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

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

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In[7]:= >>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, 0, n1] PR[k1 - k2, 0, n4] PR[k1 + p1, 0, n2] 
 
>      PR[k1 + p1 + p2, 0, n3], N/A]}
  F polynomial during this iteration 

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

 
                                  2 - eps - z3     z3
>   {INT[{k2[mu1], k2[mu2]}, ((-1)             (-s)   Gamma[-z1] 
 
>        Gamma[2 - eps - n1 - n2 - n4 - z1 - z2] Gamma[-z2] Gamma[n2 + z2] 
 
>        Gamma[3 - eps - n1 - n2 - n3 - z3] Gamma[-z3] Gamma[n1 + z1 + z3] 
 
>        Gamma[-2 + eps + n1 + n2 + n3 + n4 + z1 + z2 + z3]) / 
 
>      (Gamma[n1] Gamma[n2] Gamma[n3] Gamma[5 - 2 eps - n1 - n2 - n3 - n4] 
 
>        Gamma[n4]), PR[k2, 0, n5 - z1] PR[k2 + p1, 0, -z2] 
 
>      PR[k2 + p1 + p2, 0, -2 + eps + n1 + n2 + n3 + n4 + n6 + z1 + z2 + z3] 
 
>      PR[k2 + p1 + p2 + p4, 0, n7], N/A], 
 
                           2 - eps - z3     z3
>    INT[{k2[mu2]}, -(((-1)             (-s)   Gamma[-z1] 
 
>          Gamma[2 - eps - n1 - n2 - n4 - z1 - z2] Gamma[-z2] 
 
>          Gamma[1 + n2 + z2] Gamma[2 - eps - n1 - n2 - n3 - z3] Gamma[-z3] 
 
>          Gamma[n1 + z1 + z3] Gamma[-2 + eps + n1 + n2 + n3 + n4 + z1 + z2 + 
 
>            z3] p1[mu1]) / 
 
>        (Gamma[n1] Gamma[n2] Gamma[n3] Gamma[5 - 2 eps - n1 - n2 - n3 - n4] 
 
>          Gamma[n4])), PR[k2, 0, n5 - z1] PR[k2 + p1, 0, -z2] 
 
>      PR[k2 + p1 + p2, 0, -2 + eps + n1 + n2 + n3 + n4 + n6 + z1 + z2 + z3] 
 
>      PR[k2 + p1 + p2 + p4, 0, n7], N/A], 
 
                           2 - eps - z3     z3
>    INT[{k2[mu2]}, -(((-1)             (-s)   Gamma[-z1] 
 
>          Gamma[3 - eps - n1 - n2 - n4 - z1 - z2] Gamma[-z2] Gamma[n2 + z2] 
 
>          Gamma[2 - eps - n1 - n2 - n3 - z3] Gamma[-z3] Gamma[n1 + z1 + z3] 
 
>          Gamma[-2 + eps + n1 + n2 + n3 + n4 + z1 + z2 + z3] p1[mu1]) / 
 
>        (Gamma[n1] Gamma[n2] Gamma[n3] Gamma[5 - 2 eps - n1 - n2 - n3 - n4] 
 
>          Gamma[n4])), PR[k2, 0, n5 - z1] PR[k2 + p1, 0, -z2] 
 
>      PR[k2 + p1 + p2, 0, -2 + eps + n1 + n2 + n3 + n4 + n6 + z1 + z2 + z3] 
 
>      PR[k2 + p1 + p2 + p4, 0, n7], N/A], 
 
                           2 - eps - z3     z3
>    INT[{k2[mu2]}, -(((-1)             (-s)   Gamma[-z1] 
 
>          Gamma[3 - eps - n1 - n2 - n4 - z1 - z2] Gamma[-z2] Gamma[n2 + z2] 
 
>          Gamma[2 - eps - n1 - n2 - n3 - z3] Gamma[-z3] Gamma[n1 + z1 + z3] 
 
>          Gamma[-2 + eps + n1 + n2 + n3 + n4 + z1 + z2 + z3] p2[mu1]) / 
 
>        (Gamma[n1] Gamma[n2] Gamma[n3] Gamma[5 - 2 eps - n1 - n2 - n3 - n4] 
 
>          Gamma[n4])), PR[k2, 0, n5 - z1] PR[k2 + p1, 0, -z2] 
 
>      PR[k2 + p1 + p2, 0, -2 + eps + n1 + n2 + n3 + n4 + n6 + z1 + z2 + z3] 
 
>      PR[k2 + p1 + p2 + p4, 0, n7], N/A]}
  F polynomial during this iteration -(s X[1] X[3]) - t X[2] X[4]

>>Contracting and finalizing output
--contracting...
--finalizing output...
>>Checking Barnes 1-st lemma...

