0 and p[2] == 0 and p[3] < 0):
sqp0p3 = 0
else:
sqp0p3 = sqrt(max(p[0] + p[3], 0)) * nsr
chi[0] = sqp0p3
if (sqp0p3 == 0):
chi[1] = complex(-nhel) * sqrt(2 * p[0])
else:
chi[1] = complex(nh * p[1], -p[2]) / sqp0p3
if (nh == 1):
fop[0] = chi[0]
fop[1] = chi[1]
#fop[2] = 0
#fop[3] = 0
else:
#fop[0] = 0
#fop[1] = 0
fop[2] = chi[1]
fop[3] = chi[0]
if (nhel < 2):
# constract spinor+
sqm, fom, omega, sf, sfomeg = [0] * 2, [0] * 4, [0] * 2, [0] * 2, [
0
] * 2
chi = [0] * 2
nh = -nsr
if mass:
pp = min([p[0], sqrt(p[1]**2 + p[2]**2 + p[3]**2)])
if (pp == 0):
sqm[0] = sqrt(
abs(mass)) # possibility of negative fermion masses
sqm[1] = sign(sqm[0],
mass) # possibility of negative fermion masses
ip = -((1 + nh) / 2)
im = (1 - nh) / 2
fom[0] = im * sqm[im]
fom[1] = ip * nsr * sqm[im]
fom[2] = im * nsr * sqm[-ip]
fom[3] = ip * sqm[-ip]
else:
pp = min([p[0], sqrt(p[1]**2 + p[2]**2 + p[3]**2)])
sf[0] = (1 + nsr + (1 - nsr) * nh) * 0.5
sf[1] = (1 + nsr - (1 - nsr) * nh) * 0.5
omega[0] = sqrt(p[0] + pp)
omega[1] = mass / omega[0]
ip = (3 + nh) // 2 - 1 #-1 since ip is an index
im = (3 - nh) // 2 - 1
sfomeg[0] = sf[0] * omega[ip]
sfomeg[1] = sf[1] * omega[im]
pp3 = max([pp + p[3], 0])
chi[0] = sqrt(pp3 * 0.5 / pp)
if (pp3 == 0):
chi[1] = -nh
else:
chi[1] = complex(nh * p[1], -p[2]) / sqrt(2 * pp * pp3)
fom[0] = sfomeg[1] * chi[im]
fom[1] = sfomeg[1] * chi[ip]
fom[2] = sfomeg[0] * chi[im]
fom[3] = sfomeg[0] * chi[ip]
else:
if (p[1] == 0 == p[2] and p[3] < 0):
sqp0p3 = 0
else:
sqp0p3 = sqrt(max([p[0] + p[3], 0])) * nsr
chi[0] = sqp0p3
if (sqp0p3 == 0):
chi[1] = complex(-nhel) * sqrt(2 * p[0])
else:
chi[1] = complex(nh * p[1], -p[2]) / sqp0p3
if (nh == 1):
fom[0] = chi[0]
fom[1] = chi[1]
#fom[2] = 0
#fom[3] = 0
else:
#fom[1] = 0
#fom[2] = 0
fom[2] = chi[1]
fom[3] = chi[0]
cond1 = (pt == 0 and p[3] >= 0)
cond2 = (pt == 0 and p[3] < 0)
# spin-3/2 fermion wavefunction
if nhel == 3:
for i, j in product(range(4), range(4)):
rc[(i, j)] = ep[i] * fop[j]
elif nhel == 1:
for i, j in product(range(4), range(4)):
if cond1:
rc[(i,
j)] = sq2 / sq3 * e0[i] * fop[j] + 1 / sq3 * ep[i] * fom[j]
elif cond2:
rc[(i,
j)] = sq2 / sq3 * e0[i] * fop[j] - 1 / sq3 * ep[i] * fom[j]
else:
rc[(i,j)] = sq2/sq3*e0[i]*fop[j] + 1/sq3*ep[i]*fom[j] * \
complex(p[1],-nsr*p[2])/pt
elif nhel == -1:
for i, j in product(range(4), range(4)):
