Three decades of FCNC studies in 3-3-1 model with right-handed neutrinos: from $Z^\prime$-dominance to the alignment limit

TL;DR

The paper surveys three decades of FCNC phenomenology in the 331RHN model, highlighting the shift from $Z'$-dominance to a coherent multi-mediator picture that includes the SM-like Higgs. It shows how anomaly-induced non-universal quark assignments generate tree-level FCNC via $Z'$ and neutral scalars, and how the alignment limit $\phi+\varphi=\frac{\pi}{2}$ suppresses Higgs-mediated FCNC, reshaping viable parameter space. It also demonstrates extreme sensitivity of $Z'$ bounds to the quark-mixing parametrization, yielding allowed $m_{Z'}$ from a few hundred GeV to tens of TeV depending on the scenario, and emphasizes the necessity of treating all mediators together. The work outlines open questions about alignment’s origin and right-handed mixing, and discusses experimental prospects across HL-LHC, Belle II, LHCb, and ultra-precision kaon experiments for testing the 331RHN framework.

Abstract

Flavor-changing neutral current (FCNC) processes play a prominent role in the search for physics beyond the Standard Model (SM) due to their sensitivity to new physics at the TeV scale. Meson-antimeson transitions and rare meson decays provide stringent constraints on new physics through precision measurements of observables such as mass differences, CP asymmetries, and branching ratios. Extensions of the SM based on the $\text{SU}(3)_C \times \text{SU}(3)_L \times \text{U}(1)_N$ gauge group offer a compelling framework for flavor physics, as FCNC processes emerge inexorably at tree level due to the non-universal transformations of the quark families. Among its various realizations, the version incorporating right-handed neutrinos (331RHN) is the most phenomenologically viable. This review synthesizes three decades of theoretical developments in FCNC phenomenology within the 331RHN model, from early $Z^\prime$-dominated studies to the recent recognition of the decisive role played by the SM-like Higgs boson and the identification of the alignment limit. We demonstrate that viable parameter space spans orders of magnitude, from $m_{Z^\prime} \sim$ a few hundred GeV to $\sim 100$ TeV, depending critically on quark mixing parametrizations and scalar alignment configurations, with significant implications for experimental searches at current and future colliders.

Figures (6)

• Figure 1: Numerical results for variant I (continuous curve), variant II (dashed curve), and variant III (dashed dotted curve). Figure taken from Ref. Oliveira:2022vjo.
• Figure 2: Evolution of $(\Delta M_K)_Z$, $(\Delta M_B)_Z$, and $(\Delta M_D)_Z$ in function of $\theta_{331}$. The excluded red region represents the error of $\Delta M_{K,B,D}$. The continuous (dashed) black lines represents the contribution of $Z^\prime$ for $80\%$ ($10\%$) of the error of difference of meson masses. The continuous (dashed) horizontal purple lines represents the contribution of $10\%$ ($80\%$) of $\Delta M_{K,B,D}$. Figure taken from Ref. Oliveira:2022dav.
• Figure 3: (a) Contours on the $\cos(\phi+\varphi)$--$\tan\phi$ plane fulfilling $100\%$ (red), $10\%$ (green) and $1\%$ (blue) of the mass difference $\delta\Delta M_D ^\text{exp}$. As indicated in the figure, outwards of the contours represents excluded region of the parameter space. Here, the mixing pattern is $V_L^u=V_\text{CKM}^\dagger$ and $V_L^d=\mathbf{1}$. (b) Mass difference as a function of $\cos(\phi+\varphi)$ for $\tan(\phi)=1$ (red), $\tan\phi=50$ (green) and $\tan\phi = 0.01$ (blue). The dashed black line denotes $|\Delta M_D^h|=\delta \Delta M_D^\text{exp}$.
• Figure 4: (a) Contours on the $\cos(\phi+\varphi)$--$\tan\phi$ plane fulfilling $100\%$ of the mass differences $\delta\Delta M_M ^\text{exp}$, for mesons $K$ (red), $B_d$ (green) and $B_s$ (blue). As indicated in the figure, outwards of the contours represents excluded region of the parameter space. When combined all meson transition constraints, the only remaining allowed region is indicated by the blue contour. Here, the mixing pattern is $V_L^d=V_\text{CKM}$ and $V_L^u=\mathbf{1}$. (b) Mass difference as a function of $\cos(\phi+\varphi)$ for mesons $K$ (red), $B_d$ (green) and $B_s$ (blue), fixing $\tan \phi=1$. The dashed black line denotes $|\Delta M_M^h|=\delta \Delta M_M^\text{exp}$.
• Figure 5: (a) Contours on the $\cos(\phi+\varphi)$--$\tan\phi$ plane fulfilling $100\%$ of the mass differences $\delta\Delta M_M ^\text{exp}$, for mesons $D$ (red), $B_d$ (green) and $B_s$ (blue) ($K$ transition allows all presented plane). As indicated in the figure, outwards of the contours represents excluded region of the parameter space. Here, the mixing pattern $V_L^u$ and $V_L^d$ are explicitly provided in Eq. \ref{['VLDcase3']}. (b) Mass difference as a function of $\cos(\phi+\varphi)$ for mesons $D$ (red), $B_d$ (green) and $B_s$ (blue), fixing $\tan \phi=1$. The dashed black line denotes $|\Delta M_M^h|=\delta \Delta M_M^\text{exp}$.