New determination of |V ub /V cb | from B s 0 $$ {B}_s^0 $$ → {K − , D s − $$ {D}_s^{-} $$ }μ + ν

Abstract

Abstract We update the full set of B ¯ $$ \overline{B} $$ 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 q 2 with more precise lattice QCD results at large q 2. We obtain a consistent description of the form factors in the full q 2 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 + ν μ , we determine the ratio of Cabibbo-Kobayashi-Maskawa elements V ub V cb q 2 7 GeV 2 = 0.0801 ± 0.0047 , $$ {\left|\frac{V_{ub}}{V_{cb}}\right|}_{q^27\;{\textrm{GeV}}^2}=0.0801\pm 0.0047, $$ 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 + ν μ decays, in light of recent limits on such effects from other exclusive b → uℓν processes.

Keywords

• Bottom Quarks
• CKM Parameters
• Semi-Leptonic Decays