In[8]:= 
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In[8]:= CREATING RESIDUES LIST..........0.5646 seconds
EVALUATING RESIDUES..........0.0125 seconds
CREATING RESIDUES LIST..........0.7519 seconds
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CREATING RESIDUES LIST0.2655 seconds
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CREATING RESIDUES LIST0.2655 seconds
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CREATING RESIDUES LIST..........0.5806 seconds
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CREATING RESIDUES LIST..........0.7777 seconds
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CREATING RESIDUES LIST0.1977 seconds
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CREATING RESIDUES LIST..........1.2346 seconds
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CREATING RESIDUES LIST..........1.2335 seconds
EVALUATING RESIDUES..........0.0694 seconds

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In[11]:= Shifting contours...
Performing 23 lower-dimensional integrations with NIntegrate...1...2...3...4...5...6...7...8...9...10...11...12...13...14...15...16...17...18...19...20...21...22...23Higher-dimensional integrals
Preparing MBpart1eps0 (dim 4)
Preparing MBpart2eps0 (dim 4)
Preparing MBpart3eps0 (dim 4)
Preparing MBpart4eps0 (dim 4)
Preparing MBpart5eps0 (dim 4)
Preparing MBpart6eps0 (dim 4)
Preparing MBpart7eps0 (dim 4)
Preparing MBpart8eps0 (dim 4)
Preparing MBpart9eps0 (dim 4)
Preparing MBpart10eps0 (dim 3)
Preparing MBpart11eps0 (dim 3)
Preparing MBpart12eps0 (dim 3)
Preparing MBpart13eps0 (dim 3)
Preparing MBpart14eps0 (dim 3)
Preparing MBpart15eps0 (dim 3)
Preparing MBpart16eps0 (dim 3)
Preparing MBpart17eps0 (dim 3)
Preparing MBpart18eps0 (dim 3)
Preparing MBpart19eps0 (dim 2)
Preparing MBpart20eps0 (dim 2)
Preparing MBpart21eps0 (dim 2)
Preparing MBpart22eps0 (dim 2)
Preparing MBpart23eps0 (dim 2)
Preparing MBpart24eps0 (dim 2)
Preparing MBpart25eps0 (dim 2)
Preparing MBpart26eps0 (dim 2)
Preparing MBpart27eps0 (dim 2)
Preparing MBpart28eps0 (dim 2)
Preparing MBpart29eps0 (dim 2)
Preparing MBpart30eps0 (dim 2)
Preparing MBpart31eps0 (dim 2)
Preparing MBpart32eps0 (dim 2)
Preparing MBpart33eps0 (dim 2)
Preparing MBpart34eps-1 (dim 2)
Preparing MBpart35eps-1 (dim 2)
Preparing MBpart36eps-1 (dim 2)
Preparing MBpart37eps-1 (dim 2)
Preparing MBpart38eps-1 (dim 2)
Preparing MBpart39eps-1 (dim 2)
Preparing MBpart40eps-1 (dim 2)
Preparing MBpart41eps-1 (dim 2)
Preparing MBpart42eps-1 (dim 2)
Preparing MBpart43eps-1 (dim 2)
Preparing MBpart44eps-1 (dim 2)
Preparing MBpart45eps-1 (dim 2)
Preparing MBpart46eps-1 (dim 2)
Preparing MBpart47eps-1 (dim 2)
Running MBpart1eps0
Running MBpart2eps0
Running MBpart3eps0
Running MBpart4eps0
Running MBpart5eps0
Running MBpart6eps0
Running MBpart7eps0
Running MBpart8eps0
Running MBpart9eps0
Running MBpart10eps0
Running MBpart11eps0
Running MBpart12eps0
Running MBpart13eps0
Running MBpart14eps0
Running MBpart15eps0
Running MBpart16eps0
Running MBpart17eps0
Running MBpart18eps0
Running MBpart19eps0
Running MBpart20eps0
Running MBpart21eps0
Running MBpart22eps0
Running MBpart23eps0
Running MBpart24eps0
Running MBpart25eps0
Running MBpart26eps0
Running MBpart27eps0
Running MBpart28eps0
Running MBpart29eps0
Running MBpart30eps0
Running MBpart31eps0
Running MBpart32eps0
Running MBpart33eps0
Running MBpart34eps-1
Running MBpart35eps-1
Running MBpart36eps-1
Running MBpart37eps-1
Running MBpart38eps-1
Running MBpart39eps-1
Running MBpart40eps-1
Running MBpart41eps-1
Running MBpart42eps-1
Running MBpart43eps-1
Running MBpart44eps-1
Running MBpart45eps-1
Running MBpart46eps-1
Running MBpart47eps-1

Out[11]//InputForm= 
{0.6573389169742949 - 0.021785714285714287/eps^4 + 
  0.10497441926325224/eps^3 + 0.018095078966746166/eps^2 + 
  0.1392053443216159/eps, {0.0005806083264536956 + 
   0.00007973088710473049/eps, 0}}

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368.54user 5.66system 3:30.06elapsed 178%CPU (0avgtext+0avgdata 0maxresident)k
0inputs+0outputs (0major+534962minor)pagefaults 0swaps
