Soft-/rapidity- anomalous dimensions correspondence

TL;DR

This paper establishes a universal correspondence between ultraviolet and rapidity singularities in soft factors for multiparticle processes, providing a proof of rapidity renormalization and deriving three-loop anomalous dimensions.

Contribution

It introduces a conformal mapping-based correspondence between UV and rapidity singularities, valid to all orders, and derives explicit three-loop expressions for anomalous dimensions.

Findings

Proves the rapidity renormalization procedure for multiparton scattering.

Derives exact relation between rapidity and soft anomalous dimensions.

Calculates three-loop expressions for TMD and multiparton scattering anomalous dimensions.

Abstract

We establish a correspondence between ultraviolet singularities of soft factors for multiparticle production and rapidity singularities of soft factors for multiparton scattering. This correspondence is a consequence of the conformal mapping between scattering geometries. The correspondence is valid to all orders of perturbation theory and in this way provides one with a proof of rapidity renormalization procedure for multiparton scattering (including the transverse momentum dependent (TMD) factorization as a special case). As a by-product, we obtain an exact relation between the rapidity anomalous dimension and the well-known soft anomalous dimension. The three-loop expressions for TMD and a general multiparton scattering rapidity anomalous dimension are derived.