Measurement of the CKM matrix elements $|V_{ub}|/|V_{cb}| $ from semileptonic $B_s$-meson decays at LHCb

The Cabibbo-Kobayashi-Maskawa matrix elements $|V_{ub}|$ and $|V_{cb}|$ describe the coupling between beauty to up and beauty to charm quarks in the electroweak interaction, respectively. They can be measured using semileptonic $B$-decays which are either fully reconstructed or in an inclusive way. A discrepancy exceeding 3 standard deviations is observed which is a long-standing puzzle of flavor physics. I will discuss a new measurement made by LHCb using the decay $B_s^0 \to K^- \mu^+ \nu_{\mu}$, which is observed for the first time and can be used together with its normalization channel $B_s^0 \to D_s^- \mu^+ \nu_{\mu}$ to extract $|V_{ub}|/|V_{cb}|$ in different regions of the momentum transfer $q^2$ using theoretical form factor predictions.