DOI: 10.1140/epjc/s2002-01035-0
Massless and massive one-loop three-point functions in negative dimensional approach
A.T. Suzuki1, E.S. Santos1 and A.G.M. Schmidt1, 21 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 )
Abstract
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