Measurement of the semileptonic branching fraction of the $B_s$ meson

We report a measurement of the inclusive semileptonic branching fraction of the $B_s$ meson using data collected with the BABAR detector in the center-of-mass energy region above the ${\rm Y}(4S)$ resonance. We use the inclusive yield of $\varphi$ mesons and the $\varphi$ yield in association with a high-momentum lepton to perform a simultaneous measurement of the semileptonic branching fraction and the production rate of $B_s$ mesons relative to all $B$ mesons as a function of center-of-mass energy. The inclusive semileptonic branching fraction of the $B_s$ meson is determined to be $\mathcal{B}(B_s\to \ell \nu X)={9.5}_{-2.0}^{+2.5}(\mathrm{stat}{)}_{-1.9}^{+1.1}(\mathrm{syst})\%$, where $\ell$ indicates the average of $e$ and $\mu$.

Figure 1

Invariant mass distribution of $\varphi \to K^{+}{K}^{-}$ candidates in the energy bin $10.8275\mathrm{GeV}\le E_{\mathrm{CM}}\le 10.8425\mathrm{GeV}$: (a) inclusive $\varphi$ candidates; (b) $\varphi$-lepton candidates. The background shape is shown by the dashed curve and the total fit by the solid curve.

Figure 2

Relative (a) event, (b) $\varphi$, and (c) $\varphi$-lepton yields, normalized to the ${\mu }^{+}{\mu }^{-}$ yields. Corrections for detector efficiency have not been applied. The dotted vertical line indicates the $B_s$ production threshold.

Figure 3

Results for the fraction $f_s$ as a function of $E_{\mathrm{CM}}$. The inner error bars show the statistical uncertainties and the outer error bars the statistical and systematic uncertainties added in quadrature. The dotted line denotes the $B_s$ threshold.

Figure 4

${\chi }^2$ formed from the measured and expected yields, as described in the text, as a function of the semileptonic branching fraction. Note that since we express the branching fraction as the average of the $e$ and $\mu$ channels, the physical bound is 50%.