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 $Υ$ 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.

Figures (27)

• Figure 1: The hyperfine splitting $\Delta^{\bar{b}b}_{\mathrm{HFS}} \equiv m_{\Upsilon} - m_{\eta_b}$, computed using different heavy-quark fermion actions at different lattice spacing. The discretization error is significantly suppressed by employing the anisotropic clover action without stout smearing, and both the usage of the anisotropic action and original link are relevant.
• Figure 2: Lattice-spacing dependence of the anisotropy parameter $1/\nu$ and the renormalization-factor ratio $Z^b_{V_i} / Z^b_{V_t}$. Both quantities are well described by polynomials in $a^2$ and extrapolate to unity in the continuum limit, consistent with the restoration of Euclidean isotropy.
• Figure 3: Lattice spacing dependence of ${B^{(*)}_{l/s/c}}$ masses and bottom quark mass $m_b^{\overline{\mathrm{MS}}}(2~\mathrm{GeV})$. In the upper two panels, the points at the continuum limit display the results from PDG ParticleDataGroup:2024cfk. The black points in the lowest panel show the results of $N_f$=2+1 and 2+1+1 from FLAG FlavourLatticeAveragingGroupFLAG:2024oxs average of $m_b^{\overline{\mathrm{MS}}}(2~\mathrm{GeV})$. Data points in the panels correspond to values after the extrapolation to the physical point using the fit parameters, and the optical bands show the discretization effects (see supplemental for further details).
• Figure 4: Lattice spacing dependence of the decay constants of $\eta_b$, $\Upsilon$ and $B^{(*)}_{l,s,c}$. FLAG FlavourLatticeAveragingGroupFLAG:2024oxs averages (for $f_{B/B_s}$) and values from literature are also shown for comparison. Data points in the panels correspond to values after the extrapolation to the physical point using the fit parameters, and the optical bands show the discretization effects (see supplemental for further details).
• Figure 5: CDFs of lattice spacings at different values of $\hat{\beta}$. The red data points along the CDF curves represent the results obtained from different fit ansatzes. The orange squares above indicate the model average values, where the inner error bar shows $\sigma_{\mathrm{stat+ansatz}}$ and the outer error bar shows the total error.