QCD$\times$QED evolution of TMDs

TL;DR

This paper introduces the first QED corrections to the evolution of TMDs, extending their operator definitions to include QED effects and deriving new anomalous dimensions up to specified orders, revealing flavor universality breaking.

Contribution

It provides the first calculation of mixed QCD-QED anomalous dimensions for TMD evolution and QED corrections to matching coefficients, expanding the theoretical framework of TMDs.

Findings

QED corrections break flavor universality in TMD evolution.

Derived mixed anomalous dimensions up to order αsα.

Calculated leading-order QED corrections to TMD matching coefficients.

Abstract

We consider for the first time the QED corrections to the evolution of (un)polarized quark and gluon transverse-momentum-dependent distribution and fragmentation functions (TMDs in general). By extending their operator definition to QCD$\times$QED, we provide the mixed new anomalous dimensions up to ${\cal O}(\alpha_s\alpha)$ and the pure QED ones up to ${\cal O}(\alpha^2)$. These new corrections are universal for all TMDs up to the flavor of the considered parton, i.e., the full flavor universality of TMD evolution found in pure QCD is broken in QCD$\times$QED by the presence of the electric charge. In addition, we provide the leading-order QED corrections to the matching coefficients of the unpolarized quark TMD parton distribution function onto its integrated counterparts at ${\cal O}(\alpha_s^0\alpha)$.