New determination of |Vub/Vcb| from $$ {B}_s^0 $$ → {K−, $$ {D}_s^{-} $$}μ+ν

Abstract

Abstract We update the full set of $$ \overline{B} $$ B ¯ s → K form factors using light-cone sum rules with an on-shell kaon. Our approach determines the relevant sum rule parameters — the duality thresholds — from a Bayesian fit for the first time. Using a modified version of the Boyd-Grinstein-Lebed parametrisation, we combine our sum rule results at low momentum transfer q2 with more precise lattice QCD results at large q2. We obtain a consistent description of the form factors in the full q2 range. Applying these results to a recent LHCb measurement of branching ratios for the decays $$ {B}_s^0 $$ B s 0 → {K−, $$ {D}_s^{-} $$ D s − }μ+νμ, we determine the ratio of Cabibbo-Kobayashi-Maskawa elements$$ {\left|\frac{V_{ub}}{V_{cb}}\right|}_{q^2<7\;{\textrm{GeV}}^2}=0.0681\pm 0.0040\kern0.5em \textrm{and}\kern0.5em {\left|\frac{V_{ub}}{V_{cb}}\right|}_{q^2>7\;{\textrm{GeV}}^2}=0.0801\pm 0.0047, $$ V ub V cb q 2 < 7 GeV 2 = 0.0681 ± 0.0040 and V ub V cb q 2 > 7 GeV 2 = 0.0801 ± 0.0047 , which are mutually compatible at the 1.9σ level. We further comment on the sensitivity to Beyond the Standard Model effects through measurements of the shape of $$ {B}_s^0 $$ B s 0 → K−μ+νμ decays, in light of recent limits on such effects from other exclusive b → uℓν processes.