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subroutine uvvxxx(v1,v2,gt,vmass,tmass,twidth , uvv)
c
c This subroutine computes an off-shell tensor current from
c the two gauge bosons-tensor boson coupling.
c
c input:
c complex v1(3) : first vector v1
c complex v2(3) : second vector v2
c complex gt : coupling constant gtv=-1/Lambda
c real vmass : vector boson mass m_v
c real tmass : mass of output tensor T
c real twidth : width of output tensor T
c
c output:
c complex uvv(18) : tensor current j^mu^nu(T:v1,v2)
c
c- by Q.Li - OCT. 2006
c- Added massless tensor - P. de Aquino - Oct. 2009
c
implicit none
double complex v1(6), v2(6), gt, uvv(18)
double precision vmass, tmass, twidth
double complex yvv(6,4)
double complex KTE1,KTE2,K2E1,K1E2,K1E1,K2E2,E1E2
integer i,j
double precision pv1(4), pv2(4), pT(4)
double precision MET(4,4)
double complex cZero, d
double precision rZero, rTwo
double precision K1K2,KT2,K1KT,K2KT
parameter( rZero = 0.0d0, rTwo = 2.0d0 )
parameter( cZero = ( 0.0d0, 0.0d0 ) )
yvv(5,1) = v1(5)+v2(5)
yvv(6,1) = v1(6)+v2(6)
pv1(1) = dreal(v1(5))
pv1(2) = dreal(v1(6))
pv1(3) = dimag(v1(6))
pv1(4) = dimag(v1(5))
pv2(1) = dreal(v2(5))
pv2(2) = dreal(v2(6))
pv2(3) = dimag(v2(6))
pv2(4) = dimag(v2(5))
pT(1) = dreal(yvv(5,1))
pT(2) = dreal(yvv(6,1))
pT(3) = dimag(yvv(6,1))
pT(4) = dimag(yvv(5,1))
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
K1K2 = pv1(1)*pv2(1)-pv1(2)*pv2(2)-pv1(3)*pv2(3)-pv1(4)*pv2(4)
K1KT = pv1(1)*pT(1)-pv1(2)*pT(2)-pv1(3)*pT(3)-pv1(4)*pT(4)
K2KT = pT(1)*pv2(1)-pT(2)*pv2(2)-pT(3)*pv2(3)-pT(4)*pv2(4)
KT2 = pT(1)**2-pT(2)**2-pT(3)**2-pT(4)**2
KTE1 = pT(1)*v1(1)-pT(2)*v1(2)-pT(3)*v1(3)-pT(4)*v1(4)
KTE2 = pT(1)*v2(1)-pT(2)*v2(2)-pT(3)*v2(3)-pT(4)*v2(4)
K1E1 = pv1(1)*v1(1)-pv1(2)*v1(2)-pv1(3)*v1(3)-pv1(4)*v1(4)
K1E2 = pv1(1)*v2(1)-pv1(2)*v2(2)-pv1(3)*v2(3)-pv1(4)*v2(4)
K2E1 = pv2(1)*v1(1)-pv2(2)*v1(2)-pv2(3)*v1(3)-pv2(4)*v1(4)
K2E2 = pv2(1)*v2(1)-pv2(2)*v2(2)-pv2(3)*v2(3)-pv2(4)*v2(4)
E1E2 = v2(1)*v1(1)-v2(2)*v1(2)-v2(3)*v1(3)-v2(4)*v1(4)
if ( tmass.eq.rZero ) then
d = - gt/dcmplx( KT2, rZero )
