<< MB.m

<< AMBRE.m

int = 
        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 + p1 + p2 + p4, 0, n7] PR[k1 + p1 + p2 + p4, 
                0, -n8]}, {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} /. 
          u -> 4 m^2 - s - t;

IntPart[1]

SubLoop[integral]

IntPart[2]

repr = SubLoop[integral];

rep1 = BarnesLemma[repr, 1]

fin = 
      rep1  /.  {n1 -> 1, n2 -> 1, n3 -> 1, n4 -> 1, 
          n5 -> 1, n6 -> 1, n7 -> 1, n7 -> 1, 
          n8 -> 1}

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

fin = 
      rep1  /.  {n1 -> 1, n2 -> 1, n3 -> 1, n4 -> 1, 
          n5 -> 1, n6 -> 1, n7 -> 1, n7 -> 1, 
          n8 -> 1 + eta}

rules = 
      MBoptimizedRules[fin, 
        eta -> 0, {z1 > -1/2, z2 > z1}, {eps, eta}]

Step1cont = MBcontinue[fin, eta -> 0, rules];

after = MBexpand[Step1cont, 1, {eta, 0, 0}]

integrals = 
      after /. MBint[integrand_, rules_] :> 
          MBcontinue[integrand, eps -> 0, rules]

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

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

\(\(\( (*\ 
      sectors : 

{{0.3203772836085565`\/ep\^2 - 
              0.26661944018488715`\/ep, \(-\(0.00030840055074709047`\/ep\^2\)\) - 0.0030136395958849436`\/ep, \(-\(0.001357853530901787`\/ep\^2\)\) + 
              0.07127306807466487`\/ep}}
*) \)\(
\)\)\)

B7l4m1Nms = ((ms^2*(24*ep*(-z3 + 6*ep*z4) + 
                  29*ep^2*Log[ms]^4 + 
                  4*ep*Log[ms]^3*(13 - 12*ep*Log[x]) - 
                  12*Log[ms]^2*(-3 + 34*ep^2*z2 + 4*ep*Log[x]) + 
                  16*ep*Log[
                      ms]*(-3*z2 + 24*ep*z2*Log[x] + ep*Log[x]^3 - 
                        3*ep*(6*z2 + Log[x]^2)*Log[1 + x]) + 
                  24*ep^2*
                    Log[ms]*(7*z3 - 4*Log[x]*PolyLog[2, -x] + 
                        4*PolyLog[3, -x])))/(24*
              ep^2))

N[% /. z2 -> Zeta[2] /. z3 -> Zeta[3] /. 
                  z4 -> Zeta[4] /. ms -> -1/s /. 
              x -> t/s /. s -> -100 /. t -> -3] // 
      Expand

MBintegrate[
      ser, {s -> -100, t -> -3, m -> 1}]