Two-loop kite master integral for a correlator of two composite vertices

Abstract

We consider the most general two-loop massless correlator I(n1, n2, n3, n4, n5; x, y; D) of two composite vertices with the Bjorken fractions x and y for arbitrary indices {ni} and space-time dimension D; this correlator is represented by a “kite” diagram. The correlator I({ni}; x, y; D) is the generating function for any scalar Feynman integrals related to this kind of diagrams. We calculate I({ni}; x, y; D) and its Mellin moments in a direct way by evaluating hypergeometric integrals in the α representation. The result for I({ni}; x, y; D) is given in terms of a double hypergeometric series — the Kampé de Férriet function. In some particular but still quite general cases it reduces to a sum of generalized hypergeometric functions 3F2. The Mellin moments can be expressed through generalized Lauricella functions, which reduce to the Kampé de Férriet functions in several physically interesting situations. A number of Feynman integrals involved and relations for them are obtained.