Analytic tadpole coefficients of one-loop integrals

A bstract One remaining problem of unitarity cut method for one-loop integral reduction is that tadpole coefficients can not be straightforward obtained through this way. In paper, we reconsider the by applying differential operators over an auxiliary vector R . Using operators, establish corresponding equations at first step. Then using tensor structure coefficients, transform to recurrence relations undetermined coefficients. These solved easily iteration and obtain analytic expressions arbitrary integrals.