How to integrate divergent integrals: a pure numerical approach to complex loop calculations Original Research Article

Loop calculations involve the evaluation of divergent integrals. Usually [G. ʹt Hooft, M. Veltman, Nucl. Phys. B 44 (1972) 189] 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 ε=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/ε and the finite part.