Equivalence of recurrence relations for Feynman integrals with the same total number of external and loop momenta

Abstract

We show that the problem of solving recurrence relations for L-loop\n(R+1)-point Feynman integrals within the method of integration by parts is\nequivalent to the corresponding problem for (L+R)-loop vacuum or (L+R-1)-loop\npropagator-type integrals. Using this property we solve recurrence relations\nfor two-loop massless vertex diagrams, with arbitrary numerators and integer\npowers of propagators in the case when two legs are on the light cone, by\nreducing the problem to the well-known solution of the corresponding recurrence\nrelations for massless three-loop propagator diagrams with specific boundary\nconditions.\n