Transverse-momentum-dependent factorization at next-to-leading power

TL;DR

This paper develops a formalism for transverse momentum dependent factorization at sub-leading power in Drell-Yan and SIDIS processes, including calculations of anomalous dimensions and evolution equations, advancing precision in QCD predictions.

Contribution

It introduces a consistent treatment of sub-leading power contributions, calculates their anomalous dimensions, and establishes a one-loop factorization formalism for these processes.

Findings

Anomalous dimensions of sub-leading correlation functions are computed.

Evolution equations mix leading and sub-leading power distributions.

Hard and soft functions differ from leading power results.

Abstract

We study transverse momentum dependent factorization and resummation at sub-leading power in Drell-Yan and semi-inclusive deep inelastic scattering. In these processes the sub-leading power contributions to the cross section enter as a kinematic power correction to the leptonic tensor, and the kinematic, intrinsic, and dynamic sub-leading contributions to the hadronic tensor. By consistently treating the power counting of the interactions, we demonstrate renormalization group consistency. We calculate the anomalous dimensions of the kinematic and intrinsic sub-leading correlation functions at one loop and find that the evolution equations give rise to anomalous dimension matrices which mix leading and sub-leading power distribution functions. Additionally we calculate the hard and soft functions associated with each of these contributions. We find that these hard and soft contributions differ from those at the leading power. Finally, we calculate the rapidity anomalous dimension for the dynamic sub-leading distributions and find that it is the same as the leading power anomalous dimension. We then comment on the implications for the soft function associated with this contribution. Using this information, we establish the factorization formalism at sub-leading power for these processes at the one-loop level.