Anomalies in Hadronic $B$ Decays: an Update

Recently, $B\to PP$ decays ($B=\{B^0,B^{+},B_s^0\}$, $P=\{\pi ,K\}$) were analyzed under the assumption of flavor SU(3) symmetry (SU(3)${}_F$). Although the individual fits to $\mathrm{\Delta }S=0$ or $\mathrm{\Delta }S=1$ decays are good, it was found that the combined fit is very poor: there is a $3.6\sigma$ disagreement with the SU(3)${}_F$ limit of the standard model (SM${}_{{\mathrm{S}\mathrm{U}(3)}_F}$). One can remove this discrepancy by adding SU(3)${}_F$-breaking effects, but 1000% SU(3)${}_F$ breaking is required. In this paper, we extend this analysis to include decays in which there is an $\eta$ and/or ${\eta }^{\mathrm{\prime }}$ meson in the final state. We now find that the combined fit exhibits a $4.1\sigma$ discrepancy with the SM${}_{{\mathrm{S}\mathrm{U}(3)}_F}$, and 1000% SU(3)${}_F$-breaking effects are still required to explain the data. These results are rigorous, group-theoretically – no theoretical assumptions have been made. But when one adds some theoretical input motivated by QCD factorization, the discrepancy with the SM${}_{{\mathrm{S}\mathrm{U}(3)}_F}$ grows to $4.9\sigma$.