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OLEC - One Loop External Contractions

Andrea A. Almasy, Ievgen Dubovyk, Jochem Fleischer, Janusz Gluza, Marek Gluza, Tord Riemann

The project is based on the approach described by J. Fleischer and T. Riemann in Phys.Lett. B701 (2011) 646,
further developed in Phys.Rev. D83 (2011) 073004 and Phys.Lett. B707 (2012) 375.


RESULTS and PACKAGE for contracted tensors up to rank 3, including contractions with the metric tensor

Version 0.9 includes contractions of chords (i.e. appropriately organized external momenta) with one-loop tensor five point functions of up to rank 3. It includes the mathematica package OLECv0.9.m supplied by Contracts_examples.nb and the c++ package OLECv0.9.tgz.
It is advise to look first at the mathematica examples and arXiv:1211.3921 [hep-ph] (basic introduction and further references).

The main package is OLECv0.9.tgz. For calculation of basic scalar one-loop integrals, it can be linked with both LoopTools (LT) and OneLoop (OL).
See README and Makefiles for details.

• The Mathematica package OLECv0.9.m, version 0.9.
  Contracts_examples.nb shows how to use it. The results are compared with the previous package hexagon.m and LoopTools. For using with OneLoop, we prepared mathlink.tgz which should be downloaded and compiled.
  
  
• The C++ package OLECv0.9.tgz, version 0.9.
  It is the first, elementary package which realizes contractions of chords with tensors, based on PLB701 (2011) 646. In its present form it does not include special cases of vanishing inverse Gram determinants as supplied e.g. in PJFRY.
  
  Numerical modules inside Makefile:
  
  • example_1 - compares functions CE2(1,2),CE3(1,2,3) with equivalent, standard results. Also, CE2g, CE3g(1) are shown. Calculations with LT and OL. Results agree with these given in Contracts_examples.nb
    
  • example_2 - values for D0,C0,B0 functions obtained by scratching lines in E0 with OL and LT. SET1 is for physical kinematical points generated by MC generator in Phokhara. Results agree between LT and OL. SET2 is an example of arbitrarily chosen kinematical points (not necessarily realized in physical processes). In this case warnings and errors generated by LT and/or OL appear, see output_example_2 for details.
  
  
  
  RESULTS for contracted tensors of rank 4, including contractions with the metric tensor
  
  
• New results for rank four: for detailed explanations, see hep-ph...
  
  • Set I (the kinematics is chosen such that 3-point functions hit the IR singularities):
    OLEC_contractions.txt,
    LoopTools.txt (no results available for rank 5 in LT, so set to zero),
    GOLEM.txt (golem95-1.2.1, a bug responsible for differences corrected meantime on the svn's, see Changeset 128)
    
  • Set II (the kinematics is chosen such that 3-point functions are slightly off the IR singularities):
    OLEC_contractions.txt,
    GOLEM.txt (golem95-1.2.1, discrepencies not corrected yet)
    
    ACKNOWLEDGEMENTS
    Special thanks to Krzysztof Kajda for his tests on the contractions in modified hexagon.m package
    and to Radomir Sevillano who made some tests in c++ related to signed minors and basic relations up to rank 2.
    
    We would like to thank also Thomas Hahn (LT) and Andreas van Hameren (OL) for their help in explaining subtleties of their packages.