Eur. Phys. J. C (2017) 77: 768
https://doi.org/10.1140/epjc/s10052-017-5266-y

Regular Article - Theoretical Physics

Heavy-quark meson spectrum tests of the Oktay–Kronfeld action

¹ Department of Physics and Astronomy, Lattice Gauge Theory Research Center, FPRD, and CTP, Seoul National University, Seoul, 151-747, South Korea
² Department of Physics and Astronomy, University of Utah, Salt Lake City, UT, 84112, USA
³ Theoretical Physics Department, Fermi National Accelerator Laboratory, Batavia, IL, 60510, USA
⁴ Institute for Advanced Study, Technische Universität München, 85748, Garching, Germany
⁵ Department of Physics and Astronomy, University of Iowa, Iowa City, IA, 52242, USA
⁶ Theoretical Division T-2, Los Alamos National Laboratory, Los Alamos, NM, 87545, USA

^* e-mail: ypj@lanl.gov

Received: 9 May 2017
Accepted: 28 September 2017
Published online: 15 November 2017

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 in HQET power counting, for applications to heavy–light systems, and 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 and some 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 those 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  fm, -flavor, asqtad-staggered ensembles.