Phenomenology of semileptonic B-meson decays with form factors from lattice QCD

Abstract

We study the exclusive semileptonic $B$-meson decays $B\to K(\pi ){\ell }^{+}{\ell }^{-}$, $B\to K(\pi )\nu \bar{\nu }$, and $B\to \pi \tau \nu$, computing observables in the Standard model using the recent lattice-QCD results for the underlying form factors from the Fermilab Lattice and MILC Collaborations. These processes provide theoretically clean windows into physics beyond the Standard Model because the hadronic uncertainties are now under good control for suitably binned observables. For example, the resulting partially integrated branching fractions for $B\to \pi {\mu }^{+}{\mu }^{-}$ and $B\to K{\mu }^{+}{\mu }^{-}$ outside the charmonium resonance region are 1-2$\sigma$ higher than the LHCb Collaboration's recent measurements, where the theoretical and experimental errors are commensurate. The combined tension is 1.7$\sigma$. Combining the Standard-Model rates with LHCb's measurements yields values for the Cabibbo-Kobayashi-Maskawa (CKM) matrix elements $|V_{td}|=7.45(69)\times 10^{-3}$, $|V_{ts}|=35.7(1.5)\times 10^{-3}$, and $|V_{td}/V_{ts}|=0.201(20)$, which are compatible with the values obtained from neutral $B_{(s)}$-meson oscillations and have competitive uncertainties. Alternatively, taking the CKM matrix elements from unitarity, we constrain new-physics contributions at the electroweak scale. The constraints on the Wilson coefficients $\mathrm{Re}(C_9)$ and $\mathrm{Re}(C_{10})$ from $B\to \pi {\mu }^{+}{\mu }^{-}$ and $B\to K{\mu }^{+}{\mu }^{-}$ are competitive with those from $B\to K^{\ast }{\mu }^{+}{\mu }^{-}$, and display a 2.0$\sigma$ tension with the Standard Model. Our predictions for $B\to K(\pi )\nu \bar{\nu }$ and $B\to \pi \tau \nu$ are close to the current experimental limits.

V3: Typos in Eq. (5.13) and text corrected. Reference added. Version published in Phys. Rev. D

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