The recently-proposed quasi distributions point out a promising direction for lattice QCD to investigate the light-cone correlators, such as parton distribution functions (PDF) and distribution amplitudes (DA), directly in the x-space. Owing to its excessive simplicity, the heavy quarkonium can serve as an ideal theoretical laboratory to ascertain certain features of quasi-DA. In the framework of non-relativistic QCD (NRQCD) factorization, we compute the order-αs correction to both light-cone distribution amplitudes (LCDA) and quasi-DA associated with the lowest-lying quarkonia, with the transverse momentum UV cutoff interpreted as the renormalization scale. We confirm analytically that the quasi-DA of a quarkonium does reduce to the respective LCDA in the infinite-momentum limit. We also observe that, provided that the momentum of a charmonium reaches about 2-3 times its mass, the quasi-DAs already converge to the LCDAs to a decent level. These results might provide some useful guidance for the future lattice study of the quasi distributions.
@article{arxiv.1511.04430,
title = {Quasi Distribution Amplitude of Heavy Quarkonia},
author = {Yu Jia and Xiaonu Xiong},
journal= {arXiv preprint arXiv:1511.04430},
year = {2016}
}