Method of regions for dual conformal integrals

TL;DR

This paper introduces a DCI-preserving regularization method for dual conformal integrals that simplifies calculations and yields compact expressions, contrasting with traditional polylogarithmic results.

Contribution

The authors develop a novel regularization approach that maintains dual conformal invariance, simplifying the computation of off-shell integrals and producing more compact results.

Findings

DCI-preserving regularization simplifies two-loop five-point integrals

Results expressed in terms of Gamma functions and logarithms

Contrasts with conventional polylogarithmic expressions

Abstract

In this contribution, we present a recently introduced approach [BorkLeeOnishchenko2025] to the calculation of slightly off-shell dual conformal integrals based on the method of regions with regularization preserving dual conformal invariance (DCI). Unlike conventional dimensional regularization, which breaks DCI, our approach uses a combination of dimensional and analytic regularizations specifically designed to retain DCI throughout the calculation. Our approach drastically simplifies the computation of slightly off-shell dual conformal integrals. For the two-loop five-point DCI integrals we find that with DCI-preserving regularization, the contributions of all regions can be expressed in terms of $\Gamma$-functions, resulting in a remarkably compact final expression in terms of logarithms of cross-ratios only. This is in sharp contrast to conventional approach which yields complex polylogarithmic expressions [Belitsky&Smirnov2025]. We argue that a similar approach might be useful also for non-DCI integrals.