Probing negative dimensional integration: two-loop covariant vertex and one-loop light-cone integrals

Abstract

Negative dimensional integration method (NDIM) seems to be a very promising technique for evaluating massless and/or massive Feynman diagrams. It is unique in the sense that the method gives solutions in different regions of external momenta simultaneously. Moreover, it is a technique whereby the difficulties associated with performing parametric integrals in the standard approach are transferred to a simpler solving of a system of linear algebraic equations, thanks to the polynomial character of the relevant integrands. We employ this method to evaluate a scalar integral for a massless two-loop three-point vertex with all the external legs off-shell, and consider several special cases for it, yielding results, even for distinct simpler diagrams. We also consider the possibility of NDIM in non-covariant gauges such as the light-cone gauge and do some illustrative calculations, showing that for one-degree violation of covariance (i.e., one external, gauge-breaking, light-like vector $n_{\mu }$) the ensuing results are concordant with the ones obtained via either the usual dimensional regularization technique, or the use of principal value prescription for the gauge dependent pole, while for two-degree violation of covariance --- i.e., two external, light-like vectors $n_{\mu }$, the gauge-breaking one, and (its dual) $n_{\mu }^{\ast }$ --- the ensuing results are concordant with the ones obtained via causal constraints or the use of the so-called generalized Mandelstam-Leibbrandt prescription.

17 pages, 3 ps figures, Revtex

References in corpus (2)

• Negative Dimensional Integration: "Lab Testing" at Two Loops
• An easy way to solve two-loop vertex integrals

Cited by in corpus (10)

• Two-Loop Vertices in Quantum Field Theory: Infrared Convergent Scalar Configurations
• Two-Loop Tensor Integrals in Quantum Field Theory
• One-loop N-point equivalence among negative-dimensional, Mellin-Barnes and Feynman parametrization approaches to Feynman integrals
• Two-Loop Quark Self-Energy in a New Formalism (II): Renormalization of the Quark Propagator in the Light-Cone Gauge
• NDIM achievements: Massive, Arbitrary tensor rank and N-loop insertions in Feynman integrals
• Loop integrals in three outstanding gauges: Feynman, Light-cone and Coulomb
• A possible way to relate the "covariantization" and the negative dimensional integration methods in the light cone gauge
• Obtaining a light-like planar gauge
• Light-cone gauge integrals: Prescriptionlessness at two loops
• Not a prescription but an identity: Mandelstam-Leibbrandt