Non-planar double-box, massive and massless pentabox Feynman integrals in negative dimensional approach

TL;DR

This paper applies the negative dimensional integration method to evaluate complex two-loop Feynman diagrams, including non-planar double-box and pentabox integrals with massive and massless particles, expressing results in hypergeometric functions.

Contribution

It extends NDIM to compute non-planar double-box and pentabox integrals with arbitrary propagator exponents and dimensions, providing explicit hypergeometric function representations.

Findings

Derived explicit hypergeometric function expressions for the integrals.

Handled both massive and massless cases in a unified framework.

Demonstrated the applicability of NDIM to complex two-loop diagrams.

Abstract

Negative dimensional integration method (NDIM) is a technique which can be applied, with success, in usual covariant gauge calculations. We consider three two-loop diagrams: the scalar massless non-planar double-box with six propagators and the scalar pentabox in two cases, where six virtual particles have the same mass and in the case where all of them are massless. Our results are given in terms hypergeometric functions of Mandelstam variables and for arbitrary exponents of propagators and dimension $D$ as well.