<< 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} 

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

Fauto[0]

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

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

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

(* 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[\[Xi], 1], z4 -> Subscript[\[Xi], 2], z1 -> \[Alpha], z2 -> \[Beta]}  // InputForm


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  \[Pi]^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] // InputForm


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] // InputForm

