Method of regions for dual conformal integrals

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 $Γ$-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.

Figures (4)

• Figure 1: DCI pentabox integral. On the dual graph (shown in blue) the dashed lines denote numerators.
• Figure 2: 43 regions which contribute to small-$m^2$ asymptotics.
• Figure 3: DCI off-shell double box $DB_{\text{off}}$.
• Figure 4: DCI double box with five legs $DB_5$.