Lattice Calculation of the Intrinsic Soft Function and the Collins-Soper Kernel

TL;DR

This paper uses lattice QCD within the large momentum effective theory framework to compute the soft function and Collins-Soper kernel, essential for TMD factorization, and applies these to extract TMD wave functions and PDFs.

Contribution

It introduces a lattice QCD calculation of the soft function and Collins-Soper kernel incorporating one-loop perturbative effects, using different ensembles and methods for improved accuracy.

Findings

Calculated the intrinsic soft function and Collins-Soper kernel with lattice QCD.

Compared different approaches for determining the Collins-Soper kernel.

Applied the results to obtain TMD wave functions and PDFs for pion and proton.

Abstract

We calculate the soft function using lattice QCD in the framework of large momentum effective theory incorporating the one-loop perturbative contributions. The soft function is a crucial ingredient in the lattice determination of light cone objects using transverse-momentum-dependent (TMD) factorization. It consists of a rapidity-independent part called intrinsic soft function and a rapidity-dependent part called Collins-Soper kernel. We have adopted appropriate normalization when constructing the pseudo-scalar meson form factor that is needed in the determination of the intrinsic part and applied Fierz rearrangement to suppress the higher-twist effects. In the calculation of CS kernel we consider a CLS ensemble other than the MILC ensemble used in a previous study. We have also compared the applicability of determining the CS kernel using quasi TMDWFs and quasi TMDPDFs. As an example, the determined soft function is used to obtain the physical TMD wave functions (WFs) of pion and unpolarized iso-vector TMD parton distribution functions (PDFs) of proton.