Heavy-quark 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-quark meson spectra, demonstrating significant improvements over the Fermilab action in most cases.

Contribution

It introduces and tests the higher-order Oktay-Kronfeld action for heavy-quark systems, showing practical improvements in lattice QCD calculations.

Findings

OK action results are closer to the continuum limit than Fermilab action.

Most mass splittings with OK action show reduced discretization effects.

Hyperfine splitting results are inconclusive due to large statistical errors.

Abstract

The Oktay-Kronfeld (OK) action extends the Fermilab improvement program for massive Wilson fermions to higher order in suitable power-counting schemes. It includes dimension-six and -seven operators necessary for matching to QCD through order ${\mathrm{O}}(\Lambda^3/m_Q^3)$ in HQET power counting, for applications to heavy-light systems, and ${\mathrm{O}}(v^6)$ in NRQCD power counting, for applications to quarkonia. In the Symanzik power counting of lattice gauge theory near the continuum limit, the OK action includes all ${\mathrm{O}}(a^2)$ and some ${\mathrm{O}}(a^3)$ terms. To assess whether the theoretical improvement is realized in practice, we study combinations of heavy-strange and quarkonia masses and mass splittings, designed to isolate heavy-quark discretization effects. We find that, with one exception, the results obtained with the tree-level-matched OK action are significantly closer to the continuum limit than the results obtained with the Fermilab action. The exception is the hyperfine splitting of the bottom-strange system, for which our statistical errors are too large to draw a firm conclusion. These studies are carried out with data generated with the tadpole-improved Fermilab and OK actions on 500 gauge configurations from one of MILC's $a\approx0.12$~fm, $N_f=2+1$-flavor, asqtad-staggered ensembles.