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Manuscript Title: A numerical algorithm for efficiently obtaining a Feynman parameter representation of one-gluon loop QCD Feynman diagrams for a large number of external gluons
Authors: A. S. Kapoyannis, A. I. Karanikas, C. N. Ktorides
Program title: DILOG2
Catalogue identifier: ADXN_v1_0
Distribution format: tar.gz
Journal reference: Comput. Phys. Commun. 174(2006)631
Programming language: FORTRAN 90.
Computer: Personal Computer.
Operating system: Windows 98, XP, LINUX.
Keywords: one-gluon loop, Feynman diagram, QCD diagram.
PACS: 02.70.Rw, 12.38.Bx.
Classification: 11.5.

Nature of problem:
The computation of one gluon/ghost loop diagrams in QCD with many external gluon lines is a time consuming task, practically beyond reasonable reach of analytic procedures. We apply recently proposed master formulas towards the computation of such diagrams with an arbitrary number (M) of external gluon lines, achieving a final result which reduces the problem to one involving integrals over the standard set, for a given M, of Feynman parameters.

Solution method:
The structure of the master expressions is analysed from a numerical computation point of view. Using the properties of Grassmann variables we identify all the different forms of terms that appear in the final result. Each form is called "structure". We calculate theoretically the number of terms belonging to every "structure". We carry out the calculation organising the whole procedure into separate calculations of the terms belonging to every "structure". Terms which do not contribute to the final result are thereby avoided. The final result, extending to large values of M, is also presented with terms belonging to the same "structure" grouped together.

Restrictions:
M is coded as a 2-digit integer. Overflow in the dimension of used array is expected to appear for M ≥ 20 in a processor that uses 4-bytes integers or for M ≥ 34 in a processor with 8-bytes integers.

Running time:
Depends on M, see enclosed figures.