QCD spin effects in the heavy hybrid potentials and spectra

TL;DR

This paper investigates the spin-dependent operators in heavy quarkonium hybrids using effective field theory, computing matching coefficients at short distances, and comparing results with lattice data to understand hybrid spectra.

Contribution

It derives new spin-dependent operators for hybrids, computes their matching coefficients in the short-distance regime, and extends lattice comparisons to different light-quark masses.

Findings

Matching coefficients factorize into perturbative and nonperturbative parts.

Explicit calculation of gluonic correlators for nonperturbative contributions.

Extended comparison with lattice data for various light-quark masses.

Abstract

The spin-dependent operators for heavy quarkonium hybrids have been recently obtained in a nonrelativistic effective field theory approach up to next-to-leading order in the heavy-quark mass expansion. In the effective field theory for hybrids several operators not found in standard quarkonia appear, including an operator suppressed by only one power of the heavy-quark mass. We compute the matching coefficients for these operators in the short heavy-quark-antiquark distance regime, $r\ll 1/\Lambda_{\rm QCD}$, by matching weakly-coupled potential NRQCD to the effective field theory for hybrids. In this regime the perturbative and nonperturbative contributions to the matching coefficients factorize, and the latter can be expressed in terms of purely gluonic correlators whose form we explicitly calculate with the aid of the transformation properties of the gluon fields under discrete symmetries. We detail our previous comparison with direct lattice computations of the charmonium hybrid spectrum, from which the unknown nonperturbative contributions can be obtained, and extend it to data sets with different light-quark masses.