B decay anomalies from nonabelian local horizontal symmetry

Recent anomalies in $B\to K^{(*)}\ell\ell$ meson decays are consistent with exchange of a heavy $Z'$ vector boson. Here we try to connect such new physics to understanding the origin of flavor, by gauging generation number. Phenomenological and theoretical considerations suggest that the smallest viable flavor symmetry (not including any extra U(1) factors) is chiral ${\rm SU(3)}_L\times{\rm SU(3)}_R$, which acts only on generation indices and does not distinguish between quarks and leptons. Spontaneous breaking of the symmetry gives rise to the standard model Yukawa matrices, and masses for the 16 $Z'$-like gauge bosons, one of which is presumed to be light enough to explain the $B\to K^{(*)}\ell\ell$ anomalies. We perform a bottom-up study of this framework, showing that it is highly constrained by LHC dilepton searches, meson mixing, $Z$ decays and CKM unitarity. Similar anomalies are predicted for semileptonic decays of $B$ to lighter mesons, with excesses in the $ee,\tau\tau$ channels and deficits in $\mu\mu$, but no deviation in $\nu\nu$. The lightest $Z'$ mass is $\lesssim 6\,$TeV if the gauge coupling is $\lesssim 1$.