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 $\mathrm{\Delta }S=0$ or $\mathrm{\Delta }S=1$ 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${}_{{\mathrm{S}\mathrm{U}(3)}_F}$). One can remove this discrepancy by adding SU(3)${}_F$-breaking effects, but 1000% SU(3)${}_F$ breaking is required. 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${}_{{\mathrm{S}\mathrm{U}(3)}_F}$ grows to $4.4\sigma$.