Loop Tree Duality with generalized propagator powers: numerical UV subtraction for two-loop Feynman integrals

TL;DR

This paper develops a numerical method using Loop Tree Duality and Hopf algebra structures to efficiently subtract UV divergences in two-loop Feynman integrals with generalized propagator powers.

Contribution

It introduces an explicit LTD formula for two-loop integrals with generalized propagator powers and a recursive UV subtraction algorithm based on the $\ ext{\mathcal{R}}$ operator and Hopf algebra.

Findings

Successful numerical UV divergence subtraction for two-loop integrals

Extension of LTD to integrals with quadratic divergences

Implementation of a recursive UV subtraction algorithm

Abstract

An explicit Loop Tree Duality (LTD) formula for two-loop Feynman integrals with integer power of propagators is presented and used for a numerical UV divergence subtraction algorithm. This algorithm proceeds recursively and it is based on the $\mathcal{R}$ operator and the Hopf algebraic structure of UV divergences. After a short review of LTD and the numerical evaluation of multi-loop integrals, LTD is extended to two-loop integrals with generalized powers of propagators. The $\mathcal{R}$ operator and the tadpole UV subtraction are employed for the numerical calculation of two-loop UV divergent integrals, including the case of quadratic divergences.