Hunting for Neutrino Texture Zeros with Muon and Tau Flavor Violation

Abstract

We revisit the minimal type II seesaw mechanism generating the Majorana neutrino mass matrix $M^ν$, under the assumption that two entries of $M^ν$ vanish. Such flavor structures are known as two-zero textures. Processes with charged lepton flavor violation (CLFV), absent in the Standard Model (SM), can have sizable rates in this framework and are directly linked to the flavor structure of $M^ν$. For each allowed two-zero texture, we quantify the predicted correlations among various CLFV observables using current neutrino oscillation data and show that they lead to distinctive patterns of CLFV processes that could be discriminated between at running and upcoming experiments. In addition, together with information from colliders, the sensitivity of these correlations to renormalization group (RG) effects could shed light on the potentially ultra-high scale where new dynamics (e.g. some underlying flavor symmetry) give rise to the two-zero texture. Furthermore, we find that certain zero textures, although not third-generation specific, can suppress $μ\to e$ transitions while allowing the rate of the process $τ\to \barμee$ to be within the future experimental sensitivity, even when the RG evolution is taken into account. The lowest possible cut-off scale of the effective theory, constructed by treating the two-zero flavor structure of $M^ν$ as a CLFV spurion, can therefore reach $5-6$ TeV. Our results provide further motivation for searches for $τ$ CLFV at Belle II, as probes of new physics complementary to MEG II and the upcoming Mu3e, COMET, and Mu2e experiments, as well as for collider searches for doubly charged scalar bosons.

Figures (6)

• Figure 1: (a)-(e): Feynman diagrams contributing to CLFV processes within the full type II seesaw model. (f)-(i): Corresponding Feynman diagrams in the effective theory at low-energy scales, $q^2\ll m_{W}^2$. We do not apply the on-shell condition so a pair of quarks or charged leptons can be attached to the external gauge boson lines. Self-energy diagrams are not included for simplicity.
• Figure 2: Schematic (approximately logarithmic) representation of the energy scale hierarchy in the considered type II seesaw framework. Vertical arrows indicate the key energy scales: muon and tau masses, $m_\mu$ and $m_\tau$, the electroweak symmetry breaking scale $\Lambda_\text{EW}$, the mass of the type II seesaw scalar triplet $m_{\Delta}$, and the ultraviolet cutoff scale $\Lambda_\text{UV}$.
• Figure 3: Predicted branching ratios of various CLFV processes for textures $\mathbf{B_1}$-$\mathbf{B_4}$. The strongest constraint, $\text{BR}(\mu\to e\gamma)$ or $\text{BR}(\mu\to \bar{e} ee)$, is fixed to the value that saturates the current experimental limit (blue star). The predicted BRs for the other processes are denoted by blue dots with error bars corresponding to $3\sigma$ uncertainties from neutrino oscillation data. Red diamonds and green squares respectively indicate current and future experimental sensitivities. See the main text for details.
• Figure 4: Same as Figure \ref{['B1B4']} for textures $\mathbf{A_1}$$\mathbf{A_2}$ and $\mathbf{C}$.
• Figure 5: Predicted $\text{BR}(\mu\to e\gamma)$ within textures $\mathbf{A_1}$, $\mathbf{A_2}$, $\mathbf{B_2}$, $\mathbf{B_3}$, versus the second most constraining observable, $\text{BR}(\mu\to \bar{e} ee)$ (for all textures) and $\text{BR}(\tau \to\bar{\mu} ee)$ (for $\mathbf{B_2}$, $\mathbf{B_3}$ only). The parameters are set to $m_{\Delta}=3$ TeV and $0\le |Y_{\Delta\tau\mu}| \le 0.25$. The other entries of $Y_\Delta$ are calculated as in Appendix \ref{['expressions']}. Solid (dashed) lines represent current (future) experimental limits.