Quasi Distribution Amplitude of 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.

32 pages, 5 Figures, 1 table

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Cited by in corpus (15)

• Large-Momentum Effective Theory
• A guide to light-cone PDFs from Lattice QCD: an overview of approaches, techniques and results
• On the Renormalizability of Quasi Parton Distribution Functions
• First direct lattice-QCD calculation of the $x$-dependence of the pion parton distribution function
• Systematic uncertainties in parton distribution functions from lattice QCD simulations at the physical point
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• Parton distribution functions from reduced Ioffe-time distributions
• Parton Distribution Functions of Heavy Mesons on the Light Front
• Flavor non-singlet parton distribution functions from lattice QCD at physical quark masses via the pseudo-distribution approach
• On the power divergence in quasi gluon distribution function
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• Matching the Quasi Meson Distribution Amplitude in RI/MOM scheme
• Inverse moment of the $B$-meson quasi distribution amplitude
• Ground state pseudoscalar mesons on the light front: from the light to heavy sector