if cond1:
rc[(i,
j)] = 1 / sq3 * em[i] * fop[j] + sq2 / sq3 * e0[i] * fom[j]
elif cond2:
rc[(i,
j)] = 1 / sq3 * em[i] * fop[j] - sq2 / sq3 * e0[i] * fom[j]
else:
rc[(i,j)] = 1/sq3*em[i]*fop[j] + sq2/sq3*e0[i]*fom[j] *\
complex(p[1],-nsr*p[2])/pt
else:
for i, j in product(range(4), range(4)):
if cond1:
rc[(i, j)] = em[i] * fom[j]
elif cond2:
rc[(i, j)] = -em[i] * fom[j]
else:
rc[(i, j)] = em[i] * fom[j] * complex(p[1], -nsr * p[2]) / pt
ro[2] = rc[(0, 0)]
ro[3] = rc[(0, 1)]
ro[4] = rc[(0, 2)]
ro[5] = rc[(0, 3)]
ro[6] = rc[(1, 0)]
ro[7] = rc[(1, 1)]
ro[8] = rc[(1, 2)]
ro[9] = rc[(1, 3)]
ro[10] = rc[(2, 0)]
ro[11] = rc[(2, 1)]
ro[12] = rc[(2, 2)]
ro[13] = rc[(2, 3)]
ro[14] = rc[(3, 0)]
ro[15] = rc[(3, 1)]
ro[16] = rc[(3, 2)]
ro[17] = rc[(3, 3)]
ro[0] = rc[(4, 0)]
ro[1] = rc[(5, 0)]
return ro
def irxxxx(p, mass, nhel, nsr):
""" initialize a incoming spin 3/2 wavefunction."""
# This routines is a python translation of a routine written by
# K.Mawatari in fortran dated from the 2008/02/26
ri = WaveFunction(4)
sqh = sqrt(0.5)
sq2 = sqrt(2)
sq3 = sqrt(3)
pt2 = p[1]**2 + p[2]**2
pp = min([p[0], sqrt(pt2 + p[3]**2)])
pt = min([pp, sqrt(pt2)])
rc = {}
rc[(4, 0)] = -1.0 * complex(p[0], p[3]) * nsr
rc[(5, 0)] = -1.0 * complex(p[1], p[2]) * nsr
nsv = -nsr # nsv=+1 for final, -1 for initial
# Construct eps+
if nhel > 0:
ep = [0] * 4
if pp:
#ep[0] = 0
ep[3] = pt / pp * sqh
if pt:
pzpt = p[3] / (pp * pt) * sqh
ep[1] = complex(-p[1] * pzpt, -nsv * p[2] / pt * sqh)
ep[2] = complex(-p[2] * pzpt, nsv * p[1] / pt * sqh)
else:
ep[1] = -sqh
ep[2] = complex(0, nsv * sign(sqh, p[3]))
else:
#ep[0] = 0d0
ep[1] = -sqh
ep[2] = complex(0, nsv * sqh)
#ep[3] = 0d0
if (nhel < 0):
#construct eps-
em = [0] * 4
if (pp == 0):
#em[0] = 0
em[1] = sqh
em[2] = complex(0, nsv * sqh)
#em[3] = 0
else:
#em[0] = 0
em[3] = -pt / pp * sqh
if pt:
pzpt = -p[3] / (pp * pt) * sqh
em[1] = complex(-p[1] * pzpt, -nsv * p[2] / pt * sqh)
em[2] = complex(-p[2] * pzpt, nsv * p[1] / pt * sqh)
else:
em[1] = sqh
em[2] = complex(0, nsv * sign(sqh, p[3]))
if (abs(nhel) <= 1):
#construct eps0
e0 = [0] * 4
if (pp == 0):
#e0[0] = complex( rZero )
#e0[1] = complex( rZero )
#e0[2] = complex( rZero )
e0[3] = 1
else:
emp = p[0] / (mass * pp)
e0[0] = pp / mass
e0[3] = p[3] * emp
if pt:
e0[1] = p[1] * emp
e0[2] = p[2] * emp
#else:
