Transverse-momentum-dependent Wave Functions of the Pion from Lattice QCD

We present a lattice QCD calculation of the transverse-momentum-dependent wave function (TMDWF) of the pion using large-momentum effective theory. Numerical simulations are based on one ensemble with 2+1+1 flavors of highly improved staggered quarks with lattice spacing a=0.121 fm from the MILC collaboration, and one with 2+1 flavor clover fermions and tree-level Symanzik gauge action generated by the CLS collaboration with a=0.098 fm. As a key ingredient, the soft function is first obtained by incorporating the one-loop perturbative contributions and a proper normalization. Based on this and the equal-time quasi-TMDWF simulated on the lattice, we extract the TMDWF. The results for both lattice ensembles are compatible and a comparison with a phenomenological parametrization is made. Our studies provide a first attempt of calculation of TMDWFs which will eventually lead to crucial theory inputs for making predictions for exclusive processes under QCD factorization. Published by the American Physical Society 2024