Chiral Extrapolation of Lattice Data for Heavy Meson Hyperfine Splittings

TL;DR

This paper examines the chiral extrapolation of lattice data for heavy meson hyperfine splittings, comparing models and chiral perturbation theory to understand discrepancies with experimental values.

Contribution

It introduces two models to guide the analytic background in chiral extrapolation of lattice data for heavy meson hyperfine splittings.

Findings

Chiral loop corrections decrease hyperfine splittings.

Extrapolated splittings remain below experimental values.

Models show limited impact on matching experimental data.

Abstract

We investigate the chiral extrapolation of the lattice data for the light-heavy meson hyperfine splittings D^*-D and B^*-B to the physical region for the light quark mass. The chiral loop corrections providing non-analytic behavior in m_\pi are consistent with chiral perturbation theory for heavy mesons. Since chiral loop corrections tend to decrease the already too low splittings obtained from linear extrapolation, we investigate two models to guide the form of the analytic background behavior: the constituent quark potential model, and the covariant model of QCD based on the ladder-rainbow truncation of the Dyson-Schwinger equations. The extrapolated hyperfine splittings remain clearly below the experimental values even allowing for the model dependence in the description of the analytic background.