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The recently-proposed quasi distributions point out a promising direction forlattice QCD to investigate the light-cone correlators, such as partondistribution functions (PDF) and distribution amplitudes (DA), directly in the$x$-space. Owing to its excessive simplicity, the heavy quarkonium can serve asan ideal theoretical laboratory to ascertain certain features of quasi-DA. Inthe framework of non-relativistic QCD (NRQCD) factorization, we compute theorder-$\alpha_s$ correction to both light-cone distribution amplitudes (LCDA)and quasi-DA associated with the lowest-lying quarkonia, with the transversemomentum UV cutoff interpreted as the renormalization scale. We confirmanalytically that the quasi-DA of a quarkonium does reduce to the respectiveLCDA in the infinite-momentum limit. We also observe that, provided that themomentum of a charmonium reaches about 2-3 times its mass, the quasi-DAsalready converge to the LCDAs to a decent level. These results might providesome useful guidance for the future lattice study of the quasi distributions.

Quasi Distribution Amplitude of Heavy Quarkonia