Reduction with degenerate Gram matrix for one-loop integrals

A bstract An improved PV-reduction (Passarino-Veltman) method for one-loop integrals with auxiliary vector R has been proposed in [1, 2]. It also shown that the new is a self-completed [3]. Analytic reduction coefficients can be easily produced by recursion relations this method, where Gram determinant appears denominators. The singularity caused well-known fact and it important to address these divergences given frame. In paper, we propose systematical algorithm deal problem our method. key idea now master integral of highest topology will decomposed into combinations lower topologies. By demanding cancellation divergence obtained general coefficients, solve decomposition as Taylor series determinant. Moreover, same applied other kinds divergences.