$B\to V\ell^+\ell^-$ in the Standard Model from Light-Cone Sum Rules

Abstract

We present $B_q\to\rho$, $B_q\to\omega$, $B_q\to K^*$, $B_s\to K^*$ and $B_s\to \phi$ form factors from light-cone sum rules (LCSR) at $\mathcal{O}(\alpha_s)$ for twist-2 and 3 and $\mathcal{O}(\alpha_s^0)$ for twist-4 with updated hadronic input parameters. Three asymptotic light-cone distribution amplitudes of twist-$4$ (and $5$) are determined, necessary for the form factors to obey the equations of motion. It is argued that the latter constrain the uncertainty of tensor-to-vector form factor ratios thereby improving the prediction of zeros of helicity amplitudes of major importance for $B\to K^*\ell\ell$ angular observables. We provide easy-to-use fits to the LCSR results, including the full error correlation matrix, in all modes at low $q^2$ as well as combined fits to LCSR and lattice results covering the entire kinematic range for $B_q\to K^*$, $B_s\to K^*$ and $B_s\to \phi$. The error correlation matrix avoids the problem of overestimating the uncertainty in phenomenological applications. Using the new form factors and recent computations of non-factorisable contributions we provide Standard Model predictions for $B\to K^*\gamma$ as well as $B\to K^*\ell^+\ell^-$ and $B_s\to\phi\mu^+\mu^-$ at low dilepton invariant mass. Employing our $B \to (\rho,\omega) $ form factor results we extract the CKM element $|V_\mathrm{ub}|$ from the semileptonic decays $B\to(\rho,\omega) \ell\nu$ and find good agreement with other exclusive determinations.