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

TL;DR

The paper analyzes a U(2)F flavor model in which SU(2)F can be global or gauged, yielding a triplet of PNGBs or gauge bosons (W′) in addition to the axiflavon from U(1)F. It shows that these new bosons inherit unsuppressed flavor-violating couplings in the 1–2 sector, leading to distinctive FCNC and LFV signatures such as K→πX and μ→eX, and constrains the flavor-breaking scale vφ to be as high as ~10¹¹–10¹² GeV for light X. Heavier W′/π′ states are probed by B and τ decays and by K⁰–K̄⁰ mixing and μ→eγ, while astrophysical bounds are typically subdominant to laboratory constraints. The results demonstrate that low-energy flavor experiments can test ultra-high symmetry-breaking scales, offering sensitivity that sometimes surpasses stellar bounds and opening avenues for future tests including potential gravitational-wave signatures from the associated phase transition. The axiflavon remains a viable DM candidate in the high-vφ regime, linking flavor structure to cosmology and potentially enabling multi-messenger probes of the model.

Abstract

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 PNGB 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 $K \to πX$ and $μ\to e X$ place the most stringent constraints, probing the flavor symmetry breaking scale $v_φ$ up to $10^{11}-10^{12}$ GeV for light bosons, while heavier states are tested in $B$ and $τ$ decays, as well as by $K-\bar K$ mixing and $μ\to e γ$. 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.

Figures (2)

• Figure 1: Local $\mathbf{SU(2)_F}$ case. Regions of the $(m_{W^\prime},\,g_F)$ plane excluded by current experimental limits (cf. Appendix \ref{['app:explim']}) on quark sector (left) and lepton sector (right) processes mediated the $W^\prime$ gauge bosons. Regions above or within the colored contours are excluded. Dotted lines represent expected future bounds. Dashed lines display the astrophysical limits discussed in Appendix \ref{['app:astro']}. See the main text for details.
• Figure 2: Global $\mathbf{SU(2)_F}$ case. Regions of the $(m_{\pi^\prime},\,v_\phi)$ plane excluded by current experimental limits (cf. Appendix \ref{['app:explim']}) on quark sector (left) and lepton sector (right) processes mediated the $\pi^\prime$ PNGBs. Regions below or within the colored contours are excluded. Dotted lines represent expected future bounds. Dashed lines display the astrophysical limits discussed in Appendix \ref{['app:astro']}. See the main text for details.