Lepton Flavor Non-Universality in B decays from Dynamical Yukawas

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.