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Equivalence of Recurrence Relations for Feynman Integrals with the Same Total Number of External and Loop Momenta

P. A. Baikov·V. A. Smirnov
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Abstract

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

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P. A. Baikov, V. A. Smirnov. 2000-01-19. Equivalence of Recurrence Relations for Feynman Integrals with the Same Total Number of External and Loop Momenta. https://doi.org/10.1016/s0370-2693(00)00222-7

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