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subroutine ggggtx(va,vb,vc,vd,tc,gc,gt , vertex)
c
c This subroutine computes the portion of the amplitude of the five-point
c coupling of a tensor boson with 4 massless color octet gauge bosons
c (gluons) corresponding to the color structure f^{a,b,e} f{c,d,e}.
c
c To obtain the complete amplitude, this coupling must be called three
c times (once for each color structure) with the following permutations:
c call ggggtx(va,vb,vc,vd,tc,gc,gt , vertex1)
c call ggggtx(va,vc,vd,vb,tc,gc,gt , vertex2)
c call ggggtx(va,vd,vb,vc,tc,gc,gt , vertex3)
c corresponding to
c f^{a,b,e} f^{c,d,e}
c f^{a,c,e} f^{d,b,e}
c f^{a,d,e} f^{b,c,e}
c
c input:
c complex va(6) : boson with adjoint color index a va
c complex vb(6) : boson with adjoint color index b vb
c complex vc(6) : boson with adjoint color index c vc
c complex vd(6) : boson with adjoint color index d vd
c complex tc(18) : input tensor T
c real gc : coupling constant gs
c complex gt : coupling constant gtv=-1/Lambda
c
c output:
c complex vertex : amplitude gamma(va,vb,vc,vd,T)
c
c- by Q.Li - OCT. 2006
c
implicit none
double complex va(6), vb(6), vc(6), vd(6), tc(18), gt, vertex
double precision gc
double complex vab,vac,vad,vbc,vbd,vcd,ft(6,4),dvertx
double complex T00, T12, T13, T14, T23, T24, T34
double complex TV24,TV23,TV14,TV13
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)
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)
TV14 = rtwo*(ft(1,1)*va(1)*vd(1)+ft(2,2)*va(2)*vd(2)
&+ft(3,3)*va(3)*vd(3)+ft(4,4)*va(4)*vd(4))
TV13 = rtwo*(ft(1,1)*va(1)*vc(1)+ft(2,2)*va(2)*vc(2)
&+ft(3,3)*va(3)*vc(3)+ft(4,4)*va(4)*vc(4))
TV24 = rtwo*(ft(1,1)*vb(1)*vd(1)+ft(2,2)*vb(2)*vd(2)
&+ft(3,3)*vb(3)*vd(3)+ft(4,4)*vb(4)*vd(4))
TV23 = rtwo*(ft(1,1)*vb(1)*vc(1)+ft(2,2)*vb(2)*vc(2)
&+ft(3,3)*vb(3)*vc(3)+ft(4,4)*vb(4)*vc(4))
TV14 = TV14- T12*(va(1)*vd(2) + va(2)*vd(1))
& - T13*(va(1)*vd(3) + va(3)*vd(1))
& - T14*(va(1)*vd(4) + va(4)*vd(1))
& + T23*(va(2)*vd(3) + va(3)*vd(2))
& + T24*(va(2)*vd(4) + va(4)*vd(2))
& + T34*(va(3)*vd(4) + va(4)*vd(3))
TV13 = TV13 - T12*(va(1)*vc(2) + va(2)*vc(1))
& - T13*(va(1)*vc(3) + va(3)*vc(1))
& - T14*(va(1)*vc(4) + va(4)*vc(1))
& + T23*(va(2)*vc(3) + va(3)*vc(2))
& + T24*(va(2)*vc(4) + va(4)*vc(2))
& + T34*(va(3)*vc(4) + va(4)*vc(3))
TV24 = TV24 - T12*(vb(1)*vd(2) + vb(2)*vd(1))
& - T13*(vb(1)*vd(3) + vb(3)*vd(1))
& - T14*(vb(1)*vd(4) + vb(4)*vd(1))
& + T23*(vb(2)*vd(3) + vb(3)*vd(2))
& + T24*(vb(2)*vd(4) + vb(4)*vd(2))
& + T34*(vb(3)*vd(4) + vb(4)*vd(3))
TV23 = TV23 - T12*(vb(1)*vc(2) + vb(2)*vc(1))
& - T13*(vb(1)*vc(3) + vb(3)*vc(1))
& - T14*(vb(1)*vc(4) + vb(4)*vc(1))
& + T23*(vb(2)*vc(3) + vb(3)*vc(2))
& + T24*(vb(2)*vc(4) + vb(4)*vc(2))
& + T34*(vb(3)*vc(4) + vb(4)*vc(3))
vab = va(1)*vb(1)-va(2)*vb(2)-va(3)*vb(3)-va(4)*vb(4)
vac = va(1)*vc(1)-va(2)*vc(2)-va(3)*vc(3)-va(4)*vc(4)
vad = va(1)*vd(1)-va(2)*vd(2)-va(3)*vd(3)-va(4)*vd(4)
vbc = vb(1)*vc(1)-vb(2)*vc(2)-vb(3)*vc(3)-vb(4)*vc(4)
vbd = vb(1)*vd(1)-vb(2)*vd(2)-vb(3)*vd(3)-vb(4)*vd(4)
vcd = vc(1)*vd(1)-vc(2)*vd(2)-vc(3)*vd(3)-vc(4)*vd(4)
dvertx = -TV13*vbd-TV24*vac+TV23*vad+TV14*vbc
&+vbd*vac*T00-vad*vbc*T00
vertex = -dvertx * gc*gc*gt
return
end
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