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

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.