do i = 1,4
do j=1,4
yvv(i,j) = -(E1E2*K1K2*MET(i,j)) + K1E2*K2E1*MET(i,j)
&+ E1E2*pv1(j)*pv2(i) + E1E2*pv1(i)*pv2(j)
&- K1E2*pv2(j)*v1(i) - K1E2*pv2(i)*v1(j)
&- K2E1*pv1(j)*v2(i) + k1k2*v1(j)*v2(i)
&- K2E1*pv1(i)*v2(j) + k1k2*v1(i)*v2(j)
if ( vmass.ne.rZero ) then
yvv(i,j) = yvv(i,j)
& + vmass**2*v1(j)*v2(i) + vmass**2*v1(i)*v2(j)
else
c gauge fixing term for zero mass photon/gluon
yvv(i,j) = yvv(i,j)
& -(K1E1*K2E2*MET(i,j)) - K2E2*pv2(j)*v1(i) -
& K2E2*pv2(i)*v1(j) - K1E1*pv1(j)*v2(i) -
& K1E1*pv1(i)*v2(j)
endif
yvv(i,j) = yvv(i,j)*d
end do
enddo
else if ( tmass.gt.rZero ) then
d = - gt/dcmplx( KT2-tmass**2, tmass*twidth )
do i = 1,4
do j=1,4
yvv(i,j) = 2.0d0*K1K2*(v1(i)*v2(j)+v1(j)*v2(i))
&-2.0d0*K1K2*KTE2/tmass**2*(PT(i)*v1(j)+PT(j)*v1(i))
&-2.0d0*K1E2*(pv2(i)*v1(j)+pv2(j)*v1(i))
&+2.0d0*K1E2*K2KT/tmass**2*(PT(i)*v1(j)+PT(j)*v1(i))
&-2.0d0/3.0d0*E1E2*K1K2*MET(i,j)
&+8.0d0/3.0d0*K1K2*E1E2/tmass**2*PT(i)*PT(j)
&+2.0d0*E1E2*(pv1(i)*pv2(j)+pv1(j)*pv2(i))
&-2.0d0*K1K2*KTE1/tmass**2*(PT(i)*v2(j)+PT(j)*v2(i))
&-2.0d0*K2E1*(pv1(i)*v2(j)+pv1(j)*v2(i))
&+4.0d0*K1K2*KTE1*KTE2/3.0d0/tmass**2*MET(i,j)
&+8.0d0*K1K2*KTE1*KTE2/3.0d0/tmass**4*PT(i)*PT(j)
&+2.0d0*K2E1*KTE2/tmass**2*(pv1(i)*PT(j)+pv1(j)*PT(i))
&+2.0d0*KTE1*K1E2/tmass**2*(pv2(i)*PT(j)+pv2(j)*PT(i))
&+2.0d0*K2E1*K1E2*MET(i,j)
&-4.0d0*K2E1*K1E2/tmass**2*PT(i)*PT(j)
&-2.0d0/3.0d0/tmass**2*KT2*E1E2*K1K2*MET(i,j)
&-4.0d0/3.0d0/tmass**4*KT2*E1E2*K1K2*PT(i)*PT(j)
&+2.0d0/3.0d0/tmass**2*K2E1*K1E2*KT2*MET(i,j)
&+4.0d0/3.0d0/tmass**4*K2E1*K1E2*KT2*PT(i)*PT(j)
&-2.0d0/tmass**2*E1E2*K1KT*(pv2(i)*PT(j)+pv2(j)*PT(i))
&+2.0d0/tmass**2*K2E1*K1KT*(PT(i)*v2(j)+PT(j)*v2(i))
&-4.0d0/3.0d0/tmass**2*K2E1*KTE2*K1KT*MET(i,j)
&-8.0d0/3.0d0/tmass**4*K2E1*KTE2*K1KT*PT(i)*PT(j)
&-2.0d0/tmass**2*E1E2*K2KT*(PT(i)*pv1(j)+PT(j)*pv1(i))
&-4.0d0/3.0d0/tmass**2*KTE1*K1E2*K2KT*MET(i,j)
&-8.0d0/3.0d0/tmass**4*KTE1*K1E2*K2KT*PT(i)*PT(j)
&+4.0d0/3.0d0/tmass**2*E1E2*K2KT*K1KT*MET(i,j)
&+8.0d0/3.0d0/tmass**4*E1E2*K2KT*K1KT*PT(i)*PT(j)
&-4.0d0/3.0d0*E1E2*K1K2*MET(i,j)
&+4.0d0/3.0d0/tmass**2*E1E2*K1K2
&*PT(i)*PT(j)
