input_case nil$ % gg -> gg % -------- load_package xcolor$ sudim Nc; Ng:=Nc^2-1$ C1:=g3(a1,a2,b1)*g3(a3,a4,b1)*g3(a1,a2,b2)*g3(a3,a4,b2)/Ng^2; C2:=g3(a3,a1,b1)*g3(a2,a4,b1)*g3(a1,a2,b2)*g3(a3,a4,b2)/Ng^2; operator V,D; for all p1 let D(p1)=1/p1.p1; % propagator for all m1,p1 let V(m1,p1)=i*p1.m1; % ghost vertex for all m1,m2,m3,m4 let V(m1,m2,m3,m4)= % part of 4g vertex i*(m1.m3*m2.m4-m1.m4*m2.m3); % with one colour structure for all m1,m2,m3,p1,p2 let V(m1,m2,m3,p1,p2)= % 3g vertex i*((p2-p1).m3*m1.m2-(p1+2*p2).m1*m2.m3+(2*p1+p2).m2*m3.m1); mass p1=0,p2=0,p3=0,p4=0; mshell p1,p2,p3,p4; let p1.p2=s/2,p3.p4=s/2,p1.p3=t/2,p2.p4=t/2,p1.p4=u/2,p2.p3=u/2; vector p5,p6; p5:=p1+p2$ p6:=p5$ u:=-s-t$ index m1,m2,m3,m4,m5,m6; A0:=(-i*V(m1,m2,m5,p1,p2)*V(m3,m4,m5,p3,p4)*D(p5)+V(m1,m2,m3,m4))* (i*V(m1,m2,m6,-p1,-p2)*V(m3,m4,m6,-p3,-p4)*D(p6)-V(m1,m2,m3,m4)); A1:=V(m5,-p2)*V(m3,m4,m5,p3,p4)*V(m6,p1)*V(m3,m4,m6,-p3,-p4) *D(p5)^2$ A1:=2*(A1+sub(t=u,A1)); A2:=-V(m2,p5)*V(m3,-p4)*V(m2,p1)*V(m3,p6)*D(p5)^2$ A2:=4*(A2+sub(t=u,A2)); A3:=V(m5,-p1)*V(m5,-p4)*V(m6,p2)*V(m6,p3)*D(p5)^2$ A3:=2*(A3+sub(t=u,A3)); A0:=A0+A1+A2+A3; clear A1,A2,A3; on gcd; A0:=A0+sub(s=t,t=s,A0)+sub(s=u,A0); off gcd; p5:=p1+p3$ B0:=(-i*V(m3,m1,m5,p3,p1)*V(m2,m4,m5,p2,p4)*D(p5)+V(m3,m1,m2,m4))* (i*V(m1,m2,m6,-p1,-p2)*V(m3,m4,m6,-p3,-p4)*D(p6)-V(m1,m2,m3,m4)); B1:=-V(m3,p5)*V(m4,-p2)*D(p5)*V(m6,p1)*V(m3,m4,m6,-p3,-p4)*D(p6)$ B1:=4*(B1+sub(s=t,t=s,B1)); B2:=V(m2,-p4)*V(m3,p5)*D(p5)*V(m2,p1)*V(m3,p6)*D(p6)$ B2:=4*(B2+sub(s=t,t=s,B2)); B3:=V(m5,-p1)*V(m5,-p4)*D(p5)*V(m6,p2)*V(m6,p3)*D(p6)$ B3:=B3+sub(s=t,t=s,B3); B0:=B0+B1+B2+B3; clear B1,B2,B3; on gcd; B0:=2*(B0+sub(s=u,B0)+sub(t=u,B0)); A0:=(A0-B0/2)*(4*pi)^2/4/(64*pi*s^2/4)$ clear B0; on factor; A0; off factor; end;