Minimal U(1) two-Higgs-doublet models for quark and lepton flavour

TL;DR

This work studies minimal Abelian (U(1)) flavour symmetries within a two-Higgs-doublet model augmented by the Weinberg operator for Majorana neutrino masses. By enforcing texture-zero patterns and using the Smith Normal Form approach, it identifies four maximal quark textures and three predictive lepton textures that reproduce observed masses, mixing angles, and CP violation. The lepton sector yields concrete predictions for the atmospheric angle $\theta_{23}$, the Dirac phase $\delta^\ell$, the lightest neutrino mass $m_{\text{lightest}}$, and the neutrinoless double beta decay parameter $m_{\beta\beta}$, with distinctions between normal and inverted ordering. A comprehensive phenomenological analysis, including theoretical constraints, EWPO, scalar sector bounds, quark and lepton flavour processes, shows that Abelian symmetries can naturally suppress FCNCs and, in some models, allow scalar masses well within current collider reach. The results highlight the viability of minimal, predictive 2HDMs in reconciling flavour data with beyond-Standard-Model scalar sectors and point to concrete experimental tests in upcoming neutrino and collider experiments.

Abstract

In the context of the 2HDM, and assuming that neutrinos acquire masses via the Weinberg operator, we perform a systematic analysis to determine the minimal quark and lepton flavour patterns, compatible with masses, mixing and CP violation data, realisable by Abelian symmetries. We determine four minimal models for quarks, where the number of independent parameters matches the number of observables. For the lepton sector, three minimal predictive models are identified. Namely, we find scenarios with a preference for the upper/lower octant of the $θ_{23}$ atmospheric mixing angle, that exhibit lower bounds on the lightest neutrino masses currently probed by cosmology and testable at future neutrinoless double beta decay experiments, even for a normally-ordered neutrino masses. We investigate the phenomenology of each model taking into account all relevant theoretical, electroweak precision observables, scalar sector constraints, as well as stringent quark flavour processes such as $\overline{B} \rightarrow X_s γ$, $B_s \rightarrow μ^- μ^+$ and meson oscillations, and the charged lepton flavour-violating decays $e_α^{-} \rightarrow e_β^{-} e_γ^{+} e_δ^{-}$ and $e_α\rightarrow e_βγ$. We show that, in some cases, Abelian flavour symmetries provide a natural framework to suppress flavour-changing neutral couplings and lead to scenarios featuring heavy neutral/charged scalar masses below the TeV scale within the reach of current experiments.

Figures (5)

• Figure 1: Allowed regions at 1$\sigma$, 2$\sigma$ and 3$\sigma$ level (in grey, blue and magenta, respectively) in the plane ($\theta_{23}$,$\delta$), for the cases $2_{3,7,10}$ discussed in the main text and for both NO (upper plots) and IO (lower plots) neutrino masses. The black dot marks the best-fit (b.f.) value for each case, while the dashed contours correspond to the $\chi^2$ contours at 1$\sigma$, 2$\sigma$ and 3$\sigma$, allowed by the global fit of neutrino oscillation data (see Table \ref{['tab:data']}).
• Figure 2: Allowed regions in the plane ($m_\text{lightest}$,$\delta$) for the cases $2_{3,7,10}$ discussed in the main text for NO neutrino masses. The colour scheme is the same as in Fig. \ref{['fig:predictionst23delta']}. The vertical red line corresponds to the upper limit for $m_\text{lightest}$ extracted from the KATRIN bound on $m_\beta$. The brown shaded vertical region shows the $m_\text{lightest}$ upper-limit interval obtained from the Planck cosmological bounds on $\sum_k m_k$.
• Figure 3: Allowed regions in the plane ($m_\text{lightest}$,$\delta$) for the cases $2_{3,7,10}$ discussed in the main text for IO neutrino masses. The colour scheme is the same as in Figs. \ref{['fig:predictionst23delta']} and \ref{['fig:predictionsmlightestdeltaNO']}.
• Figure 4: Allowed regions in the ($m_\text{lightest}$,$m_{\beta\beta}$) plane for the cases $2_{3,7,10}$ discussed in the main text for NO neutrino masses. The colour scheme is the same as in Figs. \ref{['fig:predictionst23delta']} and \ref{['fig:predictionsmlightestdeltaNO']}. The dashed contours delimit the 1$\sigma$, 2$\sigma$ and 3$\sigma$ regions allowed by neutrino oscillation data only, without considering any extra constraint on $\mathbf{M}_\nu$. The coloured vertical bars correspond to the upper-bound ranges on $m_{\beta\beta}$ from EXO-200 EXO-200:2019rkq, GERDA GERDA:2020xhi, CUORE CUORE:2021mvw and KamLAND-Zen 800 KamLAND-Zen:2022tow.
• Figure 5: Allowed regions in the ($m_\text{lightest}$,$m_{\beta\beta}$) plane for the cases $2_{3,7,10}$ discussed in the main text for IO neutrino masses. The colour scheme is the same as in Figs. \ref{['fig:predictionst23delta']}, \ref{['fig:predictionsmlightestdeltaNO']}, \ref{['fig:predictionsmlightestdeltaIO']} and \ref{['fig:predictionsmlightestmbetabetaNO']}.