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Massless and massive one-loop three-point functions in negative dimensional approach

A. T. Suzuki·E. S. Santos·A. G. M. Schmidt
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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 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 D. Our approach reproduces the known results as well as other solutions as yet unknown in the literature. These new solutions occur naturally in the context of NDIM revealing a promising technique to solve Feynman integrals in quantum field theories.

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A. T. Suzuki, E. S. Santos, A. G. M. Schmidt. 2002-05-15. Massless and massive one-loop three-point functions in negative dimensional approach. https://doi.org/10.1140/epjc%2Fs2002-01035-0

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