Collins-Soper Kernel in the QCD Instanton Vacuum

TL;DR

This paper develops a framework to evaluate the Collins-Soper kernel in the QCD instanton vacuum, linking non-perturbative effects with lattice results and phenomenology for better understanding of TMD evolution.

Contribution

It introduces a method to compute the Collins-Soper kernel from the instanton vacuum, connecting non-perturbative QCD effects with lattice data and phenomenological models.

Findings

The derived CS kernel agrees with recent lattice results.

The CS kernel depends logarithmically on large quark transverse separation.

Provides a new approach for evaluating the soft function via analytical continuation.

Abstract

We outline a general framework for evaluating the non-perturbative soft functions in the QCD instanton vacuum. In particular, from the soft function we derive the Collins-Soper (CS) kernel, which drives the rapidity evolution of the transverse-momentum-dependent parton distributions. The resulting CS kernel, when supplemented with the perturbative contribution, agrees well with recent lattice results and some phenomenological parameterizations. Moreover, our CS kernel depends logarithmically on the large quark transverse separation, providing a key constraint on its phenomenological parametrization. Finally, a lattice calculation can be directly compared to our generic results in Euclidean signature, thus providing a new approach for evaluating the soft function and extracting the CS kernel by analytical continuation.