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subroutine jvvtxx(va,vb,tc,gc,gt,vmass,vwidth , jvvt)
c
c This subroutine computes an off-shell vector boson wavefunction from
c the four-point coupling of three gauge bosons and a tensor boson.
c
c input:
c complex va(6) : first vector va
c complex vb(6) : second vector vb
c complex tc(18) : input tensor T
c real gc : coupling constant gs (for gluons)
c complex gt : coupling constant gtv=-1/Lambda
c real vmass : mass of output vector v
c real vwidth : width of output vector v
c
c output:
c complex jvvt(6) : vector current j^mu(v:va,vb,T)
c
c- by Q.Li - OCT. 2006
c
implicit none
double complex va(6), vb(6), tc(18), gt, jvvt(6)
double precision gc,vmass,vwidth
double complex ft(6,4)
double complex TV1M(4),TV2M(4),TK12M(4)
double precision MET(4,4)
double complex d,T00, T12, T13, T14, T23, T24, T34
double complex V1V2,K1V2, K2V1
&,K3V1,K3V2
double precision K1K2
double complex TV12,TKV1,TKV2,
&TK3V1,TK3V2,TK312,dum
double precision pva(4), pvb(4), pvc(4),
&pv32,p31(4),p23(4),p12(4),K1K3,K2K3
integer i, j
double complex cZero
double precision rZero, rTwo
parameter( rZero = 0.0d0, rTwo = 2.0d0 )
parameter( cZero = ( 0.0d0, 0.0d0 ) )
ft(1,1) = tc(1)
ft(1,2) = tc(2)
ft(1,3) = tc(3)
ft(1,4) = tc(4)
ft(2,1) = tc(5)
ft(2,2) = tc(6)
ft(2,3) = tc(7)
ft(2,4) = tc(8)
ft(3,1) = tc(9)
ft(3,2) = tc(10)
ft(3,3) = tc(11)
ft(3,4) = tc(12)
ft(4,1) = tc(13)
ft(4,2) = tc(14)
ft(4,3) = tc(15)
ft(4,4) = tc(16)
ft(5,1) = tc(17)
ft(6,1) = tc(18)
jvvt(5) = va(5)+vb(5)+ft(5,1)
jvvt(6) = va(6)+vb(6)+ft(6,1)
pva(1) = dreal(va(5))
pva(2) = dreal(va(6))
pva(3) = dimag(va(6))
pva(4) = dimag(va(5))
pvb(1) = dreal(vb(5))
pvb(2) = dreal(vb(6))
pvb(3) = dimag(vb(6))
pvb(4) = dimag(vb(5))
pvc(1) = -dreal(jvvt(5))
pvc(2) = -dreal(jvvt(6))
pvc(3) = -dimag(jvvt(6))
pvc(4) = -dimag(jvvt(5))
pv32=pvc(1)**2-pvc(2)**2-pvc(3)**2-pvc(4)**2
if ( vmass.gt.rZero ) then
d = gc/dcmplx( pv32-vmass**2, vmass*vwidth )
else
d = gc/dcmplx( pv32, rZero )
end if
do i=1,4
do j=1,4
MET(i,j) = 0.0d0
enddo
enddo
MET(1,1) = 1.0d0
MET(2,2) = -1.0d0
MET(3,3) = -1.0d0
MET(4,4) = -1.0d0
p31(1) = pvc(1)-pva(1)
p31(2) = pvc(2)-pva(2)
p31(3) = pvc(3)-pva(3)
p31(4) = pvc(4)-pva(4)
p12(1) = pva(1)-pvb(1)
p12(2) = pva(2)-pvb(2)
p12(3) = pva(3)-pvb(3)
p12(4) = pva(4)-pvb(4)
p23(1) = pvb(1)-pvc(1)
p23(2) = pvb(2)-pvc(2)
p23(3) = pvb(3)-pvc(3)
p23(4) = pvb(4)-pvc(4)
T00 = ft(1,1)-ft(2,2)-ft(3,3)-ft(4,4)
T12 = ft(1,2) + ft(2,1)
T13 = ft(1,3) + ft(3,1)
T14 = ft(1,4) + ft(4,1)
