How to Integrate Divergent Integrals: a Pure Numerical Approach to Complex Loop Calculations

Details How to Integrate Divergent Integrals: a Pure Numerical Approach to Complex Loop Calculations How to Integrate Divergent Integrals: a Pure Numerical Approach to Complex Loop Calculations

2000-04-04

arxiv.org/abs/hep-ph/0004030v1

Nucl.Phys. B589 (2000) 475-486

Physics

High Energy Physics

High Energy Physics - Phenomenology

13 pages, 1 Postscript figure

Scientific paper

10.1016/S0550-3213(00)00391-6

Loop calculations involve the evaluation of divergent integrals. Usually [1] one computes them in a number of dimensions different than four where the integral is convergent and then one performs the analytical continuation and considers the Laurent expansion in powers of epsilon =n-4. In this paper we discuss a method to extract directly all coefficients of this expansion by means of concrete and well defined integrals in a five dimensional space. We by-pass the formal and symbolic procedure of analytic continuation; instead we can numerically compute the integrals to extract directly both the coefficient of the pole 1/epsilon and the finite part.

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