if ( vmass.ne.rZero ) then
yvv(i,j) =
& yvv(i,j)+2*vmass**2*(v1(i)*v2(j)+v1(j)*v2(i))
&-2.0d0/3.0d0*vmass**2*E1E2*MET(i,j)
&+8.0d0/3.0d0/tmass**2*vmass**2*E1E2*PT(i)*PT(j)
&-2.0d0/tmass**2*vmass**2*KTE1*(PT(i)*v2(j)+PT(j)*v2(i))
&-2.0d0/tmass**2*vmass**2*KTE2*(PT(i)*v1(j)+PT(j)*v1(i))
&+4.0d0/3.0d0/tmass**2*vmass**2*KTE1*KTE2*MET(i,j)
&+8.0d0/3.0d0/tmass**4*vmass**2*KTE1*KTE2*PT(i)*PT(j)
&-2.0d0/3.0d0/tmass**2*vmass**2*KT2*E1E2*MET(i,j)
&-4.0d0/3.0d0/tmass**4*vmass**2*KT2*E1E2*PT(i)*PT(j)
else
c gauge fixing term for zero mass photon/gluon
yvv(i,j) =
& yvv(i,j)-2.0d0*K1E1*(pv1(i)*v2(j)+pv1(j)*v2(i))
&+2.0d0/tmass**2*KTE2*K1E1*(PT(i)*pv1(j)+PT(j)*pv1(i))
&+2.0d0/3.0d0*K1E2*K1E1*MET(i,j)
&-8.0d0/3.0d0/tmass**2*K1E2*K1E1*PT(i)*PT(j)
&-2.0d0/3.0d0*K2E2*K1E1*MET(i,j)
&-4.0d0/3.0d0/tmass**2*K2E2*K1E1*PT(i)*PT(j)
&+2.0d0/3.0d0/tmass**2*K1E2*KT2*K1E1*MET(i,j)
&+4.0d0/3.0d0/tmass**4*K1E2*KT2*K1E1*PT(i)*PT(j)
&+2.0d0/3.0d0/tmass**2*K2E2*KT2*K1E1*MET(i,j)
&+4.0d0/3.0d0/tmass**4*K2E2*KT2*K1E1*PT(i)*PT(j)
&+2.0d0/tmass**2*K1KT*K1E1*(PT(i)*v2(j)+PT(j)*v2(i))
&-4.0d0/3.0d0/tmass**2*K1KT*KTE2*K1E1*MET(i,j)
&-8.0d0/3.0d0/tmass**4*K1KT*KTE2*K1E1*PT(i)*PT(j)
&-2.0d0*K2E2*(pv2(i)*v1(j)+pv2(j)*v1(i))
&+2.0d0/tmass**2*K2E2*KTE1*(pv2(i)*PT(j)+pv2(j)*PT(i))
&+2.0d0/3.0d0*K2E1*K2E2*MET(i,j)
&-8.0d0/3.0d0/tmass**2*K2E1*K2E2*PT(i)*PT(j)
&+2.0d0/3.0d0/tmass**2*KT2*K2E2*K2E1*MET(i,j)
&+4.0d0/3.0d0/tmass**4*KT2*K2E2*K2E1*PT(i)*PT(j)
&+2.0d0/tmass**2*K2E2*K2KT*(PT(i)*v1(j)+PT(j)*v1(i))
&-4.0d0/3.0d0/tmass**2*K2E2*K2KT*KTE1*MET(i,j)
&-8.0d0/3.0d0/tmass**4*K2E2*K2KT*KTE1
&*PT(i)*PT(j)
endif
yvv(i,j) = yvv(i,j)*d/2.0d0
end do
enddo
else
write(*,*) 'invalid tensor mass'
stop
end if
uvv(1) = yvv(1,1)
uvv(2) = yvv(1,2)
uvv(3) = yvv(1,3)
uvv(4) = yvv(1,4)
uvv(5) = yvv(2,1)
uvv(6) = yvv(2,2)
uvv(7) = yvv(2,3)
uvv(8) = yvv(2,4)
uvv(9) = yvv(3,1)
uvv(10) = yvv(3,2)
uvv(11) = yvv(3,3)
uvv(12) = yvv(3,4)
uvv(13) = yvv(4,1)
uvv(14) = yvv(4,2)
uvv(15) = yvv(4,3)
uvv(16) = yvv(4,4)
uvv(17) = yvv(5,1)
uvv(18) = yvv(6,1)
return
end
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