Anomalies in Hadronic $B$ Decays

In this paper, we perform fits to $B \to PP$ decays, where $B = \{B^0, B^+, B_s^0\}$ and the pseudoscalar $P = \{\pi, K\}$, under the assumption of flavor SU(3) symmetry [SU(3)$_F$]. Although the fits to $\Delta S=0$ or $\Delta S=1$ decays individually are good, the combined fit is very poor: there is a $3.6\sigma$ disagreement with the SU(3)$_F$ limit of the standard model (SM$_{\rm{SU(3)}_F}$). One can remove this discrepancy by adding SU(3)$_F$-breaking effects, but 1000% SU(3)$_F$ breaking is required. The above results are rigorous, group-theoretically - no dynamical assumptions have been made. When one adds an assumption motivated by QCD factorization, the discrepancy with the SM$_{\rm{SU(3)}_F}$ grows to $4.4\sigma$.