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

Jon A. Bailey, Carleton DeTar, Yong-Chull Jang, Andreas S. Kronfeld, Weonjong Lee, Mehmet B. Oktay
2017 European Physical Journal C: Particles and Fields  
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
more » ... 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.
doi:10.1140/epjc/s10052-017-5266-y fatcat:tk6ckcbvqfckzd7hzj7bjjmroq