Measurement of $|V_{cb}|$ with $B_s^0\to D_s^{(*)-}{\mu }^{+}{\nu }_{\mu }$ decays

The element $|V_{cb}|$ of the Cabibbo-Kobayashi-Maskawa matrix is measured using semileptonic $B_s^0$ decays produced in proton-proton collision data collected with the LHCb detector at center-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of $3{\mathrm{fb}}^{-1}$. Rates of $B_s^0\to D_s^{-}{\mu }^{+}{\nu }_{\mu }$ and $B_s^0\to D_s^{*-}{\mu }^{+}{\nu }_{\mu }$ decays are analyzed using hadronic form-factor parametrizations derived either by Caprini, Lellouch and Neubert (CLN) or by Boyd, Grinstein and Lebed (BGL). The measured values of $|V_{cb}|$ are $(41.4\pm 0.6\pm 0.9\pm 1.2)\times {10}^{-3}$ and $(42.3\pm 0.8\pm 0.9\pm 1.2)\times {10}^{-3}$ in the CLN and BGL parametrization, respectively. The first uncertainty is statistical, the second systematic, and the third is due to the external inputs used in the measurement. These results are in agreement with those obtained from decays of $B^{+}$ and $B^0$ mesons. They are the first determinations of $|V_{cb}|$ at a hadron-collider experiment and the first using $B_s^0$ meson decays.

Figure 1

Graphical representation of the helicity angles in $B\to D^{*}\mu \nu$ decays. The definitions are provided in the text.

Figure 2

Two-dimensional distributions of $p_{\perp }(D_s^{-})$ versus $m_{\text{corr}}$ for simulated (top left) $B_s^0\to D_s^{-}{\mu }^{+}{\nu }_{\mu }$ decays, (top right) $B_s^0\to D_s^{*-}{\mu }^{+}{\nu }_{\mu }$ decays, (bottom left) background decays from $B_s^0$ feed-down and $b$-hadron decays to a doubly charmed final state, and (bottom right) background decays from $B^0$ cross feed and semitauonic $B_s^0$ decays. The background components are grouped according to their shapes in the $m_{\text{corr}}$ versus $p_{\perp }(D_s^{-})$ space. The requirement $p_{\perp }(D_s^{-})[\mathrm{GeV}/c]<1.5+1.1\times (m_{\text{corr}}[\mathrm{GeV}/c^2]-4.5)$ is drawn as a dashed line; the dot-dashed line shows the tighter requirement, applied on top of the baseline, which is used in Sec. 8 to further suppress background and assess the systematic uncertainty due to the residual contamination.

Figure 3

(Top) Distribution of true value of the $w$ recoil variable versus reconstructed $p_{\perp }(D_s^{-})$ for (left) $B_s^0\to D_s^{-}{\mu }^{+}{\nu }_{\mu }$ and (right) $B_s^0\to D_s^{*-}{\mu }^{+}{\nu }_{\mu }$ simulated decays. (Bottom) Distribution of the true values of (left) $\cos {\theta }_D$ and (right) $\cos {\theta }_{\mu }$ versus reconstructed $p_{\perp }(D_s^{-})$ for $B_s^0\to D_s^{*-}{\mu }^{+}{\nu }_{\mu }$ simulated decays. Only simulated candidates that fulfill the selection requirements are shown. In each histogram the solid line represents the average of the variable displayed on the vertical axis as a function of $p_{\perp }(D_s^{-})$. The distributions of $B^0\to D^{*-}{\mu }^{+}{\nu }_{\mu }$ decays show similar features.

Figure 4

Distribution of (left) $m_{\text{corr}}$ and (right) $p_{\perp }(D^{-})$ for the inclusive sample of reference $D^{-}{\mu }^{+}$ candidates, with fit projections overlaid.

Figure 5

Distribution of (left) $m_{\text{corr}}$ and (right) $p_{\perp }(D_s^{-})$ for the inclusive sample of signal $D_s^{-}{\mu }^{+}$ candidates, with fit projections based on the CLN parametrization overlaid. The projections of the two physics background components are merged together for displaying purposes.

Figure 6

Background-subtracted distribution of $p_{\perp }(D_s^{-})$ for (left) $B_s^0\to D_s^{-}{\mu }^{+}{\nu }_{\mu }$ and (right) $B_s^0\to D_s^{*-}{\mu }^{+}{\nu }_{\mu }$ decays obtained from the fit based on the (red closed points, dashed line) CLN and (blue open points, solid line) BGL parametrizations, with corresponding fit projections overlaid.