# e0[1] = complex( rZero )
# e0[2] = complex( rZero )
if (nhel >= -1):
# constract spinor+
fip = [0] * 4
sf, omega, sfomeg, chi = [0, 0], [0, 0], [0, 0], [0, 0]
nh = nsr
if mass:
pp = min([p[0], sqrt(p[1]**2 + p[2]**2 + p[3]**2)])
if pp == 0:
sqm = sqrt(mass)
ip = (1 + nh) // 2
im = (1 - nh) // 2
fip[0] = ip * sqm
fip[1] = im * nsr * sqm
fip[2] = ip * nsr * sqm
fip[3] = im * sqm
else:
sf[0] = float(1 + nsr + (1 - nsr) * nh) * 0.5
sf[1] = float(1 + nsr - (1 - nsr) * nh) * 0.5
omega[0] = sqrt(p[0] + pp)
omega[1] = mass / omega[0]
ip = ((3 + nh) // 2) - 1 # -1 since they are index
im = ((3 - nh) // 2) - 1 # -1 since they are index
sfomeg[0] = sf[0] * omega[ip]
sfomeg[1] = sf[1] * omega[im]
pp3 = max([pp + p[3], 0])
chi[0] = sqrt(pp3 * 0.5 / pp)
if pp3 == 0:
chi[1] = -nh
else:
chi[1] = complex(nh * p[1], p[2]) / sqrt(2 * pp * pp3)
fip[0] = sfomeg[0] * chi[im]
fip[1] = sfomeg[0] * chi[ip]
fip[2] = sfomeg[1] * chi[im]
fip[3] = sfomeg[1] * chi[ip]
else:
sqp0p3 = sqrt(max([p[0] + p[3], 0])) * nsr
chi[0] = sqp0p3
if sqp0p3 == 0:
chi[1] = -nhel * sqrt(2 * p[0])
else:
chi[1] = complex(nh * p[1], p[2]) / sqp0p3
if nh == 1:
#fip[0] = complex( rZero )
#fip[1] = complex( rZero )
fip[2] = chi[0]
fip[3] = chi[1]
else:
fip[0] = chi[1]
fip[1] = chi[0]
#fip(3) = complex( rZero )
#fip(4) = complex( rZero )
if (nhel <= 1):
# constract spinor-
fim = [0] * 4
sf, omega, sfomeg, chi = [0, 0], [0, 0], [0, 0], [0, 0]
nh = -nsr
if mass:
pp = min([p[0], sqrt(p[1]**2 + p[2]**2 + p[3]**2)])
if pp == 0:
sqm = sqrt(mass)
ip = (1 + nh) / 2
im = (1 - nh) / 2
fim[0] = ip * sqm
fim[1] = im * nsr * sqm
fim[2] = ip * nsr * sqm
fim[3] = im * sqm
else:
sf[0] = float(1 + nsr + (1 - nsr) * nh) * 0.5
sf[1] = float(1 + nsr - (1 - nsr) * nh) * 0.5
omega[0] = sqrt(p[0] + pp)
omega[1] = mass / omega[0]
ip = (3 + nh) // 2 - 1
im = (3 - nh) // 2 - 1
sfomeg[0] = sf[0] * omega[ip]
sfomeg[1] = sf[1] * omega[im]
pp3 = max([pp + p[3], 0])
chi[0] = sqrt(pp3 * 0.5 / pp)
if pp3 == 0:
chi[1] = -nh
else:
chi[1] = complex(nh * p[1], p[2]) / sqrt(2 * pp * pp3)
fim[0] = sfomeg[0] * chi[im]
fim[1] = sfomeg[0] * chi[ip]
fim[2] = sfomeg[1] * chi[im]
fim[3] = sfomeg[1] * chi[ip]
else:
sqp0p3 = sqrt(max([p[0] + p[3], 0])) * nsr
chi[0] = sqp0p3
if sqp0p3 == 0:
chi[1] = -nhel * sqrt(2 * p[0])
else:
chi[1] = complex(nh * p[1], p[2]) / sqp0p3
if nh == 1:
