Standard Model predictions for $B\to K{\ell }^{+}{\ell }^{-}$, $B\to K{\ell }_1^{-}{\ell }_2^{+}$ and $B\to K\nu \bar{\nu }$ using form factors from $N_f=2+1+1$ lattice QCD

Abstract

We use HPQCD's recent lattice QCD determination of $B\to K$ scalar, vector and tensor form factors to determine Standard Model differential branching fractions for $B\to K{\ell }^{+}{\ell }^{-}$, $B\to K{\ell }_1^{+}{\ell }_2^{-}$ and $B\to K\nu \overline{\nu }$. These form factors are calculated across the full $q^2$ range of the decay and have smaller uncertainties than previous work, particularly at low $q^2$. For $B\to K{\ell }^{+}{\ell }^{-}$ we find the Standard Model branching fraction in the $q^2$ region below the squared $J/\psi$ mass to exceed the LHCb results, with tensions as high as $4.2\sigma$ for $B^{+}\to K^{+}{\mu }^{+}{\mu }^{-}$. For the high $q^2$ region we see $2.7\sigma$ tensions. The tensions are much reduced by applying shifts to Wilson coefficients $C_9$ and $C_{10}$ in the effective weak Hamiltonian, moving them away from their Standard Model values consistent with those indicated by other $B$ phenomenology. We also update results for lepton-flavour ratios $R_e^{\mu }$ and $R_{\mu }^{\tau }$ and the `flat term', $F_H^{\ell }$ in the differential branching fraction for $\ell \in \{e,\mu ,\tau \}$. Our results for the form-factor-dependent contributions needed for searches for lepton-flavour-violating decays $B\to K{\ell }_1^{-}{\ell }_2^{+}$ achieve uncertainties of 7%. We also compute the branching fraction $\mathcal{B}(B\to K\nu \bar{\nu })$ with an uncertainty below 10%, for comparison with future experimental results.

arXiv comment28 pages, 38 figures. Version accepted by Physical Review D. Updated to reflect a change in the scale of alpha_EW

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