Improved Nonrelativistic QCD for Heavy Quark Physics

TL;DR

This work develops an improved NRQCD framework for heavy-quark physics on the lattice, combining a rigorous power-counting scheme with tree-level relativistic and finite-spacing corrections to keep systematic errors below 10%. It provides a continuum NRQCD Lagrangian with calibrated coefficients, a lattice formulation with corrected derivatives and gauge actions, and a corrected evolution equation that enables efficient heavy-quark propagation. The authors also introduce a mean-field tadpole treatment to estimate and mitigate radiative corrections, discuss removing tadpoles, and assess nonperturbative contributions, arguing they are typically small at realistic lattice spacings. Together, these components establish a pathway toward high-precision lattice studies of heavy quarkonia (e.g., ψ, Υ) and related bound states, with prospects for extending to D and B mesons and including light-quark vacuum polarization effects in future work.

Abstract

We construct an improved version of nonrelativistic QCD for use in lattice simulations of heavy quark physics, with the goal of reducing systematic errors from all sources to below 10\%. We develop power counting rules to assess the importance of the various operators in the action and compute all leading order corrections required by relativity and finite lattice spacing. We discuss radiative corrections to tree level coupling constants, presenting a procedure that effectively resums the largest such corrections to all orders in perturbation theory. Finally, we comment on the size of nonperturbative contributions to the coupling constants.