Massless and massive one-loop three-point functions in negative dimensional approachA.T. Suzuki1, E.S. Santos1 and A.G.M. Schmidt1, 2
1 Universidade Estadual Paulista Instituto de Física Teórica, Rua Pamplona 145 São Paulo, SP CEP 01405-900, Brazil
2 Universidade Federal do Paraná, Departamento de Física Caixa Postal 19044 Curitiba PR CEP 81531-990, Brazil
(Received: 14 April 2002 / Revised version: 18 July 2002 / Published online: 7 October 2002 )
In this article we present the complete massless and massive one-loop triangle diagram results using the negative dimensional integration method (NDIM). We consider the following cases: massless internal fields; one massive, two massive with the same mass m and three equal masses for the virtual particles. Our results are given in terms of hypergeometric and hypergeometric-type functions of the external momenta (and masses for the massive cases) where the propagators in the Feynman integrals are raised to arbitrary exponents and the dimension of the space-time is D. Our approach reproduces the known results; it produces other solutions as yet unknown in the literature as well. These new solutions occur naturally in the context of NDIM revealing a promising technique to solve Feynman integrals in quantum field theories.
© Società Italiana di Fisica, Springer-Verlag 2002