The first observation of the suppressed semileptonic $B_s^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ decay is reported. Using a data sample recorded in $pp$ 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 $[1.06\pm 0.05(\mathrm{stat})\pm 0.08(\mathrm{syst})]\times {10}^{-4}$, 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 Cabibbo-Kobayashi-Maskawa matrix elements $|V_{ub}|/|V_{cb}|$ at low and high $B_s^0\to K^{-}$ momentum transfer.

• Received 9 December 2020
• Accepted 21 January 2021

DOI:https://doi.org/10.1103/PhysRevLett.126.081804

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