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We present a first lattice QCD calculation of thetransverse-momentum-dependent wave functions (TMDWFs) of the pion usinglarge-momentum effective theory. Numerical simulations are based on oneensemble with 2+1+1 flavors of highly improved staggered quarks action withlattice spacing $a=0.121$~fm from the MILC Collaboration, and one with 2 +1flavor clover fermions and tree-level Symanzik gauge action generated by theCLS Collaboration with $a=0.098$~fm. As a key ingredient, the soft function isfirst obtained by incorporating the one-loop perturbative contributions and aproper normalization. Based on this and the equal-time quasi-TMDWFs simulatedon the lattice, we extract the light-cone TMDWFs. The results are comparablebetween the two lattice ensembles and a comparison with phenomenologicalparametrization is made. Our studies provide a first attempt of $ab$ $initio$calculation of TMDWFs which will eventually lead to crucial theory inputs formaking predictions for exclusive processes under QCD factorization.

Transverse-Momentum-Dependent Wave Functions of Pion from Lattice QCD