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

Lattice calculation of the intrinsic soft function and the Collins-Soper kernel

“…In all cases the valence quarks are chosen heavier than the sea quarks for the sake of better signals. The difference due to different spatial size and/or valence/sea masses should be minor [32,37], but will be explicitely investigated in future work. To further improve the signal, hypercubic (HYP) smeared fat links [54] have been used for the staple links in all calculations.…”

“…TMDWF provides a description for the partonic structure of hadrons in terms of probability amplitudes. It can be obtained using lattice QCD and LaMET as well [31,32].…”

“…It can also be extracted from lattice calculable ratios of either Mellin moments of quasi TMDPDFs/beam functions [39][40][41][42][43] or TMD wave functions (WFs) via a matching procedure. Both tree-level matching [31,35,37] and one loop matching [32] have been explored. In this work, we extract the CS kernel for a CLS ensemble in the framework of LaMET, trying to include one-loop contributions as JHEP08(2023)172 in [32].…”

“…Both tree-level matching [31,35,37] and one loop matching [32] have been explored. In this work, we extract the CS kernel for a CLS ensemble in the framework of LaMET, trying to include one-loop contributions as JHEP08(2023)172 in [32]. Besides, we investigate the pros and cons of extracting the CS kernel from quasi TMDWFs and quasi TMDPDFs.…”

“…(2.3) becomes feasible. In [32] the physical TMDWFs are calculated for the first time and in [46] the physical unpolarized TMDPDF of the proton is investigated for the first time on a MILC ensemble. In this work, we discuss TMDWFs and TMDPDFs as applications of the soft function in TMD physics.…”