Lattice computation of the TMD soft function and CS kernel

Anthony Francis¹, Issaku Kanamori³, C.-J. David Lin¹, Wayne Morris^1*, Yong Zhao²

¹Physics, National Yang Ming Chiao Tung University, Hsinchu, Taiwan
²Theory, Argonne National Lab, Lemont, IL, USA
³Field Theory Research Team, RIKEN Center for Computational Scienece, Kobe, Japan

* Presenter:Wayne Morris, email:waynemorris@nycu.edu.tw

The TMD soft function may be obtained by formulating the Wilson line in terms of auxiliary 1-dimensional
fermion fields on the lattice. We take inspiration from heavy quark effective theory (HQET) in order to define
the auxiliary field. Our computation takes place in the region of the lattice that corresponds to the “spacelike”
region in Minkowski space in order to obtain the Collins soft function. The matching of our result to the Collins
soft function is achieved through the mapping of the auxiliary field directional vector to the Wilson line rapidity. I
present some exploratory numerical results of our lattice calculation, and discuss the methodology employed.

Keywords: Hadron structure, TMDs, Parton distributions, Lattice , Quantum chromodynamics