NDIM achievements: Massive, Arbitrary tensor rank and N-loop insertions in Feynman integrals

TL;DR

This paper introduces the NDIM technique to efficiently compute complex multi-loop Feynman integrals in quantum field theory, including cases with arbitrary tensor ranks and N-insertions, simplifying calculations beyond one-loop level.

Contribution

The work extends NDIM to handle two-loop integrals with arbitrary tensor ranks and N-insertions, providing new computational methods for complex Feynman integrals.

Findings

Successfully computed two-loop scalar integrals with three different masses

Extended NDIM to massless cases with arbitrary tensor rank

Calculated N-insertions in two-loop diagrams

Abstract

One of the main difficulties in studying Quantum Field Theory, in the perturbative regime, is the calculation of D-dimensional Feynman integrals. In general, one introduces the so-called Feynman parameters and associated with them the cumbersome parametric integrals. Solving these integrals beyond the one-loop level can be a difficult task. Negative dimensional integration method (\ndim{}) is a technique whereby such problem is dramatically reduced. In this work we present the calculation of two-loop integrals in three diferent cases: scalar ones with three diferent masses, massless with arbitrary tensor rank, with N-insertions of a 2-loop diagram.