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

TL;DR

This paper accurately determines bottom quark masses, bottom meson spectra, and decay constants using improved lattice QCD techniques across multiple ensembles, achieving high precision and reliable continuum extrapolation.

Contribution

It introduces a non-perturbative renormalization method and demonstrates effective calculations of bottom quark properties on coarser lattices with controlled discretization errors.

Findings

Bottom quark mass: 4.185(37) GeV in MSbar scheme.

Full S-wave bottom meson spectrum with <0.1% uncertainty.

Decay constants and ratios for bottom mesons provided.

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.