Bottomonium Hyperfine Splitting on the Lattice and in the Continuum

TL;DR

This paper refines lattice nonrelativistic QCD calculations of bottomonium hyperfine splitting, achieving results that align well with experimental data by incorporating radiative improvements and high-order corrections.

Contribution

It introduces a semianalytic evaluation of Wilson coefficients and uses the nonrelativistic renormalization group to improve hyperfine splitting predictions in lattice QCD.

Findings

Predicted hyperfine splitting: 52.9 ± 5.5 MeV

Results agree with Belle experimental measurements

Reconciles continuum and lattice QCD predictions

Abstract

We revise the analysis of the bottomonium hyperfine splitting within the lattice nonrelativistic QCD. The Wilson coefficients of the radiatively improved lattice action are evaluated by a semianalytic approach based on the asymptotic expansion about the continuum limit. The nonrelativistic renormalization group is used to estimate the high-order radiative corrections. Our result for the $1S$ hyperfine splitting is $M_{\Upsilon(1S)}-M_{\eta_b(1S)}=52.9\pm 5.5~{\rm MeV}$. It reconciles the predictions of the continuum and lattice QCD and is in very good agreement with the most accurate experimental measurement by Belle collaboration.