  The basic features of quark and lepton mass matrices can be successfully
explained by natural minima of a generic potential with dynamical Yukawa fields
invariant under the $[\mathrm{SU(3)}]^5\times \mathcal{O}(3)$ flavor symmetry.
If this symmetry is gauged, in order to avoid potentially dangerous Goldstone
bosons, and small perturbations are added to exactly fit the observed pattern
of fermion masses, the spectrum of massive flavor gauge bosons can naturally
explain the hints for new physics in $b\to s \ell^+\ell^-$ transitions,
including $R_K$. In particular, the desired pattern of the Standard Model
Yukawa couplings is compatible with a gauged $\mathrm{U(1)}_q$ in the quark
sector, and $\mathrm{U(1)}_{\mu-\tau}$ in the lepton sector spontaneously
broken around the TeV scale. In order to explain the aforementioned
experimental hints, the corresponding neutral gauge bosons are required to mix,
yielding to potentially observable signals in dimuon resonance searches at the
LHC.
