Accurate B meson and Bottomonium masses and decay constants from the tadpole improved clover ensembles

Abstract

We present a determination of the bottom quark mass, the masses of S-wave bottom mesons, and their decay constants using an anisotropic clover fermion discretization for the heavy quark, on $2+1$ flavor isotropic QCD ensembles. Our analysis is based on 16 ensembles spanning 6 lattice spacings, with pion masses in the range of 135-350 MeV and several values of the strange quark mass. We demonstrate that the effective anisotropy parameter for the heavy quark approaches unity with controllable $\mathcal{O}(a^2)$ corrections. A non-perturbative renormalization procedure is developed and validated through predictions of the bottom quark mass and decay constants. This framework enables calculations at the physical $b$-quark mass even on lattices with spacing $a \sim 0.1$ fm, where $m_b a \sim 2.5$, while keeping discretization errors in hadronic matrix elements at the $\sim 10$% level which can be eliminated properly through the continuum extrapolation. Using the physical $\Upsilon$ mass as input, we obtain $m_b^{\overline{\mathrm{MS}}}(m_b) = 4.185(37)$ GeV and the full spectrum of S-wave bottom mesons with 0.1% uncertainty or less. Pseudoscalar and vector decay constants and their ratios for all kinds of S-wave bottom mesons are also provided.