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

• Published in: arXiv.org 2017-01
• Main Authors: Bailey, Jon A, Yong-Chull Jang, Lee, Weonjong, DeTar, Carleton, Kronfeld, Andreas S, Oktay, Mehmet B
• Format: Article
• Language: English
• Subjects: Fermions; Flavor (particle physics); Gauge theory; Quarks
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.1701.00345

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.