Padé approximants to <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>B</mml:mi><mml:mo stretchy="false">→</mml:mo><mml:mi>π</mml:mi><mml:mo>ℓ</mml:mo><mml:msub><mml:mi>ν</mml:mi><mml:mo>ℓ</mml:mo></mml:msub></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>B</mml:mi><mml:mi>s</mml:mi></mml:msub><mml:mo stretchy="false">→</mml:mo><mml:mi>K</mml:mi><mml:mo>ℓ</mml:mo><mml:msub><mml:mi>ν</mml:mi><mml:mo>ℓ</mml:mo></mml:msub></mml:math> and determination of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mo stretchy="false">|</mml:mo><mml:msub><mml:mi>V</mml:mi><mml:mrow><mml:mi>u</mml:mi><mml:mi>b</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">|</mml:mo></mml:math>
Sergi Gonzàlez-Solís, Pere Masjuan, Camilo Rojas
Abstract
In light of the first observation of the semileptonic decay ${B}_{s}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ by the LHCb Collaboration, we revisit the determination of the Cabibbo-Kobayashi-Maskawa parameter $|{V}_{ub}|$ from exclusive semileptonic $B$-meson decays. A controlled theoretical input on the Standard Model $B\ensuremath{\rightarrow}\ensuremath{\pi}$ and ${B}_{s}\ensuremath{\rightarrow}K$ vector and scalar form factors from Lattice QCD in the large ${q}^{2}$ region, in combination with experimental measurements of the differential $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ and ${B}_{s}^{0}\ensuremath{\rightarrow}{K}^{\ensuremath{-}}{\ensuremath{\mu}}^{+}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ branching ratio distributions, has allowed us determine $|{V}_{ub}|=3.86(11)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ and $|{V}_{ub}|=3.58(9)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ from the analyses of the individual decay channels, respectively, and $|{V}_{ub}|=3.68(5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$ from a simultaneous analysis of both decays, which is only a 1.4% error and differs by $1.8\ensuremath{\sigma}$ with respect to the value from inclusive determinations $|{V}_{ub}|=4.25(12{)}_{\ensuremath{-}14}^{+15}(23)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. Our results are based on the use of Pad\'e approximants to the participating form factors, highlighting the importance of the decay ${B}_{s}\ensuremath{\rightarrow}K\ensuremath{\mu}{\ensuremath{\nu}}_{\ensuremath{\mu}}$ in complementing the traditional $B\ensuremath{\rightarrow}\ensuremath{\pi}\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ one in the exclusive determination of $|{V}_{ub}|$ and allowing us to obtain, to the best of our knowledge, the first correlated results for the $B\ensuremath{\rightarrow}\ensuremath{\pi}$ and ${B}_{s}\ensuremath{\rightarrow}K$ vector and scalar form factors. We hope that our study strengthens the case for precise measurements of the differential ${B}_{s}\ensuremath{\rightarrow}K\ensuremath{\ell}{\ensuremath{\nu}}_{\ensuremath{\ell}}$ decay rate with a finer resolution of the ${q}^{2}$ bins, as it would definitely allow achieving more conclusive results for $|{V}_{ub}|$.