Anomalies in Hadronic $B \to VV$ Decays

Recently, a fit of charmless $B\to PP$ decays ($B \in \{B^0, B^+, B_s^0\}$, $P \in \{ \pi, K, \eta, \eta' \}$) to the latest data was performed under the assumption of flavour SU(3) symmetry [SU(3)$_F$]. It was found that there is a $4.1\sigma$ disagreement with the SU(3)$_F$ limit of the Standard Model [$\rm SM_{SU(3)_F}$]. In this paper, we extend this analysis to charmless $B \to VV$ decays ($V \in \{\rho, K^*, \phi, \omega\}$). The fit examining $B \to \rho K^*$ decays, assuming only isospin symmetry, is found to be acceptable. When we fit to $B \to VV$ decays with $V \in \{ \rho, K^* \}$ within SU(3)$_F$, we find a $5.2\sigma$ discrepancy with SM$_{SU(3)_F}$. Finally, when $B \to VV$ decays with $V \in \{ \rho, K^*, \phi, \omega \}$ are considered, the discrepancy grows to $>7\sigma$. The theoretical input in this analysis is modest, so our results are quite rigorous, group theoretically, and hold almost exactly in the SU(3)$_F$ limit. Although it seems unlikely that the introduction of $\sim 30$% SU(3)$_F$-breaking effects can account for this discrepancy, this must be verified.