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 on MILC lattices, demonstrating improved accuracy over previous methods.

Contribution

It introduces and tests the OK action with higher-order operators for better heavy-quark discretization error reduction in lattice QCD simulations.

Findings

Improved heavy-meson mass calculations on finer lattices.

Reduced discretization errors compared to previous actions.

Enhanced agreement with theoretical expectations.

Abstract

We present heavy-meson spectrum results obtained using the Oktay--Kronfeld (OK) action on MILC asqtad lattices. The OK action was designed to improve the heavy-quark action of the Fermilab formulation, such that heavy-quark discretization errors are reduced. The OK action includes dimension-6 and -7 operators necessary for tree-level matching to QCD through order $\mathrm{O}(\Lambda^3/m_Q^3)$ for heavy-light mesons and $\mathrm{O}(v^6)$ for quarkonium, or, equivalently, through $\mathrm{O}(a^2)$ with some $\mathrm{O}(a^3)$ terms with Symanzik power counting. To assess the improvement, we extend previous numerical tests with heavy-meson masses by analyzing data generated on a finer ($a \approx 0.12\;$fm) lattice with the correct tadpole factors for the $c_5$ term in the action. We update the analyses of the inconsistency parameter and the hyperfine splittings for the rest and kinetic masses.