Quasi Distribution Amplitude of Heavy Quarkonia

TL;DR

This paper calculates the order-$\\alpha_s$ corrections to the quasi-distribution amplitudes of heavy quarkonia within NRQCD, demonstrating their convergence to light-cone DAs at high momenta, aiding future lattice QCD studies.

Contribution

It provides the first analytical calculation of quasi-DA corrections for heavy quarkonia and shows their convergence to LCDAs at accessible momenta, guiding lattice QCD investigations.

Findings

Quasi-DA reduces to LCDA in the infinite-momentum limit.

Quasi-DAs converge to LCDAs at 2-3 times the quarkonium mass.

Order-$\alpha_s$ corrections are explicitly computed for heavy quarkonia.

Abstract

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-$\alpha_s$ 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.