<< MB.m

<< AMBRE.m

(*
    2 - 
        loop massive topology,   Fig  .5    
*)

B1 = 
        Fullintegral[
{1}, 
{PR[k1, m, 
                n1] PR[k1 + p1, 0, n2] PR[k1 + p1 + p2, m, n3] 
              PR[k1 - k2, 0, n4] PR[k2, m, n5] PR[k2 + p1 + p2, m, n6] 
              PR[k2 - p3, 0, n7]}, {k2, k1}];

invariants = {p1^2 -> m^2, p2^2 -> m^2, p3^2 -> m^2, 
          p4^2 -> m^2, p1*p2 -> 1/2*s - m^2, 
          p3*p4 -> 1/2 s - m^2, p1*p3 -> 1/2*t - m^2, 
          p2*p4 -> 1/2*t - m^2, p2*p3 -> 1/2*u - m^2, 
          p1*p4 -> 1/2*u - m^2};

IntPart[1]

SubLoop[integral]

Fauto[0]

fupc = fupc /. u -> 4 m^2 - s - t // Expand

SubLoop[integral]

IntPart[2]

SubLoop[integral];

Fauto[0]

fupc = fupc /. u -> 4 m^2 - s - t // Expand

repr = SubLoop[integral];

BarnesLemma[repr, 1]

fin = % /. {n1 -> 1, n2 -> 1, n3 -> 1, n4 -> 1, 
          n5 -> 1, n6 -> 1, n7 -> 1}

invariants = {p1^2 -> m^2, p2^2 -> m^2, p3^2 -> m^2, 
              p4^2 -> m^2, p1*p2 -> 1/2*s - m^2, 
              p3*p4 -> 1/2 s - m^2, p1*p3 -> 1/2*t - m^2, 
              p2*p4 -> 1/2*t - m^2, p2*p3 -> 1/2*u - m^2, 
              p1*p4 -> 1/2*u - m^2} /. u -> 4 m^2 - s - t // 
          Expand;

IntPart[1]

SubLoop[integral]

IntPart[2]

SubLoop[integral];

BarnesLemma[repr, 1]

fin = % /. {n1 -> 1, n2 -> 1, n3 -> 1, n4 -> 1, 
          n5 -> 1, n6 -> 1, n7 -> 1}

rules = MBoptimizedRules[fin, eps -> 0, {}, {eps}]

integrals = 
        MBcontinue[fin, eps -> 0, rules, 
          Verbose -> False];

ser = 
      MBexpand[{integrals}, 
        Exp[2*eps EulerGamma], 
{eps, 
          0, -1}]

MBintegrate[ser, {s -> -1/2, t -> -3, m -> 1}, 
        Verbose -> False] // AbsoluteTiming

MBintegrate[ser, {s -> -2, t -> -3, m -> 1}, 
        Verbose -> False] // AbsoluteTiming