T23 = ft(2,3) + ft(3,2)
T24 = ft(2,4) + ft(4,2)
T34 = ft(3,4) + ft(4,3)
V1V2 = va(1)*vb(1) - va(2)*vb(2) - va(3)*vb(3) - va(4)*vb(4)
K1V2 = pva(1)*vb(1) - pva(2)*vb(2) - pva(3)*vb(3) - pva(4)*vb(4)
K2V1 = pvb(1)*va(1) - pvb(2)*va(2) - pvb(3)*va(3) - pvb(4)*va(4)
K3V1 = pvc(1)*va(1) - pvc(2)*va(2) - pvc(3)*va(3) - pvc(4)*va(4)
K3V2 = pvc(1)*vb(1) - pvc(2)*vb(2) - pvc(3)*vb(3) - pvc(4)*vb(4)
K1K3 = pva(1)*pvc(1)-pva(2)*pvc(2)-pva(3)*pvc(3)-pva(4)*pvc(4)
K2K3 = pvb(1)*pvc(1)-pvb(2)*pvc(2)-pvb(3)*pvc(3)-pvb(4)*pvc(4)
TV12 = rtwo*(ft(1,1)*va(1)*vb(1)+ft(2,2)*va(2)*vb(2)
&+ft(3,3)*va(3)*vb(3)+ft(4,4)*va(4)*vb(4))
TKV1 = rtwo*(ft(1,1)*p23(1)*va(1)+ft(2,2)*p23(2)*va(2)
&+ft(3,3)*p23(3)*va(3)+ft(4,4)*p23(4)*va(4))
TKV2 = rtwo*(ft(1,1)*p31(1)*vb(1)+ft(2,2)*p31(2)*vb(2)
&+ft(3,3)*p31(3)*vb(3)+ft(4,4)*p31(4)*vb(4))
TK3V1 = rtwo*(ft(1,1)*pvc(1)*va(1)+ft(2,2)*pvc(2)*va(2)
&+ft(3,3)*pvc(3)*va(3)+ft(4,4)*pvc(4)*va(4))
TK3V2 = rtwo*(ft(1,1)*pvc(1)*vb(1)+ft(2,2)*pvc(2)*vb(2)
&+ft(3,3)*pvc(3)*vb(3)+ft(4,4)*pvc(4)*vb(4))
TK312 = rtwo*(ft(1,1)*pvc(1)*p12(1)+ft(2,2)*pvc(2)*p12(2)
&+ft(3,3)*pvc(3)*p12(3)+ft(4,4)*pvc(4)*p12(4))
TV12 = TV12 - T12*(va(1)*vb(2) + va(2)*vb(1))
& - T13*(va(1)*vb(3) + va(3)*vb(1))
& - T14*(va(1)*vb(4) + va(4)*vb(1))
& + T23*(va(2)*vb(3) + va(3)*vb(2))
& + T24*(va(2)*vb(4) + va(4)*vb(2))
& + T34*(va(3)*vb(4) + va(4)*vb(3))
TKV1 = TKV1 - T12*(p23(1)*va(2) + p23(2)*va(1))
& - T13*(p23(1)*va(3) + p23(3)*va(1))
& - T14*(p23(1)*va(4) + p23(4)*va(1))
& + T23*(p23(2)*va(3) + p23(3)*va(2))
& + T24*(p23(2)*va(4) + p23(4)*va(2))
& + T34*(p23(3)*va(4) + p23(4)*va(3))
TKV2 = TKV2 - T12*(p31(1)*vb(2) + p31(2)*vb(1))
& - T13*(p31(1)*vb(3) + p31(3)*vb(1))
& - T14*(p31(1)*vb(4) + p31(4)*vb(1))
& + T23*(p31(2)*vb(3) + p31(3)*vb(2))
& + T24*(p31(2)*vb(4) + p31(4)*vb(2))
& + T34*(p31(3)*vb(4) + p31(4)*vb(3))
TK3V1 = TK3V1 - T12*(pvc(1)*va(2) + pvc(2)*va(1))
& - T13*(pvc(1)*va(3) + pvc(3)*va(1))
& - T14*(pvc(1)*va(4) + pvc(4)*va(1))
& + T23*(pvc(2)*va(3) + pvc(3)*va(2))
& + T24*(pvc(2)*va(4) + pvc(4)*va(2))
& + T34*(pvc(3)*va(4) + pvc(4)*va(3))
TK3V2 = TK3V2 - T12*(pvc(1)*vb(2) + pvc(2)*vb(1))
& - T13*(pvc(1)*vb(3) + pvc(3)*vb(1))
& - T14*(pvc(1)*vb(4) + pvc(4)*vb(1))
& + T23*(pvc(2)*vb(3) + pvc(3)*vb(2))
& + T24*(pvc(2)*vb(4) + pvc(4)*vb(2))
& + T34*(pvc(3)*vb(4) + pvc(4)*vb(3))
TK312 = TK312 - T12*(pvc(1)*p12(2) + pvc(2)*p12(1))
& - T13*(pvc(1)*p12(3) + pvc(3)*p12(1))
& - T14*(pvc(1)*p12(4) + pvc(4)*p12(1))
& + T23*(pvc(2)*p12(3) + pvc(3)*p12(2))
