Crossed Topology in Two-Loop Dispersive Approach

TL;DR

This paper extends the dispersive approach to crossed two-loop box topologies, providing a compact analytical form that facilitates automated calculations through numerical integration and differentiation.

Contribution

It introduces a novel extension of the dispersive approach to complex crossed two-loop diagrams using Feynman tricks and Passarino-Veltman functions.

Findings

Derived a compact analytical expression for crossed two-loop scalar diagrams.

Enabled automation of complex two-loop calculations.

Reduced computational complexity in two-loop dispersive calculations.

Abstract

We extend existing dispersive approach in subloop insertion to the case of crossed two-loop box type topologies. Based on the ideas of the Feynman trick, mass shift approach and dispersive representation of two-point Passarino-Veltman function we expressed two-loop scalar diagrams in the compact analytical form suitable for the automatization of the calculations. The results are expressed in a way that the numerical integration over Feynman and dispersive parameters and differentiation with respect to mass shift parameters are required in the final stage only.