Automatized analytic continuation of Mellin-Barnes integrals

نویسنده

  • M. Czakon
چکیده

I describe a package written in MATHEMATICA that automatizes typical operations performed during evaluation of Feynman graphs with Mellin-Barnes (MB) techniques. The main procedure allows to analytically continue a MB integral in a given parameter without any intervention from the user and thus to resolve the singularity structure in this parameter. The package can also perform numerical integrations at specified kinematic points, as long as the integrands have satisfactory convergence properties. I demonstrate that, at least in the case of massive graphs in the physical region, the convergence may turn out to be poor, making nä ive numerical integration of MB integrals unusable. I present possible solutions to this problem, but argue that full automatization in such cases may not be achievable. Programming language used: MATHEMATICA, Fortran 77 for numerical evaluation Memory required to execute with typical data: Sufficient for a typical installation of MATHEMATICA. No. of bytes in distributed program, including test data: 337900 Distribution format: ASCII Libraries used: CUBA [1] for numerical evaluation of multidimensional integrals and CERNlib [2] for the implementation of Γ and ψ functions in Fortran. Nature of physical problem: Analytic continuation of Mellin-Barnes integrals in a parameter and subsequent numerical evaluation. This is necessary for evaluation of Feynman integrals from Mellin-Barnes representations. Method of solution: Recursive accumulation of residue terms occurring when singularities cross integration contours. Numerical integration of multidimen-sional integrals with the help of the CUBA library. Restrictions on the complexity of the problem: Limited by the size of the available storage space. Typical running time: Depending on the problem. Usually seconds for moderate dimensionality integrals.

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عنوان ژورنال:
  • Computer Physics Communications

دوره 175  شماره 

صفحات  -

تاریخ انتشار 2006