Lattice QCD Calculations of Transverse-Momentum-Dependent Soft Function through Large-Momentum Effective Theory.

The transverse-momentum-dependent (TMD) soft function is a key ingredient in QCD factorization of Drell-Yan and other processes with relatively small transverse momentum. We present a lattice QCD study of this function at moderately large rapidity on a $2+1$ flavor CLS dynamic ensemble with $a=0.098\text{ }\text{ }\mathrm{fm}$. We extract the rapidity-independent (or intrinsic) part of the soft function through a large-momentum-transfer pseudoscalar meson form factor and its quasi-TMD wave function using leading-order factorization in large-momentum effective theory. We also investigate the rapidity-dependent part of the soft function---the Collins-Soper evolution kernel---based on the large-momentum evolution of the quasi-TMD wave function.