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First observation of the decay $B_s^0 \to K^-\mu^+\nu_\mu$ and measurement of $|V_{ub}|/|V_{cb}|$

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Abstract

The first observation of the suppressed semileptonic $B_s^0 \to K^-\mu^+\nu_\mu$ decay is reported. Using a data sample recorded in {\it pp} collisions in 2012 with the LHCb detector, corresponding to an integrated luminosity of 2 $\mathrm{fb}^{-1}$, the branching fraction $\mathcal{B}(B_s^0 \to K^-\mu^+\nu_\mu)$ is measured to be $(1.06\pm0.05 (\mathrm{stat})\pm0.08 (\mathrm{syst}))\times 10^{-4}$, where the first uncertainty is statistical and the second one represents the combined systematic uncertainties. The decay $B_s^0 \to D_s^-\mu^+\nu_\mu$, where $D_s^-$ is reconstructed in the final state $K^+K^-\pi^-$, is used as a normalization channel to minimize the experimental systematic uncertainty. Theoretical calculations on the form factors of the $B_s^0 \to K^-$ and $B_s^0 \to D_s^-$ transitions are employed to determine the ratio of the CKM matrix elements ${|V_{ub}|}/{|V_{cb}|}$ at low and high $B_s^0 \to K^-$ momentum transfer.

Figures and captions

Distribution of $m_{\rm corr}$ for (top) the signal $ B ^0_ s \rightarrow K ^- \mu ^+ \nu_\mu$, with (left) $ q^2 <7\text{ Ge V} ^2 /c^4 $ and (right) $ q^2 >7\text{ Ge V} ^2 /c^4 $, and (bottom) the normalization $ B ^0_ s \rightarrow D ^-_ s \mu ^+ \nu_\mu$ channel. The points represent data, while the resulting fit components are shown as histograms.

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Measurements of $|V_{ub}|/|V_{cb}|$ in this Letter and in Ref [7], and ratio inferred from the PDG [27] averages of exclusive $|V_{ub}|$ and $|V_{cb}|$ measurements, where the $\Lambda ^0_ b \rightarrow p\mu ^- \bar{\nu}_\mu$ result is not included. The form factor calculation used in each case is mentioned [32,33,34].

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Tables and captions

Relative systematic uncertainties on the ratio $\mathcal{B}( B ^0_ s \rightarrow K ^- \mu ^+ \nu_\mu)/\mathcal{B}( B ^0_ s \rightarrow D ^-_ s \mu ^+ \nu_\mu)$, in percent.

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Supplementary Material [file]

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Created on 06 March 2021.