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 21 . 06 . 2010 at 23:05 last modified 18 Jun 2010 last executed on In[3]:= In[3]:= MBnum v.0.1, last modified: 18.06.09 In[4]:= In[4]:= Barnes Routines, v 1.1.1 of July 23, 2009 In[5]:= In[5]:= In[6]:= In[6]:= In[7]:= In[8]:= In[8]:= >>External momenta = p1[mu1] p1[mu2] p1[mu3] >>Starting LoopByLoop calculation --iteration nr: 1 with momentum: k2 Run ?INT to see description of below output > {INT[{k2[mu3]}, 1, PR[k2, 0, n2] PR[-k1 + k2, 0, n3] PR[k2 + p1, 0, n5], > N/A]} F polynomial during this iteration > -(PR[k1, 0] X[1] X[2]) - s X[1] X[3] - PR[k1 + p1, 0] X[2] X[3] --iteration nr: 2 with momentum: k1 Run ?INT to see description of below output > {INT[{k1[mu1], k1[mu2], k1[mu3]}, 2 - eps - z2 z2 > ((-1) (-s) Gamma[2 - eps - n2 - n3 - z1] Gamma[-z1] > Gamma[3 - eps - n2 - n5 - z2] Gamma[-z2] Gamma[n2 + z1 + z2] > Gamma[-2 + eps + n2 + n3 + n5 + z1 + z2]) / > (Gamma[n2] Gamma[n3] Gamma[5 - 2 eps - n2 - n3 - n5] Gamma[n5]), > PR[k1, 0, n1 - z1] PR[k1 + p1, 0, > -2 + eps + n2 + n3 + n4 + n5 + z1 + z2], N/A], 2 - eps - z2 z2 > INT[{k1[mu1], k1[mu2]}, -(((-1) (-s) > Gamma[3 - eps - n2 - n3 - z1] Gamma[-z1] > Gamma[2 - eps - n2 - n5 - z2] Gamma[-z2] Gamma[n2 + z1 + z2] > Gamma[-2 + eps + n2 + n3 + n5 + z1 + z2] p1[mu3]) / > (Gamma[n2] Gamma[n3] Gamma[5 - 2 eps - n2 - n3 - n5] Gamma[n5])), > PR[k1, 0, n1 - z1] PR[k1 + p1, 0, > -2 + eps + n2 + n3 + n4 + n5 + z1 + z2], N/A]} F polynomial during this iteration -(s X[1] X[2]) >>Contracting and finalizing output --contracting... --finalizing output... >>Checking Barnes 1-st lemma... >> Barnes 1st Lemma will be checked for: {z2, z1} << 2 Starting with dim= > representation... 1. Checking z2 2. Checking z1>> Representation after 1st Barnes Lemma: << Could not apply Barnes-Lemma >> Barnes 1st Lemma will be checked for: {z2, z1} << 2 Starting with dim= > representation... 1. Checking z2 2. Checking z1>> Representation after 1st Barnes Lemma: << Could not apply Barnes-Lemma >> Barnes 1st Lemma will be checked for: {z2, z1} << 2 Starting with dim= > representation... 1. Checking z2 2. Checking z1>> Representation after 1st Barnes Lemma: << Could not apply Barnes-Lemma >> Barnes 1st Lemma will be checked for: {z2, z1} << 2 Starting with dim= > representation... 1. Checking z2 2. Checking z1>> Representation after 1st Barnes Lemma: << Could not apply Barnes-Lemma >> Barnes 1st Lemma will be checked for: {z2, z1} << 2 Starting with dim= > representation... 