Schouten identities for Feynman graph amplitudes; the Master Integrals for the two-loop massive sunrise graph

Abstract

A new class of identities for Feynman graph amplitudes, dubbed Schouten identities, valid at fixed integer value of the dimension d is proposed. The identities are then used in the case of the two loop sunrise graph with arbitrary masses for recovering the second order differential equation for the scalar amplitude in d=2 dimensions, as well as a chained sets of equations for all the coefficients of the expansions in (d-2). The shift from $d\approx 2$ to $d\approx 4$ dimensions is then discussed.

Comments: 30 pages, 1 figure, minor typos in the text corrected, results unchanged. Version accepted for publication on Nuclear Physics B