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subroutine fvtoxx(fo,vc,tc,gc,gt,fmass,fwidth , fvto)
c
c This subroutine computes an off-shell fermion wavefunction from a
c flowing-out external fermion, a gauge boson and a tensor boson.
c
c input:
c complex fo(6) : flow-out fermion <fo|
c complex vc(6) : input vector v
c complex tc(18) : input tensor T
c complex gc(2) : coupling constants gvf
c complex gt : coupling constant gtfv=-1/Lambda/2
c real fmass : mass of output fermion f'
c real fwidth : width of output fermion f'
c
c output:
c complex fvto(6) : off-shell fermion <fo,v,T:f'|
c
c- by Q.Li - OCT. 2006
c
implicit none
double complex fo(6), vc(6), tc(18), gc(2),gt, fvto(6)
double precision fmass, fwidth
double complex ft(6,4)
double complex d, T00, T12, T13, T14, T23, T24, T34
double precision pi(4), pi2
integer i
double precision rZero, rTwo
parameter( rZero = 0.0d0, rTwo = 2.0d0 )
double complex cone
parameter( cone = ( 0.0d0, 1.0d0 ))
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)
fvto(5) = fo(5) + ft(5,1) +vc(5)
fvto(6) = fo(6) + ft(6,1) +vc(6)
pi(1) = dreal(fvto(5))
pi(2) = dreal(fvto(6))
pi(3) = dimag(fvto(6))
pi(4) = dimag(fvto(5))
pi2 = pi(1)**2-pi(2)**2-pi(3)**2-pi(4)**2
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)
if ( fmass.gt.rZero ) then
d = -1.0d0/dcmplx( pi2-fmass**2, fmass*fwidth )
else
d = -1.0d0/dcmplx( pi2, rZero )
end if
fvto(1) = gc(2)*(pi(2) + cone*pi(3))*(fo(1)*(T12*vc(1)
& - cone*T13*vc(1) - T23*(-(cone*vc(2)) + vc(3)) +
& 2.d0*T00*(-vc(2) + cone*vc(3)) - T24*vc(4)
& + cone*T34*vc(4)) +
& fo(2)*(T12*vc(2) + T24*vc(2) + T13*vc(3)
&+ T34*vc(3) + T14*(-vc(1) + vc(4)) + 2.d0*T00*(vc(1) + vc(4))))
& + fmass*gc(1)*(fo(4)*(-(T12*vc(1)) - cone*T13*vc(1)
& - T23*(-(cone*vc(2)) - vc(3)) + 2.d0*T00*(vc(2) + cone*vc(3)) +
& T24*vc(4) + cone*T34*vc(4)) + fo(3)*
& (T12*vc(2) + T24*vc(2) + T13*vc(3) + T34*vc(3)
& + T14*(-vc(1) + vc(4)) + 2.d0*T00*(vc(1) + vc(4)))) +
& gc(2)*(pi(1) + pi(4))*(fo(2)*(T12*vc(1) + cone*T13*vc(1)
&- T23*(cone*vc(2) + vc(3)) + 2.d0*T00*(-vc(2) - cone*vc(3)) -
& T24*vc(4) - cone*T34*vc(4)) + fo(1)*
& (T12*vc(2) - T24*vc(2) + T13*vc(3) - T34*vc(3)
&+ 2.d0*T00*(vc(1) - vc(4)) + T14*(vc(1) + vc(4))))
fvto(2) = gc(2)*(pi(1) - pi(4))*(fo(1)*(T12*vc(1) - cone*T13*vc(1)
& - T23*(-(cone*vc(2)) + vc(3)) + 2.d0*T00*(-vc(2) + cone*vc(3))
& - T24*vc(4) + cone*T34*vc(4)) + fo(2)*
& (T12*vc(2) + T24*vc(2) + T13*vc(3) + T34*vc(3)
& + T14*(-vc(1) + vc(4)) + 2.d0*T00*(vc(1) + vc(4)))) +
& gc(2)*(pi(2) - cone*pi(3))*(fo(2)*(T12*vc(1)
& + cone*T13*vc(1) - T23*(cone*vc(2) + vc(3)) +
& 2.d0*T00*(-vc(2) - cone*vc(3)) - T24*vc(4)
& - cone*T34*vc(4)) +
& fo(1)*(T12*vc(2) - T24*vc(2) + T13*vc(3)
& - T34*vc(3) + 2.d0*T00*(vc(1) - vc(4)) + T14*(vc(1) + vc(4))))
& +fmass*gc(1)*(fo(3)*(-(T12*vc(1)) + cone*T13*vc(1)
& - T23*(cone*vc(2) - vc(3)) + 2.d0*T00*(vc(2) - cone*vc(3)) +
& T24*vc(4) - cone*T34*vc(4)) + fo(4)*
& (T12*vc(2) - T24*vc(2) + T13*vc(3) - T34*vc(3)
& + 2.d0*T00*(vc(1) - vc(4)) + T14*(vc(1) + vc(4))))
fvto(3) = gc(1)*(pi(1) - pi(4))*(fo(4)*(-(T12*vc(1))
& - cone*T13*vc(1) - T23*(-(cone*vc(2)) - vc(3)) +
