Tuning the hopping parameter in the Oktay-Kronfeld action for charm and bottom quarks on a MILC HISQ ensemble

TL;DR

This paper presents the tuning of the hopping parameter for charm and bottom quarks using the Oktay-Kronfeld action on a specific HISQ ensemble, providing key results for heavy meson properties.

Contribution

It introduces a method for tuning the hopping parameter in the Oktay-Kronfeld action for heavy quarks on a MILC HISQ ensemble, with new estimates of hyperfine splittings and the inconsistency parameter.

Findings

Estimated hyperfine splittings for heavy-light and heavy-heavy mesons.

Evaluated the inconsistency parameter for the heavy meson system.

Provided tuned hopping parameters for charm and bottom quarks.

Abstract

The first step in the calculation of semi-leptonic form factors in the decay of heavy mesons is the tuning of the hopping parameter $\kappa$ for the charm and bottom quark masses. Results for the Oktay-Kronfeld (OK) action are presented for one $N_f=2+1+1$ HISQ ensemble generated by the MILC collaboration at $a\approx 0.12\,\mathrm{fm}$ and $M_\pi\approx 310$ MeV. Estimates of hyperfine splitting of heavy-light and heavy-heavy mesons are presented and the inconsistency parameter is evaluated.