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

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Abstract

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 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.

Figures and captions

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

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Two-dimensional distributions of $ p_{\perp} ( D ^-_ s )$ vs. $ m_{\text{corr}}$ for simulated (top-left) $ B ^0_ s \rightarrow D ^-_ s \mu ^+ \nu _\mu $ decays, (top-right) $ B ^0_ s \rightarrow D _{ s }^{*-} \mu ^+ \nu _\mu $ decays, (bottom-left) background decays from $ B ^0_ s $ 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 ^0_ s $ decays. The background components are grouped according to their shapes in the $ m_{\text{corr}}$ vs. $ p_{\perp} ( D ^-_ s )$ space. The requirement $ p_{\perp} ( D ^-_ s ) [\text{ Ge V /}c ] < 1.5 + 1.1 \times ( m_{\text{corr}} [\text{ Ge V /}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. ??? to further suppress background and assess the systematic uncertainty due to the residual contamination.

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(Top) Distribution of true value of the $w$ recoil variable versus reconstructed $ p_{\perp} ( D ^-_ s )$ for (left) $ B ^0_ s \rightarrow D ^-_ s \mu ^+ \nu _\mu $ and (right) $ B ^0_ s \rightarrow 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 ^0_ s \rightarrow 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 \rightarrow D _{( s )}^- \mu ^+ \nu _\mu $ decays show similar features.

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

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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.

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Background-subtracted distribution of $ p_{\perp} ( D ^-_ s )$ for (left) $ B ^0_ s \rightarrow D ^-_ s \mu ^+ \nu _\mu $ and (right) $ B ^0_ s \rightarrow 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.

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Animated gif made out of all figures.

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Tables and captions

Functions describing the differential decay rate of $ B \rightarrow D ^{*} \mu\nu$ decays, separately for the cases in which the $ D ^{*}$ meson decays to $ D \gamma$ or $ D \pi^0$.

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Pole masses for the $ B _ c ^+$ resonances considered in the BGL parameterization of the $ B ^0_ s $ decays, with the $\tilde{\chi}_{J^P}(0)$ constants of the outer functions and the $C_{J^P}$ constants of the Blaschke factors \cite{Bigi:2017njr}. For $ B ^0$ decays, the Blaschke factors do not include the last $1^-$ resonance and $C_{1^\pm}$ have both unit value.

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External inputs based on experimental measurements.

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External inputs based on theory calculations. The values and their correlations are derived in Appendix ???, based on Ref. \cite{McLean:2019qcx}.

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Fit results in the CLN parametrization. The uncertainty is split into two contributions, statistical $\text{ (stat)}$ and that due to the external inputs $\text{ (ext)}$ .

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Fit results in the BGL parametrization. The uncertainty is split into two contributions, statistical $\text{ (stat)}$ and that due to the uncertainty on the external inputs $\text{ (ext)}$ .

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Summary of the uncertainties affecting the measured parameters. The upper section reports the systematic uncertainties due to the external inputs $\text{ (ext)}$ , the middle section those due to the experimental methods $\text{ (syst)}$ , and the lower section the statistical uncertainties $\text{ (stat)}$ . For the first source of uncertainty the multiplication by $\tau$ holds only for the $ |V_{ c b }|$ fits.

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Coefficients of the $f_+(w)$ form factor in the BCL parametrization from Ref. \cite{McLean:2019qcx}.

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Detailed results for the $ |V_{ c b }|$ fits. The uncertainties on the free parameters include the statistical contribution and that due to the external inputs.

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Correlations (in %) for the $ |V_{ c b }|$ fit in the CLN parametrization. The top section includes contributions from statistical sources and external inputs, the bottom section contributions from the experimental systematic uncertainties.

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Correlations (in %) for the $ |V_{ c b }|$ fit in the BGL parametrization. The top section includes contributions from statistical sources and external inputs, the bottom section contributions from the experimental systematic uncertainties.

[Error creating the table]

Detailed results for the $\mathcal{R}$ and $\mathcal{R}^*$ fit. The uncertainties on the free parameters include the statistical contribution and that due to the external inputs.

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Correlations (in %) for the $\mathcal{R}$ and $\mathcal{R}^*$ fit. The top section includes contributions from statistical sources and external inputs, the bottom section contributions from the experimental systematic uncertainties.

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Supplementary Material [file]

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Created on 27 February 2021.