Transverse-Momentum-Dependent Structures of the Proton from Lattice QCD

Recent years have seen rapid progress in lattice QCD calculations of the partonic structures of the proton. Among them, one approach that has found wide application is the large-momentum effective theory (LaMET), where the parton observables are related to Euclidean matrix elements in a highly boosted proton state through a factorization formula that expands in the large momentum. LaMET has enabled systematic lattice calculations of collinear parton distribution functions (PDFs), which have reached remarkable precision over the past years. Recently, it has also been extended to the transverse-momentum-dependent (TMD) PDFs, and methods have been proposed to calculate both the TMD beam and soft functions on the lattice. In this talk, I will go over the developments in the LaMET calculation of TMDPDFs and show the exploratory lattice results that demonstrate the feasibility of these methods.