Anomalies in Hadronic $B$ Decays

In this talk, I describe a global fit to $B\to PP$ decays, where $B=\{B^0,B^{+},B_s^0\}$ and the pseudoscalar $P=\{\pi ,K\}$, under the assumption of flavour SU(3) symmetry [SU(3)${}_F$]. It is found that the individual fits to $\mathrm{\Delta }S=0$ or $\mathrm{\Delta }S=1$ decays are good, but the combined fit is very poor: there is a $3.6\sigma$ disagreement with the standard model. (This is quite a bit larger than the anomaly in $b\to s{\mathrm{\ell }}^{+}{\mathrm{\ell }}^{-}$ transitions.) This discrepancy can be removed by adding SU(3)${}_F$-breaking effects, but 1000% SU(3)${}_F$ breaking is required, considerably more than the $\sim 20\mathrm{\%}$ breaking of $f_K\mathrm{/}{f}_{\pi }-1$. These results are rigorous, group-theoretically – no theoretical assumptions have been made. But when one adds a single assumption motivated by QCD factorization, the discrepancy grows to $4.4\sigma$. These are the anomalies in hadronic $B$ decays. Although one cannot yet claim that new physics is present, it is clear that something very unexpected is going on.