1. Checking z2 2. Checking z1>> Representation after 1st Barnes Lemma: << Could not apply Barnes-Lemma >> Barnes 1st Lemma will be checked for: {z2, z1} << 2 Starting with dim= > representation... 1. Checking z2 2. Checking z1>> Representation after 1st Barnes Lemma: << Could not apply Barnes-Lemma In[9]:= In[9]:= In[10]:= In[10]:= repr={-(((-1)^(n1 + n2 + n3 + n4 + n5)*(-s)^(-2*eps - n1 - n2 - n3 - n4 - n5)*s^7*Gamma[2 - eps - n2 - n3 - z1]*Gamma[-z1]*Gamma[5 - eps - n1 + z1]*Gamma[3 - eps - n2 - n5 - z2]*Gamma[4 - 2*eps - n2 - n3 - n4 - n5 - z1 - z2]*Gamma[-z2]*Gamma[-4 + 2*eps + n1 + n2 + n3 + n4 + n5 + z2]*Gamma[n2 + z1 + z2]*Gamma[-2 + eps + n2 + n3 + n5 + z1 + z2])/(Gamma[n2]*Gamma[n3]*Gamma[5 - 2*eps - n2 - n3 - n5]*Gamma[n5]*Gamma[n1 - z1]*Gamma[9 - 3*eps - n1 - n2 - n3 - n4 - n5 - z2]*Gamma[-2 + eps + n2 + n3 + n4 + n5 + z1 + z2])), -((-1)^(n1 + n2 + n3 + n4 + n5)*(-s)^(-2*eps - n1 - n2 - n3 - n4 - n5)*s^7*Gamma[2 - eps - n2 - n3 - z1]*Gamma[-z1]*Gamma[4 - eps - n1 + z1]*Gamma[3 - eps - n2 - n5 - z2]*Gamma[5 - 2*eps - n2 - n3 - n4 - n5 - z1 - z2]*Gamma[-z2]*Gamma[-5 + 2*eps + n1 + n2 + n3 + n4 + n5 + z2]*Gamma[n2 + z1 + z2]*Gamma[-2 + eps + n2 + n3 + n5 + z1 + z2])/(2*Gamma[n2]*Gamma[n3]*Gamma[5 - 2*eps - n2 - n3 - n5]*Gamma[n5]*Gamma[n1 - z1]*Gamma[9 - 3*eps - n1 - n2 - n3 - n4 - n5 - z2]*Gamma[-2 + eps + n2 + n3 + n4 + n5 + z1 + z2]), -((-1)^(n1 + n2 + n3 + n4 + n5)*(-s)^(-2*eps - n1 - n2 - n3 - n4 - n5)*s^7*Gamma[2 - eps - n2 - n3 - z1]*Gamma[-z1]*Gamma[4 - eps - n1 + z1]*Gamma[3 - eps - n2 - n5 - z2]*Gamma[5 - 2*eps - n2 - n3 - n4 - n5 - z1 - z2]*Gamma[-z2]*Gamma[-5 + 2*eps + n1 + n2 + n3 + n4 + n5 + z2]*Gamma[n2 + z1 + z2]*Gamma[-2 + eps + n2 + n3 + n5 + z1 + z2])/(2*Gamma[n2]*Gamma[n3]*Gamma[5 - 2*eps - n2 - n3 - n5]*Gamma[n5]*Gamma[n1 - z1]*Gamma[9 - 3*eps - n1 - n2 - n3 - n4 - n5 - z2]*Gamma[-2 + eps + n2 + n3 + n4 + n5 + z1 + z2]), -((-1)^(n1 + n2 + n3 + n4 + n5)*(-s)^(-2*eps - n1 - n2 - n3 - n4 - n5)*s^7*Gamma[2 - eps - n2 - n3 - z1]*Gamma[-z1]*Gamma[4 - eps - n1 + z1]*Gamma[3 - eps - n2 - n5 - z2]*Gamma[5 - 2*eps - n2 - n3 - n4 - n5 - z1 - z2]*Gamma[-z2]*Gamma[-5 + 2*eps + n1 + n2 + n3 + n4 + n5 + z2]*Gamma[n2 + z1 + z2]*Gamma[-2 + eps + n2 + n3 + n5 + z1 + z2])/(2*Gamma[n2]*Gamma[n3]*Gamma[5 - 2*eps - n2 - n3 - n5]*Gamma[n5]*Gamma[n1 - z1]*Gamma[9 - 3*eps - n1 - n2 - n3 - n4 - n5 - z2]*Gamma[-2 + eps + n2 + n3 + n4 + n5 + z1 + z2]), -(((-1)^(n1 + n2 + n3 + n4 + n5)*(-s)^(-2*eps - n1 - n2 - n3 - n4 - n5)*s^7*Gamma[3 - eps - n2 - n3 - z1]*Gamma[-z1]*Gamma[4 - eps - n1 + z1]*Gamma[2 - eps - n2 - n5 - z2]*Gamma[4 - 2*eps - n2 - n3 - n4 - n5 - z1 - z2]*Gamma[-z2]*Gamma[-4 + 2*eps + n1 + n2 + n3 + n4 + n5 + z2]*Gamma[n2 + z1 + z2]*Gamma[-2 + eps + n2 + n3 + n5 + z1 + z2])/(Gamma[n2]*Gamma[n3]*Gamma[5 - 2*eps - n2 - n3 - n5]*Gamma[n5]*Gamma[n1 - z1]*Gamma[8 - 3*eps - n1 - n2 - n3 - n4 - n5 - z2]*Gamma[-2 + eps + n2 + n3 + n4 + n5 + z1 + z2])), -((-1)^(n1 + n2 + n3 + n4 + n5)*(-s)^(-2*eps - n1 - n2 - n3 - n4 - n5)*s^7*Gamma[3 - eps - n2 - n3 - z1]*Gamma[-z1]*Gamma[3 - eps - n1 + z1]*Gamma[2 - eps - n2 - n5 - z2]*Gamma[5 - 2*eps - n2 - n3 - n4 - n5 - z1 - z2]*Gamma[-z2]*Gamma[-5 + 2*eps + n1 + n2 + n3 + n4 + n5 + z2]*Gamma[n2 + z1 + z2]*Gamma[-2 + eps + n2 + n3 + n5 + z1 + z2])/(2*Gamma[n2]*Gamma[n3]*Gamma[5 - 2*eps - n2 - n3 - n5]*Gamma[n5]*Gamma[n1 - z1]*Gamma[8 - 3*eps - n1 - n2 - n3 - n4 - n5 - z2]*Gamma[-2 + eps + n2 + n3 + n4 + n5 + z1 + z2])} Length=6 MBrules::norules: no rules could be found to regulate this integral MBrules::norules: no rules could be found to regulate this integral MBrules::norules: no rules could be found to regulate this integral General::stop: Further output of MBrules::norules will be suppressed during this calculation. ETA's will be aplied on positions: {} 1. Calculating 'no eta' parts... Running MBcontinue... Running MBexpand... 2. Calculating 'eta' parts... No 'eta' parts found!!! In[11]:= In[11]:= before lemmas In[12]:= In[12]:= Shifting contours... Performing 7 lower-dimensional integrations with NIntegrate...1...2...3...4...5...6...7Higher-dimensional integrals Preparing MBpart1eps1 (dim 2) Preparing MBpart2eps1 (dim 2) Preparing MBpart3eps1 (dim 2) Preparing MBpart4eps1 (dim 2) Preparing MBpart5eps0 (dim 2) Preparing MBpart6eps0 (dim 2) Preparing MBpart7eps0 (dim 2) Preparing MBpart8eps0 (dim 2) Running MBpart1eps1 Running MBpart2eps1 Running MBpart3eps1 Running MBpart4eps1 Running MBpart5eps0 Running MBpart6eps0 Running MBpart7eps0 Running MBpart8eps0 Out[12]//InputForm= {-178.17989228662293 - 7.56250000000172435545742075614406256568`15.954589770191005/eps^2 - 20.45058399896632161346074706412279003467`15.868670493443501/eps + 18.364245687817288*eps, {0.01719355032101746 + 0.024846461019004607*eps, 0}} In[13]:= In[13]:= 16.86user 0.31system 0:17.25elapsed 99%CPU (0avgtext+0avgdata 0maxresident)k 0inputs+0outputs (2major+125100minor)pagefaults 0swaps