New relationships between Feynman integrals

• Published in: Physics letters. B Vol. 670; no. 1; pp. 67 - 72
• Main Author: Tarasov, O.V.
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier B.V 04.12.2008; Elsevier
• Subjects: Appell hypergeometric function; Exact sciences and technology; Feynman integrals; Functional equations; Nuclear physics; Physics; The physics of elementary particles and fields; Feynman integrals; Functional equations; 12.20.Ds; 02.30.Ks; 02.30.Gp; 12.38.Bx; Appell hypergeometric function; Invariant; Vertex; Integral equations; Kinematics; Propagator
• ISSN: 0370-2693; 1873-2445
• DOI: 10.1016/j.physletb.2008.10.021

New types of relationships between Feynman integrals are presented. It is shown that Feynman integrals satisfy functional equations connecting integrals with different values of scalar invariants and masses. A method is proposed for obtaining such relations. The derivation of functional equations for one-loop propagator- and vertex-type integrals is given. It is shown that a propagator-type integral can be written as a sum of two integrals with modified scalar invariants and one propagator massless. The vertex-type integral can be written as a sum over vertex integrals with all but one propagator massless and one external momenta squared equal to zero. It is demonstrated that the functional equations can be used for the analytic continuation of Feynman integrals to different kinematic domains.