Abstract
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.
Highlights
With the Higgs boson discovery at the LHC, the Standard Model (SM) of particle physics stands out as a great success story
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 → s + − transitions, including RK
The desired pattern of the Standard Model Yukawa couplings is compatible with a gauged U(1)q in the quark sector, and U(1)μ−τ in the lepton sector spontaneously broken around the TeV scale
Summary
With the Higgs boson discovery at the LHC, the Standard Model (SM) of particle physics stands out as a great success story. In this paper we focus on the phenomenology of the potentially lightest vector states, associated to some of the residual unbroken subgroups This setup naturally leads to a gauged Lμ −Lτ symmetry [61,62,63,64,65,66,67,68,69] in the lepton sector [57] and an independent Abelian symmetry in the quark sector, U(1)q, that may have interesting implications for the observed deviations from the SM in b → sμ+μ−. In contrast to Ref. [28], the presence of two neutral gauge bosons make the collider signatures of this model quite different, allowing for lighter gauge bosons
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