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

The first observation of the suppressed semileptonic $B_s^0 to K^-mu^+ u_mu$ 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 mbox{$mathcal{B}(B_s^0 to K^-mu^+ u_mu)$} is measured to be $(1.06pm0.05~(mathrm{stat})pm0.08~(mathrm{syst}))times 10^{-4}$, where the first uncertainty is statistical and the second one represents the combined systematic uncertainties. The decay $B_s^0 to D_s^-mu^+ u_mu$, 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.