<<AMBREv3.0.m

<<PlanarityTestv1.1.m

B7NP=PR[k1+k2+p1+p2+p3,0,n1] PR[k1+k2,0,n2] PR[k1,0,n3] PR[k1+p1,0,n4] PR[k1+p1+p2,0,n5] PR[k2+p3,0,n6] PR[k2,0,n7];

?PlanarityTest

PlanarityTest[{B7NP},{k1,k2},DrawGraph->True];

?invariants

invariants={p1^2->0,p2^2->0,p3^2->0,p1*p2->1/2*s,p1*p3->1/2*t,p2*p3->1/2*u};

?MBreprNP

MBreprNP[{1},{B7NP},{k1,k2}]

Fauto[0]

fupc = fupc //.{s r_. + t r_. + u r_. -> 0}

repr=MBreprNP[{1},{B7NP},{k1,k2}]

finrepr = First[repr] /.{n1->1,n2->1,n3->1,n4->1,n5->1,n6->1,n7->1}

(* after simple shift and renamings this answer can be converted to the original result by B.Tausk arXiv:hep-ph/9909506 Eqs.(8)-(10) *)

finrepr/.{z1->a}/.{a->-3-2 eps-z1-z2-z3-z4}/.{z3->(Subscript[ξ, 1]),z4->(Subscript[ξ, 2]),z1->α,z2->β}

Quit[]

<<AMBREv3.0.m

B7NP=PR[k1+k2+p1+p2+p3,0,n1] PR[k1+k2,0,n2] PR[k1,0,n3] PR[k1+p1,0,n4] PR[k1+p1+p2,0,n5] PR[k2+p3,0,n6] PR[k2,0,n7];

invariants={p1^2->0,p2^2->0,p3^2->0,p1*p2->1/2*s,p1*p3->1/2*t,p2*p3->1/2*u};

?SimplifyFpoly

SimplifyFpoly[{s+t+u->0}];

repr=MBreprNP[{1},{B7NP},{k1,k2}]

finrepr = First[repr] /.{n1->1,n2->1,n3->1,n4->1,n5->1,n6->1,n7->1}

<<MB.m

<<MBresolve.m

step1=MBresolve[finrepr,eps];

step2=MBexpand[step1,Exp[2*eps*EulerGamma],{eps,0,0}];
MBanalytic=MBmerge[step2]

MBintegrate[MBanalytic,{s->-1,t->-1,u->-1}]

(*analytical result for point s=t=u=-1,Eq.(21) from arXiv:hep-ph/9909506 (devided by  π^d Gamma[3+2eps]) *)

result=-395.26+113.63/eps-22.828/eps^2-3/eps^3+1.75/eps^4

(* coefficient to convert to AMBRE notation *)

coeff=-Series[Exp[2*eps*EulerGamma] Gamma[3+2 eps],{eps,0,4}]

fin=coeff*result

(* FIESTA crosscheck *)

FIESTAPath="/home/dubovyk/workspace/FIESTA3.0/";
Get[FIESTAPath<>"FIESTA3.m"];
UsingQLink=True;UsingC=True;

SDEvaluate[UF[{k1,k2},{-(k1+k2+p1+p2+p3)^2,-(k1+k2)^2,-k1^2,-(k1+p1)^2,-(k1+p1+p2)^2,-(k2+p3)^2,-k2^2},{p1^2->0,p2^2->0,p3^2->0,p1*p2->1/2*s,p1*p3->1/2*t,p2*p3->1/2*u,s->-1,t->-1,u->-1}],{1,1,1,1,1,1,1},0]

UFpoly=UF[{k1,k2},{-(k1+k2+p1+p2+p3)^2,-(k1+k2)^2,-k1^2,-(k1+p1)^2,-(k1+p1+p2)^2,-(k2+p3)^2,-k2^2},{p1^2->0,p2^2->0,p3^2->0,p1*p2->1/2*s,p1*p3->1/2*t,p2*p3->1/2*u}]//.{s r_. + t r_. + u r_. -> 0}/.{s->-1,t->-1,u->-1}

SDEvaluate[UFpoly,{1,1,1,1,1,1,1},0]