Phenomenology of Non-Abelian Gauge and Goldstone Bosons in a U(2) Flavor Model

We investigate the phenomenological implications of the bosons associated with the $SU(2)_F$ subgroup in a simple and realistic $U(2)_F$ flavor model. While the Nambu-Goldstone boson of the $U(1)_F$ factor behaves as a standard QCD axion (an axiflavon) with suppressed flavor-violating couplings, the three degrees of freedom from $SU(2)_F$ have not been studied before. This work focuses on these states, considering both the case where $SU(2)_F$ is a global symmetry, yielding pseudo-Nambu-Goldstone bosons (PNGBs), and the case where it is a gauge symmetry with a potentially small coupling, yielding a triplet of (possibly) light gauge bosons. In both scenarios, these new bosons naturally feature unsuppressed flavor-violating couplings to Standard Model fermions in the mass basis. We derive the resulting predictions for flavor-changing neutral currents and lepton flavor violation, including exotic decays of mesons and leptons. Our analysis shows that processes like $K \to \pi X$ and $\mu \to e X$ place the most stringent constraints, probing the flavor symmetry breaking scale $v_\phi$ up to $10^{11}-10^{12}$~GeV for light bosons, while heavier states are tested in $B$ and $\tau$ decays, as well as by $K-\bar K$ mixing and $\mu\to e \gamma$. We demonstrate that low-energy flavor experiments provide a powerful probe of this framework, capable of testing ultra-high symmetry breaking scales that surpass the limits set by astrophysical observations.