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subroutine vvvkxx(wm,wp,tc,g, vertex)
c
c This subroutine computes an amplitude of the three-point coupling of
c two gauge bosons and a Kaluza-Klein tensor boson.
c
c input:
c complex wm(6) : vector flow-in V
c complex wp(6) : vector flow-out V~
c complex tc(6,4) : tensor KK mode T
c complex g(1) : coupling constant -kappa/2
c real g(2) : V boson mass m_V
c
c output:
c complex vertex : amplitude gamma(wm,wp,tc)
c
implicit none
double complex wm(18), wp(18), tc(18), vertex,g(2)
double precision vmass
double complex T12, T13, T14, T23, T24, T34
double complex V1V2, k1V2, k2V1
double complex Tkk, TVV, Tk1V2, Tk2V1, dum
double precision pwm(4), pwp(4), F
integer i, j
double complex cZero
double precision rZero, rTwo
parameter( rZero = 0.0d0, rTwo = 2.0d0 )
parameter( cZero = ( 0.0d0, 0.0d0 ) )
c
vmass = dreal(g(2))
pwm(1) = dreal(wm(5))
pwm(2) = dreal(wm(6))
pwm(3) = dimag(wm(6))
pwm(4) = dimag(wm(5))
pwp(1) = dreal(wp(5))
pwp(2) = dreal(wp(6))
pwp(3) = dimag(wp(6))
pwp(4) = dimag(wp(5))
T12 = tc( 2) + tc( 5)
T13 = tc( 3) + tc( 9)
T14 = tc( 4) + tc(13)
T23 = tc( 7) + tc(10)
T24 = tc( 8) + tc(14)
T34 = tc(12) + tc(15)
V1V2 = wm(1)*wp(1) - wm(2)*wp(2) - wm(3)*wp(3) - wm(4)*wp(4)
k1V2 = pwm(1)*wp(1) - pwm(2)*wp(2) - pwm(3)*wp(3) - pwm(4)*wp(4)
k2V1 = pwp(1)*wm(1) - pwp(2)*wm(2) - pwp(3)*wm(3) - pwp(4)*wm(4)
F = pwm(1)*pwp(1) - pwm(2)*pwp(2) - pwm(3)*pwp(3) - pwm(4)*pwp(4)
if ( vmass.ne.rZero ) then
F = F + vmass**2
end if
Tkk = cZero
TVV = cZero
Tk1V2 = cZero
Tk2V1 = cZero
do i = 1,4
dum = tc(i+4*(i-1))*pwm(i)
Tkk = Tkk + dum*pwp(i)
Tk1V2 = Tk1V2 + dum*wp(i)
dum = tc(i+4*(i-1))*wm(i)
TVV = TVV + dum*wp(i)
Tk2V1 = Tk2V1 + dum*pwp(i)
end do
Tkk = rTwo*Tkk
TVV = rTwo*TVV
Tk1V2 = rTwo*Tk1V2
Tk2V1 = rTwo*Tk2V1
Tkk = Tkk - T12*(pwm(1)*pwp(2) + pwm(2)*pwp(1))
& - T13*(pwm(1)*pwp(3) + pwm(3)*pwp(1))
& - T14*(pwm(1)*pwp(4) + pwm(4)*pwp(1))
& + T23*(pwm(2)*pwp(3) + pwm(3)*pwp(2))
& + T24*(pwm(2)*pwp(4) + pwm(4)*pwp(2))
& + T34*(pwm(3)*pwp(4) + pwm(4)*pwp(3))
Tk1V2 = Tk1V2 - T12*(pwm(1)*wp(2) + pwm(2)*wp(1))
& - T13*(pwm(1)*wp(3) + pwm(3)*wp(1))
& - T14*(pwm(1)*wp(4) + pwm(4)*wp(1))
& + T23*(pwm(2)*wp(3) + pwm(3)*wp(2))
& + T24*(pwm(2)*wp(4) + pwm(4)*wp(2))
& + T34*(pwm(3)*wp(4) + pwm(4)*wp(3))
TVV = TVV - T12*(wm(1)*wp(2) + wm(2)*wp(1))
& - T13*(wm(1)*wp(3) + wm(3)*wp(1))
& - T14*(wm(1)*wp(4) + wm(4)*wp(1))
& + T23*(wm(2)*wp(3) + wm(3)*wp(2))
& + T24*(wm(2)*wp(4) + wm(4)*wp(2))
& + T34*(wm(3)*wp(4) + wm(4)*wp(3))
Tk2V1 = Tk2V1 - T12*(wm(1)*pwp(2) + wm(2)*pwp(1))
& - T13*(wm(1)*pwp(3) + wm(3)*pwp(1))
& - T14*(wm(1)*pwp(4) + wm(4)*pwp(1))
& + T23*(wm(2)*pwp(3) + wm(3)*pwp(2))
& + T24*(wm(2)*pwp(4) + wm(4)*pwp(2))
& + T34*(wm(3)*pwp(4) + wm(4)*pwp(3))
vertex = (tc(1)-tc(6)-tc(11)-tc(16))*( k1V2*k2V1 - V1V2*F )
& + F*TVV + V1V2*Tkk - k2V1*Tk1V2 - k1V2*Tk2V1
C vertex = F*TVV + V1V2*Tkk - k2V1*Tk1V2 - k1V2*Tk2V1
vertex = vertex * g(1)
c
return
end
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