& + T24*(pvc(2)*p12(4) + pvc(4)*p12(2))
& + T34*(pvc(3)*p12(4) + pvc(4)*p12(3))
do j=1,4
TV1M(j) =
&MET(j,1)*(ft(1,1)*va(1)-ft(2,1)*va(2)
&-ft(3,1)*va(3)-ft(4,1)*va(4))
&-MET(j,2)*(ft(1,2)*va(1)-ft(2,2)*va(2)
&-ft(3,2)*va(3)-ft(4,2)*va(4))
&-MET(j,3)*(ft(1,3)*va(1)-ft(2,3)*va(2)
&-ft(3,3)*va(3)-ft(4,3)*va(4))
&-MET(j,4)*(ft(1,4)*va(1)-ft(2,4)*va(2)
&-ft(3,4)*va(3)-ft(4,4)*va(4))
&+
&MET(j,1)*(ft(1,1)*va(1)-ft(1,2)*va(2)
&-ft(1,3)*va(3)-ft(1,4)*va(4))
&-MET(j,2)*(ft(2,1)*va(1)-ft(2,2)*va(2)
&-ft(2,3)*va(3)-ft(2,4)*va(4))
&-MET(j,3)*(ft(3,1)*va(1)-ft(3,2)*va(2)
&-ft(3,3)*va(3)-ft(3,4)*va(4))
&-MET(j,4)*(ft(4,1)*va(1)-ft(4,2)*va(2)
&-ft(4,3)*va(3)-ft(4,4)*va(4))
TV2M(j) =
&MET(j,1)*(ft(1,1)*vb(1)-ft(2,1)*vb(2)
&-ft(3,1)*vb(3)-ft(4,1)*vb(4))
&-MET(j,2)*(ft(1,2)*vb(1)-ft(2,2)*vb(2)
&-ft(3,2)*vb(3)-ft(4,2)*vb(4))
&-MET(j,3)*(ft(1,3)*vb(1)-ft(2,3)*vb(2)
&-ft(3,3)*vb(3)-ft(4,3)*vb(4))
&-MET(j,4)*(ft(1,4)*vb(1)-ft(2,4)*vb(2)
&-ft(3,4)*vb(3)-ft(4,4)*vb(4))
&+
&MET(j,1)*(ft(1,1)*vb(1)-ft(1,2)*vb(2)
&-ft(1,3)*vb(3)-ft(1,4)*vb(4))
&-MET(j,2)*(ft(2,1)*vb(1)-ft(2,2)*vb(2)
&-ft(2,3)*vb(3)-ft(2,4)*vb(4))
&-MET(j,3)*(ft(3,1)*vb(1)-ft(3,2)*vb(2)
&-ft(3,3)*vb(3)-ft(3,4)*vb(4))
&-MET(j,4)*(ft(4,1)*vb(1)-ft(4,2)*vb(2)
&-ft(4,3)*vb(3)-ft(4,4)*vb(4))
TK12M(j) =
&MET(j,1)*(ft(1,1)*p12(1)-ft(2,1)*p12(2)
&-ft(3,1)*p12(3)-ft(4,1)*p12(4))
&-MET(j,2)*(ft(1,2)*p12(1)-ft(2,2)*p12(2)
&-ft(3,2)*p12(3)-ft(4,2)*p12(4))
&-MET(j,3)*(ft(1,3)*p12(1)-ft(2,3)*p12(2)
&-ft(3,3)*p12(3)-ft(4,3)*p12(4))
&-MET(j,4)*(ft(1,4)*p12(1)-ft(2,4)*p12(2)
&-ft(3,4)*p12(3)-ft(4,4)*p12(4))
&+
&MET(j,1)*(ft(1,1)*p12(1)-ft(1,2)*p12(2)
&-ft(1,3)*p12(3)-ft(1,4)*p12(4))
&-MET(j,2)*(ft(2,1)*p12(1)-ft(2,2)*p12(2)
&-ft(2,3)*p12(3)-ft(2,4)*p12(4))
&-MET(j,3)*(ft(3,1)*p12(1)-ft(3,2)*p12(2)
&-ft(3,3)*p12(3)-ft(3,4)*p12(4))
&-MET(j,4)*(ft(4,1)*p12(1)-ft(4,2)*p12(2)
&-ft(4,3)*p12(3)-ft(4,4)*p12(4))
enddo
do i=1,4
jvvt(i) = TV12*p12(i)+TKV1*vb(i)+TKV2*va(i)
&+(-p12(i)*V1V2-vb(i)*K2V1+vb(i)*K3V1
& +va(i)*K1V2-va(i)*K3V2)*T00
&-K1V2*TV1M(i)+K3V2*TV1M(i)
&+V1V2*TK12M(i)
&+K2V1*TV2M(i)-K3V1*TV2M(i)
enddo
if ( vmass.gt.rZero ) then
do i=1,4
jvvt(i) = jvvt(i)
&+(K1V2*pvc(i)
&-K3V2*TKV1*pvc(i)-K3V2*TK3V1*pvc(i)
&-K1K3*TV12*pvc(i)+K2K3*TV12*pvc(i)
&-V1V2*TK312*pvc(i)
&-K2V1*TK3V2*pvc(i)+K3V1*TK3V2*pvc(i)
&-K3V1*TKV2*pvc(i))/vmass**2
&+(-pvc(i)*K1V2*K3V1+pvc(i)*K2V1*K3V2
&+pvc(i)*V1V2*K1K3-pvc(i)*V1V2*K2K3
&)/vmass**2*T00
enddo
endif
do i=1,4
jvvt(i) = -jvvt(i) * d*gt
enddo
return
end
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