Update on Heavy-Meson Spectrum Tests of the Oktay--Kronfeld Action

TL;DR

This paper evaluates the Oktay--Kronfeld action's effectiveness in reducing discretization errors in heavy-meson spectrum calculations, demonstrating significant improvements over previous methods across charm and bottom quark masses.

Contribution

It provides updated numerical evidence that the Oktay--Kronfeld action improves heavy-quark discretization effects in meson spectrum calculations, extending previous analyses.

Findings

OK action reduces heavy-quark discretization effects

Results show significant improvement in meson spectrum accuracy

Hyperfine splitting near B_s mass inconclusive due to low statistics

Abstract

We present updated results of a numerical improvement test with heavy-meson spectrum for the Oktay--Kronfeld (OK) action. The OK action is an extension of the Fermilab improvement program for massive Wilson fermions including all dimension-six and some dimension-seven bilinear terms. Improvement terms are truncated by HQET power counting at $\mathrm{O}(\Lambda^3/m_Q^3)$ for heavy-light systems, and by NRQCD power counting at $\mathrm{O}(v^6)$ for quarkonium. They suffice for tree-level matching to QCD to the given order in the power-counting schemes. To assess the improvement, we generate new data with the OK and Fermilab action that covers both charm and bottom quark mass regions on a MILC coarse $(a \approx 0.12~\text{fm})$ $2+1$ flavor, asqtad-staggered ensemble. We update the analyses of the inconsistency quantity and the hyperfine splittings for the rest and kinetic masses. With one exception, the results clearly show that the OK action significantly reduces heavy-quark discretization effects in the meson spectrum. The exception is the hyperfine splitting of the heavy-light system near the $B_s$ meson mass, where statistics are too low to draw a firm conclusion, despite promising results.