$B$- and $D$-meson leptonic decay constants from four-flavor lattice QCD

Abstract

We calculate the leptonic decay constants of heavy-light pseudoscalar mesons with charm and bottom quarks in lattice quantum chromodynamics on four-flavor QCD gauge-field configurations with dynamical $u$, $d$, $s$, and $c$ quarks. We analyze over twenty isospin-symmetric ensembles with six lattice spacings down to $a\approx 0.03$~fm and several values of the light-quark mass down to the physical value $\frac{1}{2}(m_u+m_d)$. We employ the highly-improved staggered-quark (HISQ) action for the sea and valence quarks; on the finest lattice spacings, discretization errors are sufficiently small that we can calculate the $B$-meson decay constants with the HISQ action for the first time directly at the physical $b$-quark mass. We obtain the most precise determinations to-date of the $D$- and $B$-meson decay constants and their ratios, $f_{D^{+}}=212.7(0.6)$~MeV, $f_{D_s}=249.9(0.4)$~MeV, $f_{D_s}/f_{D^{+}}=1.1749(16)$, $f_{B^{+}}=189.4(1.4)$~MeV, $f_{B_s}=230.7(1.3)$~MeV, $f_{B_s}/f_{B^{+}}=1.2180(47)$, where the errors include statistical and all systematic uncertainties. Our results for the $B$-meson decay constants are three times more precise than the previous best lattice-QCD calculations, and bring the QCD errors in the Standard-Model predictions for the rare leptonic decays $\overline{\mathcal{B}}(B_s\to {\mu }^{+}{\mu }^{-})=3.64(11)\times 10^{-9}$, $\overline{\mathcal{B}}(B^0\to {\mu }^{+}{\mu }^{-})=1.00(3)\times 10^{-10}$, and $\overline{\mathcal{B}}(B^0\to {\mu }^{+}{\mu }^{-})/\overline{\mathcal{B}}(B_s\to {\mu }^{+}{\mu }^{-})=0.0273(9)$ to well below other sources of uncertainty. As a byproduct of our analysis, we also update our previously published results for the light-quark-mass ratios and the scale-setting quantities $f_{p4s}$, $M_{p4s}$, and $R_{p4s}$. We obtain the most precise lattice-QCD determination to date of the ratio $f_{K^{+}}/f_{{\pi }^{+}}=1.1950{(}_{-23}^{+16})$~MeV.

Errors related to the standard model prediction for the rare leptonic decays are fixed in the abstract and Eqs. (7.44), (7.45), and (8.3)

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