Coulomb Artifacts and Bottomonium Hyperfine Splitting in Lattice NRQCD

TL;DR

This paper investigates Coulomb artifacts in lattice NRQCD calculations of heavy quarkonium, revealing that naive matching introduces errors and proposing an improved method that yields more accurate bottomonium hyperfine splitting results.

Contribution

It demonstrates that proper asymptotic expansion matching controls discretization errors and resolves discrepancies in hyperfine splitting predictions.

Findings

Naive perturbative matching causes spurious Coulomb artifacts.

Correct matching based on asymptotic expansion improves accuracy.

Predicted bottomonium hyperfine splitting: 52.9 ± 5.5 MeV.

Abstract

We study the role of the lattice artifacts associated with the Coulomb binding effects in the analysis of the heavy quarkonium within lattice NRQCD. We find that a "naive" perturbative matching generates spurious linear Coulomb artifacts, which result in a large systematic error in the lattice predictions for the heavy quarkonium spectrum. This effect is responsible, in particular, for the discrepancy between the recent determinations of the bottomonium hyperfine splitting in the radiatively improved lattice NRQCD [1, 2]. We show that the correct matching procedure which provides full control over discretization errors is based on the asymptotic expansion of the lattice theory about the continuum limit, which gives $M_{\Upsilon(1S)}-M_{\eta_b(1S)}=52.9\pm 5.5~{\rm MeV}$ [1].