Lattice extraction of the Collins-Soper kernel using the auxiliary field representation of the Wilson line

TL;DR

This paper introduces a lattice QCD approach to extract the Collins-Soper kernel via auxiliary field representation of Wilson lines, employing two methods to improve precision and facilitate matching to Minkowski space.

Contribution

It proposes a novel lattice formulation using auxiliary fermion fields to compute the Collins-Soper kernel, exploring two extraction methods for enhanced accuracy.

Findings

Preliminary extraction of the CS kernel using the double ratio method.

Methodology for mapping auxiliary field directions to Wilson line rapidity.

Discussion of the potential for high-precision lattice calculations of the CS kernel.

Abstract

The Collins-Soper (CS) kernel may be obtained through the TMD soft function by formulating the Wilson line in terms of 1-dimensional auxiliary fermion fields on the lattice. Our computation takes place in the region of the lattice that corresponds to the "spacelike" region in Minkowski space, i.e., Collins' scheme. We explore two methods for obtaining the CS kernel. The "ratio method"; which would allow us to obtain the soft function as well as the CS kernel. And the "double ratio"; which allows us to achieve a high degree of statistical precision, but only produces the CS kernel. The matching of our result to Minkowski space is achieved through the mapping of the complex auxiliary field directional vector to the Wilson line rapidity. We present a preliminary extraction of the CS kernel using the "double ratio", and discuss the methodology employed.