#fip[0] = complex( rZero )
#fip[1] = complex( rZero )
fim[2] = chi[0]
fim[3] = chi[1]
else:
fim[0] = chi[1]
fim[1] = chi[0]
#fip(3) = complex( rZero )
#fip(4) = complex( rZero )
# recurent relation put her for optimization
cond1 = (pt == 0 and p[3] >= 0)
cond2 = (pt == 0 and p[3] < 0)
# spin-3/2 fermion wavefunction
if nhel == 3:
for i, j in product(range(4), range(4)):
rc[(i, j)] = ep[i] * fip[j]
elif nhel == 1:
for i, j in product(range(4), range(4)):
if cond1:
rc[(i,
j)] = sq2 / sq3 * e0[i] * fip[j] + 1 / sq3 * ep[i] * fim[j]
elif cond2:
rc[(i,
j)] = sq2 / sq3 * e0[i] * fip[j] - 1 / sq3 * ep[i] * fim[j]
else:
rc[(i,j)] = sq2/sq3*e0[i]*fip[j] + \
1/sq3*ep[i]*fim[j] *complex(p[1],nsr*p[2])/pt
elif nhel == -1:
for i, j in product(range(4), range(4)):
if cond1:
rc[(i,
j)] = 1 / sq3 * em[i] * fip[j] + sq2 / sq3 * e0[i] * fim[j]
elif cond2:
rc[(i,
j)] = 1 / sq3 * em[i] * fip[j] - sq2 / sq3 * e0[i] * fim[j]
else:
rc[(i,j)] = 1/sq3*em[i]*fip[j] + \
sq2/sq3*e0[i]*fim[j] *complex(p[1],nsr*p[2])/pt
else:
for i, j in product(range(4), range(4)):
if cond1:
rc[(i, j)] = em[i] * fim[j]
elif cond2:
rc[(i, j)] = -em[i] * fim[j]
else:
rc[(i, j)] = em[i] * fim[j] * complex(p[1], nsr * p[2]) / pt
ri[2] = rc[(0, 0)]
ri[3] = rc[(0, 1)]
ri[4] = rc[(0, 2)]
ri[5] = rc[(0, 3)]
ri[6] = rc[(1, 0)]
ri[7] = rc[(1, 1)]
ri[8] = rc[(1, 2)]
ri[9] = rc[(1, 3)]
ri[10] = rc[(2, 0)]
ri[11] = rc[(2, 1)]
ri[12] = rc[(2, 2)]
ri[13] = rc[(2, 3)]
ri[14] = rc[(3, 0)]
ri[15] = rc[(3, 1)]
ri[16] = rc[(3, 2)]
ri[17] = rc[(3, 3)]
ri[0] = rc[(4, 0)]
ri[1] = rc[(5, 0)]
return ri
def txxxxx(p, tmass, nhel, nst):
""" initialize a tensor wavefunction"""
tc = WaveFunction(5)
sqh = sqrt(0.5)
sqs = sqrt(1 / 6)
pt2 = p[1]**2 + p[2]**2
pp = min(p[0], sqrt(pt2 + p[3]**2))
pt = min(pp, sqrt(pt2))
ft = {}
ft[(4, 0)] = complex(p[0], p[3]) * nst
ft[(5, 0)] = complex(p[1], p[2]) * nst
if (nhel >= 0):
#construct eps+
ep = [0] * 4
if (pp == 0):
#ep[0] = 0
ep[1] = -sqh
ep[2] = complex(0, nst * sqh)
#ep[3] = 0
else:
#ep[0] = 0
ep[3] = pt / pp * sqh
if (pt != 0):
pzpt = p[3] / (pp * pt) * sqh
ep[1] = complex(-p[1] * pzpt, -nst * p[2] / pt * sqh)
ep[2] = complex(-p[2] * pzpt, nst * p[1] / pt * sqh)
else:
ep[1] = -sqh
ep[2] = complex(0, nst * sign(sqh, p[3]))
if (nhel <= 0):
#construct eps-
em = [0] * 4
if (pp == 0):
#em[0] = 0
em[1] = sqh
