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qlI4DNS41.f
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subroutine qlI4DNS41(Y,musq,Ival0)
implicit none
include 'qlconstants.f'
c-----Implementation of Eq.~(41) of
c----- %\cite{Denner:1991qq}
c----- %\cite{Denner:1991qq}
c----- \bibitem{Denner:1991qq}
c----- A.~Denner, U.~Nierste and R.~Scharf,
c----- %``A Compact expression for the scalar one loop four point function,''
c----- Nucl.\ Phys.\ B {\bf 367}, 637 (1991).
c----- %%CITATION = NUPHA,B367,637;%%
double complex Ival0,discr,wlog(2),cln,z(2),k(4,4),lnsum,
. qlLi2omprod,a,b,c,d,bsq,fourac
double precision musq,Y(4,4),iep
integer i,j
do i=1,4
do j=1,4
k(i,j)=dcmplx(2d0*Y(i,j)/musq)
enddo
enddo
a=k(2,4)*k(3,4)
b=k(1,3)*k(2,4)+k(1,2)*k(3,4)-k(1,4)*k(2,3)
c=k(1,2)*k(1,3)
d=k(2,3)
bsq=b**2
fourac=4d0*a*c
discr=sqrt(bsq-fourac)
if (abs(discr) .lt. 1d-10*max(dble(bsq),dble(fourac))) then
z(1)=0.5d0*b/a
wlog(1)=dcmplx(dreal(cln(z(1),+1d0)))
Ival0=
. +k(3,4)*(cln(k(3,4),-1d0)+wlog(1)-cln(k(1,3),-1d0))
. /(k(3,4)*z(1)-k(1,3))
. +k(2,4)*(cln(k(2,4),-1d0)+wlog(1)-cln(k(1,2),-1d0))
. /(k(2,4)*z(1)-k(1,2))
. -(wlog(1)
. +cln(k(2,3),-1d0)+cln(k(1,4),-1d0)
. -cln(k(1,3),-1d0)-cln(k(1,2),-1d0))/z(1)
Ival0=Ival0/(musq**2*a)
return
else
C----wlogi=log(-xi),zi=-xi
z(1)=0.5d0*(b-discr)/a
z(2)=0.5d0*(b+discr)/a
iep=sign(1d0,dreal(d))
C-----z(1) comes with + i*ep*d
C-----z(2) comes with - i*ep*d
wlog(1)=cln(z(1),+iep)
wlog(2)=cln(z(2),-iep)
lnsum=+cln(k(1,2),-1d0)+cln(k(1,3),-1d0)
. -cln(k(1,4),-1d0)-cln(k(2,3),-1d0)
Ival0=czip
do j=1,2
iep=-dfloat(2*j-3)*iep
Ival0=Ival0+dfloat(2*j-3)*(
. -0.5d0*wlog(j)**2+wlog(j)*lnsum
. -qlLi2omprod(k(3,4),k(1,3),z(j),iep)
. -qlLi2omprod(k(2,4),k(1,2),z(j),iep))
enddo
Ival0=Ival0/(musq**2*discr)
endif
return
end

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