Padé approximants to $B\to \pi \ell {\nu }_{\ell }$ and $B_s\to K\ell {\nu }_{\ell }$ and determination of $|V_{ub}|$

Abstract

In light of the first observation of the semileptonic decay $B_s^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ by the LHCb collaboration, we revisit the determination of the CKM parameter $|V_{ub}|$ from exclusive semileptonic $B$-meson decays. A controlled theoretical input on the Standard Model $B\to \pi$ and $B_s\to K$ vector and scalar form factors from Lattice QCD in the large $q^2$ region, in combination with experimental measurements of the differential $B\to \pi \ell {\nu }_{\ell }$ and $B_s^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ branching ratio distributions, has allowed us determine $|V_{ub}|=3.86(11)\times 10^{-3}$ and $|V_{ub}|=3.58(9)\times 10^{-3}$ from the analyses of the individual decay channels, respectively, and $|V_{ub}|=3.68(5)\times 10^{-3}$ from a simultaneous analysis of both decays, which is only a $1.4\%$ error and differs by $1.8\sigma$ with respect to the value from inclusive determinations $|V_{ub}|=4.25(12{)}_{-14}^{+15}(23)\times 10^{-3}$. Our results are based on the use of Padé approximants to the participating form factors, highlight the importance of the decay $B_s\to K\mu {\nu }_{\mu }$ in complementing the traditional $B\to \pi \ell {\nu }_{\ell }$ one in the exclusive determination of $|V_{ub}|$, and allow obtain, to the best of our knowledge, the first correlated results for the $B\to \pi$ and $B_s\to K$ vector and scalar form factors. We hope that our study strengthens the case for precise measurements of the differential $B_s\to K\ell {\nu }_{\ell }$ decay rate with a finer resolution of the $q^2$ bins, as it would definitely allow achieving more conclusive results for $|V_{ub}|$.

16 pages, 10 figures

References in corpus (13)

• Light-cone sum rules for $B\to \pi$ form factors revisited
• Study of B --> pi l nu and B --> rho l nu Decays and Determination of |V_ub|
• $B\to \pi \ell \nu$ and $B_s\to K\ell \nu$ form factors and $|V_{ub}|$ from 2+1-flavor lattice QCD with domain-wall light quarks and relativistic heavy quarks
• Can the differences in the determinations of $V_{ub}$ and $V_{cb}$ be explained by New Physics?
• Branching fraction and form-factor shape measurements of exclusive charmless semileptonic B decays, and determination of |V_{ub}|
• $B_s\to K\ell \nu$ form factors from lattice QCD
• B, Bs -> K form factors: an update of light-cone sum rule results
• Extrapolation and unitarity bounds for the $B\to \pi$ form factor
• The $\bar{B}\to \pi$ form factors from QCD and their impact on $|V_{ub}|$
• First observation of the decay $B_s^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ and a measurement of $|V_{ub}|/|V_{cb}|$
• A comprehensive study on the semileptonic decay of heavy flavor mesons
• Some Remarks on the Pade Unitarization of Low-Energy Amplitudes
• A closer look at the extraction of $|V_{ub}|$ from $B\to \pi l\nu$

Cited by in corpus (7)

• Form factors of $B\to \pi \ell \nu$ and a determination of $|V_{ub}|$ with Möbius domain-wall-fermions
• Heavy + heavy and heavy + light pseudoscalar to vector semileptonic transitions
• Investigating the ratio of CKM matrix elements $|V_{ub}|/|V_{cb}|$ from semileptonic decay $B_s^0\to K^{-}{\mu }^{+}{\nu }_{\mu }$ and kaon twist-2 distribution amplitude
• Extractions of $|V_{ub}|/|V_{cb}|$ from a combined study of the exclusive $b\to u(c)\ell {\nu }_{\ell }$ decays
• Loopy Determinations of $V_{ub}$ and $V_{cb}$
• Re-evaluation of the isoscalar mixing angle within selected mesonic nonets
• Determination of $B$-meson distribution amplitudes from $B\to \pi ,K,D$ transition form factors