A Roadmap for neutrino charge assignments in $U(2)_F$ Flavor Models: Implications for LFV processes and leptonic anomalous magnetic moments

Abstract

We build upon a simple $U(2)_F$ model of flavor, in which all fermion masses and mixing hierarchies arise from powers of two small parameters controlling $U(2)_F$ breaking. In the original formulation, an isomorphism to the discrete $D_6\times U(1)_F$ symmetry was invoked to generate a Majorana neutrino mass term. Here, we retain the successful features of that model for the charged leptons and quarks, while exploring alternative neutrino charge assignments within the $U(2)_F$ framework. This approach allows us to generate Majorana neutrino masses via the see-saw mechanism without introducing any additional symmetries nor invoking any isomorphism. We further examine the implications of our models for Lepton Flavor Violating (LFV) decays, analyzing the processes $μ\rightarrow eγ$, $τ\rightarrowμγ$ and $τ\rightarrow eγ$ and their connection with the leptonic anomalous magnetic moments. We show that within the Standard Model Effective Field Theory (SMEFT) approach the current limits on the branching ratios of $μ\rightarrow eγ$ LFV decays obtained in our $U(2)_F$ models are not compatible with the central value of the recent measurement of the $(g-2)_μ$, thereby suggesting that either $(g-2)_μ$ must be very close to the Standard Model predictions, as the latest experimental and theoretical results seem to suggest, or the invoked flavor symmetry is not appropriate to describe an anomalous muon magnetic moment.

Figures (6)

• Figure 1: Graphic representation of the three Models that come out in the $SU(2)_F$ application to Majorana neutrinos. The numbers $1,2,3$ correspond to $N_1,N_2,N_3$. Different colours correspond to different $SU(2)_F$ representations (for example, Model D has the blue corresponding to the doublet and the red corresponding to the singlet).
• Figure 2: Distributions of the absolute value of $m_{\beta\beta}$ in terms of the lightest neutrino mass $m_L$. For each plot, all the valid representations for the viable patterns belonging to the given Model are collected, with a red or blue point, respectively, for Scenario A or B. The green zone corresponds to the $3\sigma$ confidence region for NO. The red exclusion region corresponds to the latest KamLAND-Zen upper limit on $\lvert m_{\beta\beta} \rvert$KamLAND-Zen:2024eml, while the grey exclusion region corresponds to the PLANCK 2018 upper limit on $m_L$Planck:2018vygDiValentino:2019dzu.
• Figure 3: Distribution of $m_{\beta}$ in terms of the lightest neutrino mass $m_L$. For each plot, all the valid representations for the viable patterns belonging to the given Model are collected, with a red or blue point, respectively, for Scenario A or B. The green zone corresponds to the $3\sigma$ confidence region for NO, while the grey exclusion region corresponds to the PLANCK 2018 upper limit on $m_L$Planck:2018vygDiValentino:2019dzu.
• Figure 4: Correlations among $|\Delta a_e|$ and $|\Delta a_\tau|$ arising in the A-Scenario (B-Scenario) and represented with red (green) points, obtained considering the reference value for the anomalous magnetic moment as listed in Tab. \ref{['refValues']}. The numerical analysis is done assigning random values to the Wilson Coefficients in the $[\lambda,\lambda^{-1}]$ interval. In solid (dashed) blue line the 3$\sigma$ bound for the expected deviation from the SM prediction of the electron magnetic moment according to the latest observations based on Cesium (Rubidium) atomic recoil experiments. In the inset, with the same color code, we show the frequency distributions of the value of $\Delta a_e$ in A-Scenario and B-Scenario. See the main text for further details.
• Figure 5: $| \mathcal{C}^\prime_{e\tau}|$ in $1/\Lambda^2[\text{TeV}^{-2}]$ unit versus $| \mathcal{C}^\prime_{\tau e}|$. The dark grey region is excluded by the experiments. In red (green) the predictions in the A-Scenario (B-Scenario) in light of the $(g-2)_\mu$. In black (blue) the predictions in the A-Scenario (B-Scenario) relaxing the requirement to reproduce the current $(g-2)_\mu$ value and using the current upper bound $\mathcal{B}(\mu\rightarrow e\gamma)$ as a constraint.