& 2.d0*T00*(vc(2) + cone*vc(3)) + T24*vc(4) + cone*T34*vc(4))
& +fo(3)*(T12*vc(2) + T24*vc(2) + T13*vc(3)
& + T34*vc(3) + T14*(-vc(1) + vc(4)) + 2.d0*T00*(vc(1) + vc(4))))
& + fmass*gc(2)*(fo(2)*(T12*vc(1) + cone*T13*vc(1)
&- T23*(cone*vc(2) + vc(3)) + 2.d0*T00*(-vc(2) - cone*vc(3))
& - T24*vc(4) -
& cone*T34*vc(4)) + fo(1)*(T12*vc(2)
& - T24*vc(2) + T13*vc(3) - T34*vc(3) + 2.d0*T00*(vc(1) - vc(4))
& + T14*(vc(1) + vc(4)))) + gc(1)*(-pi(2) - cone*pi(3))*
& (fo(3)*(-(T12*vc(1)) + cone*T13*vc(1)
&- T23*(cone*vc(2) - vc(3))
& + 2.d0*T00*(vc(2) - cone*vc(3)) + T24*vc(4) -
& cone*T34*vc(4)) + fo(4)*(T12*vc(2) - T24*vc(2)
& + T13*vc(3) - T34*vc(3) + 2.d0*T00*(vc(1) - vc(4)) +
& T14*(vc(1) + vc(4))))
fvto(4) = fmass*gc(2)*(fo(1)*
& (T12*vc(1) - cone*T13*vc(1) - T23*(-(cone*vc(2)) + vc(3))
& + 2.d0*T00*(-vc(2) + cone*vc(3)) - T24*vc(4) +
& cone*T34*vc(4)) + fo(2)*(T12*vc(2) + T24*vc(2)
& + T13*vc(3) + T34*vc(3) + T14*(-vc(1) + vc(4)) +
& 2.d0*T00*(vc(1) + vc(4)))) + gc(1)*(-pi(2) + cone*pi(3))*
& (fo(4)*(-(T12*vc(1)) - cone*T13*vc(1) - T23*(-(cone*vc(2))
& - vc(3)) + 2.d0*T00*(vc(2) + cone*vc(3)) + T24*vc(4) +
& cone*T34*vc(4)) + fo(3)*(T12*vc(2) + T24*vc(2)
& + T13*vc(3) + T34*vc(3) + T14*(-vc(1) + vc(4)) +
& 2.d0*T00*(vc(1) + vc(4)))) + gc(1)*(pi(1) + pi(4))*
& (fo(3)*(-(T12*vc(1)) + cone*T13*vc(1) - T23*(cone*vc(2)
& - vc(3)) + 2.d0*T00*(vc(2) - cone*vc(3)) + T24*vc(4) -
& cone*T34*vc(4)) + fo(4)*(T12*vc(2) - T24*vc(2)
& + T13*vc(3) - T34*vc(3) + 2.d0*T00*(vc(1) - vc(4)) +
& T14*(vc(1) + vc(4))))
fvto(1) = fvto(1)+
&gc(2)*(pi(2) + cone*pi(3))*(-2*fo(1)*(ft(2,2)*vc(2)
& - cone*ft(3,3)*vc(3)) -
& 2*fo(2)*(ft(1,1)*vc(1) - ft(4,4)*vc(4))) +
& fmass*gc(1)*(-2*fo(4)*(-(ft(2,2)*vc(2)) - cone*ft(3,3)*vc(3))
& - 2*fo(3)*(ft(1,1)*vc(1) - ft(4,4)*vc(4))) +
& gc(2)*(pi(1) + pi(4))*(-2*fo(2)*(ft(2,2)*vc(2)
&+ cone*ft(3,3)*vc(3)) - 2*fo(1)*(ft(1,1)*vc(1) + ft(4,4)*vc(4)))
fvto(2) = fvto(2)+
&gc(2)*(pi(1) - pi(4))*(-2*fo(1)*(ft(2,2)*vc(2)-cone*ft(3,3)*vc(3))
& - 2*fo(2)*(ft(1,1)*vc(1) - ft(4,4)*vc(4))) +
& gc(2)*(pi(2)-cone*pi(3))*(-2*fo(2)*(ft(2,2)*vc(2)
& + cone*ft(3,3)*vc(3))-2*fo(1)*(ft(1,1)*vc(1) + ft(4,4)*vc(4))) +
& fmass*gc(1)*(-2*fo(3)*(-(ft(2,2)*vc(2)) + cone*ft(3,3)*vc(3))
& - 2*fo(4)*(ft(1,1)*vc(1) + ft(4,4)*vc(4)))
fvto(3) = fvto(3)+
&gc(1)*(pi(1) - pi(4))*(-2*fo(4)*(-(ft(2,2)*vc(2))
& - cone*ft(3,3)*vc(3)) - 2*fo(3)*(ft(1,1)*vc(1)-ft(4,4)*vc(4)))+
& fmass*gc(2)*(-2*fo(2)*(ft(2,2)*vc(2) + cone*ft(3,3)*vc(3))
& - 2*fo(1)*(ft(1,1)*vc(1) + ft(4,4)*vc(4))) +
& gc(1)*(-pi(2) - cone*pi(3))*(-2*fo(3)*(-(ft(2,2)*vc(2))
& + cone*ft(3,3)*vc(3)) - 2*fo(4)*(ft(1,1)*vc(1) + ft(4,4)*vc(4)))
fvto(4) = fvto(4)+
&fmass*gc(2)*(-2*fo(1)*(ft(2,2)*vc(2) - cone*ft(3,3)*vc(3))
& - 2*fo(2)*(ft(1,1)*vc(1) - ft(4,4)*vc(4))) +
& gc(1)*(-pi(2) + cone*pi(3))*(-2*fo(4)*(-(ft(2,2)*vc(2))
& - cone*ft(3,3)*vc(3)) - 2*fo(3)*(ft(1,1)*vc(1)-ft(4,4)*vc(4)))+
& gc(1)*(pi(1) + pi(4))*(-2*fo(3)*(-(ft(2,2)*vc(2))
&+ cone*ft(3,3)*vc(3)) - 2*fo(4)*(ft(1,1)*vc(1) + ft(4,4)*vc(4)))
do i = 1,4
fvto(i) = -fvto(i)*d*gt
end do
return
end
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