Mathematica 7.0 for Linux x86 (64-bit)
Copyright 1988-2008 Wolfram Research, Inc.

In[1]:= MB 1.2
by Michal Czakon
improvements by Alexander Smirnov
more info in hep-ph/0511200
last modified 2 Jan 09

In[2]:= 
In[2]:= AMBRE by K.Kajda   ver: 2.0 
last modified 18 Jun 2010

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In[3]:= MBresolve 1.0
by Alexander Smirnov
more info in arXiv:0901.0386
last modified 4 Jan 09

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In[6]:= >>External momenta = p1[mu1] p2[mu2]
>>Starting LoopByLoop calculation
--iteration nr: 1 with momentum: k1
  Run ?INT to see description of below output 

 
>   {INT[{k1[mu1]}, 1, PR[k1, m, n1] PR[k1 - k2, 0, n4] PR[k1 + p1, 0, n2] 
 
>      PR[k1 + p1 + p2, m, n3], N/A]}
  F polynomial during this iteration 

 
     2                2
>   m  FX[X[1] + X[4]]  - PR[k2, m] X[1] X[2] - PR[k2 + p1, 0] X[2] X[3] - 
 
>    s X[1] X[4] - PR[k2 + p1 + p2, m] X[2] X[4]
--iteration nr: 2 with momentum: k2
  Run ?INT to see description of below output 

 
                                  2 - eps - z1 - z4   2 z1     z4
>   {INT[{k2[mu1], k2[mu2]}, ((-1)                  (m )   (-s)   Gamma[-z1] 
 
>        Gamma[-z2] Gamma[-z3] Gamma[n2 + z3] 
 
>        Gamma[3 - eps - n1 - n2 - n3 - z1 - z4] Gamma[-z4] 
 
>        Gamma[-2 + eps + n1 + n2 + n3 + n4 + z1 + z2 + z3 + z4] 
 
>        Gamma[2 - eps - n1 - n2 - n4 + z1 - z2 - z3 - z5] Gamma[-z5] 
 
>        Gamma[-2 z1 + z5] Gamma[n1 + z2 + z4 + z5]) / 
 
>      (Gamma[n1] Gamma[n2] Gamma[n3] Gamma[5 - 2 eps - n1 - n2 - n3 - n4] 
 
>        Gamma[n4] Gamma[-2 z1]), 
 
>     PR[k2, m, n5 - z2] PR[k2 + p1, 0, -z3] 
 
>      PR[k2 + p1 + p2, m, -2 + eps + n1 + n2 + n3 + n4 + n6 + z1 + z2 + z3 + 
 
>        z4] PR[k2 + p1 + p2 + p4, 0, n7], N/A], 
 
                           2 - eps - z1 - z4   2 z1     z4
>    INT[{k2[mu2]}, -(((-1)                  (m )   (-s)   Gamma[-z1] 
 
>          Gamma[-z2] Gamma[-z3] Gamma[1 + n2 + z3] 
 
>          Gamma[2 - eps - n1 - n2 - n3 - z1 - z4] Gamma[-z4] 
 
>          Gamma[-2 + eps + n1 + n2 + n3 + n4 + z1 + z2 + z3 + z4] 
 
>          Gamma[2 - eps - n1 - n2 - n4 + z1 - z2 - z3 - z5] Gamma[-z5] 
 
>          Gamma[-2 z1 + z5] Gamma[n1 + z2 + z4 + z5] p1[mu1]) / 
 
>        (Gamma[n1] Gamma[n2] Gamma[n3] Gamma[5 - 2 eps - n1 - n2 - n3 - n4] 
 
>          Gamma[n4] Gamma[-2 z1])), 
 
>     PR[k2, m, n5 - z2] PR[k2 + p1, 0, -z3] 
 
>      PR[k2 + p1 + p2, m, -2 + eps + n1 + n2 + n3 + n4 + n6 + z1 + z2 + z3 + 
 
>        z4] PR[k2 + p1 + p2 + p4, 0, n7], N/A], 
 
                           2 - eps - z1 - z4   2 z1     z4
>    INT[{k2[mu2]}, -(((-1)                  (m )   (-s)   Gamma[-z1] 
 
>          Gamma[-z2] Gamma[-z3] Gamma[n2 + z3] 
 
>          Gamma[2 - eps - n1 - n2 - n3 - z1 - z4] Gamma[-z4] 
 
>          Gamma[-2 + eps + n1 + n2 + n3 + n4 + z1 + z2 + z3 + z4] 
 
>          Gamma[3 - eps - n1 - n2 - n4 + z1 - z2 - z3 - z5] Gamma[-z5] 
 
>          Gamma[-2 z1 + z5] Gamma[n1 + z2 + z4 + z5] p1[mu1]) / 
 
>        (Gamma[n1] Gamma[n2] Gamma[n3] Gamma[5 - 2 eps - n1 - n2 - n3 - n4] 
 
>          Gamma[n4] Gamma[-2 z1])), 
 
>     PR[k2, m, n5 - z2] PR[k2 + p1, 0, -z3] 
 
>      PR[k2 + p1 + p2, m, -2 + eps + n1 + n2 + n3 + n4 + n6 + z1 + z2 + z3 + 
 
>        z4] PR[k2 + p1 + p2 + p4, 0, n7], N/A], 
 
                           2 - eps - z1 - z4   2 z1     z4
>    INT[{k2[mu2]}, -(((-1)                  (m )   (-s)   Gamma[-z1] 
 
>          Gamma[-z2] Gamma[-z3] Gamma[n2 + z3] 
 
>          Gamma[2 - eps - n1 - n2 - n3 - z1 - z4] Gamma[-z4] 
 
>          Gamma[-2 + eps + n1 + n2 + n3 + n4 + z1 + z2 + z3 + z4] 
 
>          Gamma[3 - eps - n1 - n2 - n4 + z1 - z2 - z3 - z5] Gamma[-z5] 
 
>          Gamma[-2 z1 + z5] Gamma[n1 + z2 + z4 + z5] p2[mu1]) / 
 
>        (Gamma[n1] Gamma[n2] Gamma[n3] Gamma[5 - 2 eps - n1 - n2 - n3 - n4] 
 
>          Gamma[n4] Gamma[-2 z1])), 
 
>     PR[k2, m, n5 - z2] PR[k2 + p1, 0, -z3] 
 
>      PR[k2 + p1 + p2, m, -2 + eps + n1 + n2 + n3 + n4 + n6 + z1 + z2 + z3 + 
 
>        z4] PR[k2 + p1 + p2 + p4, 0, n7], N/A]}
  F polynomial during this iteration 

 
     2                2
>   m  FX[X[1] + X[3]]  - s X[1] X[3] - t X[2] X[4]
>>Contracting and finalizing output
--contracting...
--finalizing output...
>>Checking Barnes 1-st lemma...

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In[10]:= Shifting contours...
Performing 0 lower-dimensional integrations with NIntegrateHigher-dimensional integrals
Preparing MBpart1eps0 (dim 6)
Preparing MBpart2eps0 (dim 6)
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Running MBpart1eps0
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Out[10]//InputForm= 
{3.1856087527833665 + 0.28816956184198367/eps^2 + 1.0383483331257786/eps, 
 {0.005591041239099738 + 0.000014019208708515693/eps^2 + 
   0.00012982806565473454/eps, 0}}

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945.77user 8.59system 11:11.33elapsed 142%CPU (0avgtext+0avgdata 0maxresident)k
0inputs+0outputs (0major+609347minor)pagefaults 0swaps
