Regularization of IR divergent loop integrals

We report results of a new numerical regularization technique for infrared (IR) divergent loop integrals using dimensional regularization, where a positive regularization parameter ε, satisfying that the dimension d = 4 + 2ε, is introduced in the integrand to keep the integral from diverging as long as ε > 0. A sequence of integrals is computed for decreasing values of ε, in order to carry out a linear extrapolation as ε → 0. Each integral in the sequence is calculated according to the Direct Computation Method (DCM) to handle (threshold) integrand singularities in the interior of the domain. The technique of this paper is applied to one-loop N-point functions. In order to simplify the computation of the integrals for small ε, particularly in the case of a threshold singularity, a reduction of the N-point function is performed numerically to a set of 3-point and 4-point integrals, and DCM is applied to the resulting vertex and box integrals.