em[2] = complex(0, nst * sqh)
#em[3] = 0
else:
#em[0] = 0
em[3] = -pt / pp * sqh
if pt:
pzpt = -p[3] / (pp * pt) * sqh
em[1] = complex(-p[1] * pzpt, -nst * p[2] / pt * sqh)
em[2] = complex(-p[2] * pzpt, nst * p[1] / pt * sqh)
else:
em[1] = sqh
em[2] = complex(0, nst * sign(sqh, p[3]))
if (abs(nhel) <= 1):
#construct eps0
e0 = [0] * 4
if (pp == 0):
#e0[0] = complex( rZero )
#e0[1] = complex( rZero )
#e0[2] = complex( rZero )
e0[3] = 1
else:
emp = p[0] / (tmass * pp)
e0[0] = pp / tmass
e0[3] = p[3] * emp
if pt:
e0[1] = p[1] * emp
e0[2] = p[2] * emp
#else:
# e0[1] = complex( rZero )
# e0[2] = complex( rZero )
if nhel == 2:
for j in range(4):
for i in range(4):
ft[(i, j)] = ep[i] * ep[j]
elif nhel == -2:
for j in range(4):
for i in range(4):
ft[(i, j)] = em[i] * em[j]
elif tmass == 0:
for j in range(4):
for i in range(4):
ft[(i, j)] = 0
elif nhel == 1:
for j in range(4):
for i in range(4):
ft[(i, j)] = sqh * (ep[i] * e0[j] + e0[i] * ep[j])
elif nhel == 0:
for j in range(4):
for i in range(4):
ft[(i, j)] = sqs * (ep[i] * em[j] + em[i] * ep[j] +
2 * e0[i] * e0[j])
elif nhel == -1:
for j in range(4):
for i in range(4):
ft[(i, j)] = sqh * (em[i] * e0[j] + e0[i] * em[j])
else:
raise Exception, 'invalid helicity TXXXXXX'
tc[2] = ft[(0, 0)]
tc[3] = ft[(0, 1)]
tc[4] = ft[(0, 2)]
tc[5] = ft[(0, 3)]
tc[6] = ft[(1, 0)]
tc[7] = ft[(1, 1)]
tc[8] = ft[(1, 2)]
tc[9] = ft[(1, 3)]
tc[10] = ft[(2, 0)]
tc[11] = ft[(2, 1)]
tc[12] = ft[(2, 2)]
tc[13] = ft[(2, 3)]
tc[14] = ft[(3, 0)]
tc[15] = ft[(3, 1)]
tc[16] = ft[(3, 2)]
tc[17] = ft[(3, 3)]
tc[0] = ft[(4, 0)]
tc[1] = ft[(5, 0)]
return tc
def ixxxxx(p, fmass, nhel, nsf):
"""Defines an inflow fermion."""
fi = WaveFunction(2)
fi[0] = complex(-1.0 * p[0] * nsf, -1.0 * p[3] * nsf)
fi[1] = complex(-1.0 * p[1] * nsf, -1.0 * p[2] * nsf)
nh = nhel * nsf
if (fmass != 0.):
pp = min(p[0], sqrt(p[1]**2 + p[2]**2 + p[3]**2))
if (pp == 0.):
sqm = [sqrt(abs(fmass))]
sqm.append(sign(sqm[0], fmass))
ip = (1 + nh) // 2
im = (1 - nh) // 2
fi[2] = ip * sqm[ip]
fi[3] = im * nsf * sqm[ip]
fi[4] = ip * nsf * sqm[im]
fi[5] = im * sqm[im]
else:
sf = [(1 + nsf + (1 - nsf) * nh) * 0.5,
(1 + nsf - (1 - nsf) * nh) * 0.5]
omega = [sqrt(p[0] + pp), fmass / (sqrt(p[0] + pp))]
ip = (1 + nh) // 2
im = (1 - nh) // 2
sfomeg = [sf[0] * omega[ip], sf[1] * omega[im]]
pp3 = max(pp + p[3], 0.)
