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arXiv · 2302.09961

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

Min-Huan Chu·Jin-Chen He·Jun Hua·Jian Liang·Xiangdong Ji·Andreas Schafer·Hai-Tao Shu·Yushan Su·Ji-Hao Wang·Wei Wang·Yi-Bo Yang·Jun Zeng·Jian-Hui Zhang·Qi-An Zhang
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Abstract

We present a first lattice QCD calculation of the transverse-momentum-dependent wave functions (TMDWFs) 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 action 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-TMDWFs simulated on the lattice, we extract the light-cone TMDWFs. The results are comparable between the two lattice ensembles and a comparison with phenomenological parametrization is made. Our studies provide a first attempt of $ab$ $initio$ calculation of TMDWFs which will eventually lead to crucial theory inputs for making predictions for exclusive processes under QCD factorization.

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Min-Huan Chu, Jin-Chen He, Jun Hua, Jian Liang, Xiangdong Ji, Andreas Schafer, Hai-Tao Shu, Yushan Su, Ji-Hao Wang, Wei Wang, Yi-Bo Yang, Jun Zeng, Jian-Hui Zhang, Qi-An Zhang. 2023-02-20. Transverse-Momentum-Dependent Wave Functions of Pion from Lattice QCD. https://arxiv.org/abs/2302.09961

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