A probabilistic angle on one-loop scalar integrals

Recasting the N-point one-loop scalar integral as a probabilistic problem allows the derivation of integral recurrence relations, as well as exact analytical expressions in the most common cases. expansions are derived by writing a formula that relates an N-point function in decimal dimensions to an N-point function in integer dimensions. As an example, we give relations for the massive five-point function in n=4−2ϵ and n=6−2ϵ dimensions. The reduction of tensor integrals of rank two with N = 5 is achieved showing the method's potential. No hypergeometric functions are involved. Results are expressed as integrals of arcsine functions, whose analytical continuation is well known.