if (pp3 == 0.):
chi1 = complex(-nh, 0.)
else:
chi1 = complex(nh*p[1]/sqrt(2.*pp*pp3),\
p[2]/sqrt(2.*pp*pp3))
chi = [complex(sqrt(pp3 * 0.5 / pp)), chi1]
fi[2] = sfomeg[0] * chi[im]
fi[3] = sfomeg[0] * chi[ip]
fi[4] = sfomeg[1] * chi[im]
fi[5] = sfomeg[1] * chi[ip]
else:
sqp0p3 = sqrt(max(p[0] + p[3], 0.)) * nsf
if (sqp0p3 == 0.):
chi1 = complex(-nhel * sqrt(2. * p[0]), 0.)
else:
chi1 = complex(nh * p[1] / sqp0p3, p[2] / sqp0p3)
chi = [complex(sqp0p3, 0.), chi1]
if (nh == 1):
fi[2] = complex(0., 0.)
fi[3] = complex(0., 0.)
fi[4] = chi[0]
fi[5] = chi[1]
else:
fi[2] = chi[1]
fi[3] = chi[0]
fi[4] = complex(0., 0.)
fi[5] = complex(0., 0.)
return fi
def vxxxxx(p, vmass, nhel, nsv):
""" initialize a vector wavefunction. nhel=4 is for checking BRST"""
vc = WaveFunction(3)
sqh = sqrt(0.5)
nsvahl = nsv * abs(nhel)
pt2 = p[1]**2 + p[2]**2
pp = min(p[0], sqrt(pt2 + p[3]**2))
pt = min(pp, sqrt(pt2))
vc[0] = complex(p[0] * nsv, p[3] * nsv)
vc[1] = complex(p[1] * nsv, p[2] * nsv)
if (nhel == 4):
if (vmass == 0.):
vc[2] = 1.
vc[3] = p[1] / p[0]
vc[4] = p[2] / p[0]
vc[5] = p[3] / p[0]
else:
vc[2] = p[0] / vmass
vc[3] = p[1] / vmass
vc[4] = p[2] / vmass
vc[5] = p[3] / vmass
return vc
if (vmass != 0.):
hel0 = 1. - abs(nhel)
if (pp == 0.):
vc[2] = complex(0., 0.)
vc[3] = complex(-nhel * sqh, 0.)
vc[4] = complex(0., nsvahl * sqh)
vc[5] = complex(hel0, 0.)
else:
emp = p[0] / (vmass * pp)
vc[2] = complex(hel0 * pp / vmass, 0.)
vc[5] = complex(hel0 * p[3] * emp + nhel * pt / pp * sqh)
if (pt != 0.):
pzpt = p[3] / (pp * pt) * sqh * nhel
vc[3] = complex(hel0*p[1]*emp-p[1]*pzpt, \
-nsvahl*p[2]/pt*sqh)
vc[4] = complex(hel0*p[2]*emp-p[2]*pzpt, \
nsvahl*p[1]/pt*sqh)
else:
vc[3] = complex(-nhel * sqh, 0.)
vc[4] = complex(0., nsvahl * sign(sqh, p[3]))
else:
pp = p[0]
pt = sqrt(p[1]**2 + p[2]**2)
vc[2] = complex(0., 0.)
vc[5] = complex(nhel * pt / pp * sqh)
if (pt != 0.):
pzpt = p[3] / (pp * pt) * sqh * nhel
vc[3] = complex(-p[1] * pzpt, -nsv * p[2] / pt * sqh)
vc[4] = complex(-p[2] * pzpt, nsv * p[1] / pt * sqh)
else:
vc[3] = complex(-nhel * sqh, 0.)
vc[4] = complex(0., nsv * sign(sqh, p[3]))
return vc