On the Numerical Evaluation of Loop Integrals With Mellin-Barnes Representations

Details On the Numerical Evaluation of Loop Integrals With Mellin-Barnes Representations On the Numerical Evaluation of Loop Integrals With Mellin-Barnes Representations

2010-01-19

arxiv.org/abs/1001.3243v1

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pp. LaTeX

Scientific paper

An improved method is presented for the numerical evaluation of multi-loop integrals in dimensional regularization. The technique is based on Mellin-Barnes representations, which have been used earlier to develop algorithms for the extraction of ultraviolet and infrared divergencies. The coefficients of these singularities and the non-singular part can be integrated numerically. However, the numerical integration often does not converge for diagrams with massive propagators and physical branch cuts. In this work, several steps are proposed which substantially improve the behavior of the numerical integrals. The efficacy of the method is demonstrated by calculating several two-loop examples, some of which have not been known before.

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