Oscillating neutrinos and mu --> e, gamma

TL;DR

This work analyzes lepton-flavour violation in supersymmetric see-saw models by deriving the most general neutrino Yukawa structure ${\bf Y_\nu}$ from low-energy neutrino data and studying the RG-induced off-diagonal slepton masses. Predictions for BR$(l_i \rightarrow l_j \gamma)$ are shown to be typically large in the LAMSW-favored solar solution when the largest neutrino Yukawa coupling is ${\cal O}(1)$, often exceeding current bounds, with specific textures or gauge-mediated scenarios providing potential escapes. The analysis emphasizes the central role of the matrix ${\bf Y_\nu^+}{\bf Y_\nu}$ in driving LFV, explores several neutrino mass spectra (hierarchical, degenerate, quasi-degenerate), and discusses implications for high-energy models such as SO(10) with top-neutrino unification. The results suggest that most unified scenarios are tightly constrained or excluded unless textures are finely tuned or SUSY-breaking mediation suppresses RG effects, highlighting promising prospects for testing SUSY and neutrino mass mechanisms via future LFV experiments.

Abstract

If neutrino masses and mixings are suitable to explain the atmospheric and solar neutrino fluxes, this amounts to contributions to FCNC processes, in particular mu --> e, gamma. If the theory is supersymmetric and the origin of the masses is a see-saw mechanism, we show that the prediction for BR(mu --> e, gamma) is in general larger than the experimental upper bound, especially if the largest Yukawa coupling is O(1) and the solar data are explained by a large angle MSW effect, which recent analyses suggest as the preferred scenario. Our analysis is bottom-up and completely general, i.e. it is based just on observable low-energy data. The work generalizes previous results of the literature, identifying the dominant contributions. Application of the results to scenarios with approximate top-neutrino unification, like SO(10) models, rules out most of them unless the leptonic Yukawa matrices satisfy very precise requirements. Other possible ways-out, like gauge mediated SUSY breaking, are also discussed.

Figures (9)

• Figure 1: Feynman diagrams contributing to $l_i\rightarrow l_j, \gamma$. $\tilde{\nu}_X$ and $\tilde{l}_X$ with $X=1,\cdots, 3$ ($4,\cdots, 6$) represent the mass eigenstates of "left" ("right") sneutrinos and charged sleptons, respectively. $\tilde{\chi}^-_A$, $A=1, 2$, denote the charginos, whereas $\tilde{\chi}^0_A$, $A=1,\cdots, 4$, denote the neutralinos.
• Figure 2: Dominant Feynman diagrams contributing to $l_i\rightarrow l_j, \gamma$ in the mass-insertion approximation. $\tilde{L}_i$ are the slepton doublets in the basis where the gauge interactions and the charged-lepton Yukawa couplings are flavour-diagonal. $\tilde{\chi}_A$ denote the charginos and neutralinos, as in Fig. 1.
• Figure 3: Branching ratio of the process $\mu\rightarrow e, \gamma$ vs. the unknown angle $\hat{\theta}_1$ for the case of hierarchical (left and right) neutrinos and two typical sets of supersymmetric parameters, as indicated in the plots. The dashed lines correspond to the present and forthcoming upper bounds. A top-neutrino "unification" condition has been used to fix the value of the largest neutrino Yukawa coupling at high energy. $\hat{\theta}_1$ is taken real for simplicity, so the two limits $\hat{\theta}_1=0,\pi$ of the horizontal axis represent the same physical point. In the upper plot the curves corresponding to $m_0=300$ GeV and $m_0=500$ GeV are almost indistinguishable. The same is true in the lower plot for the curves corresponding to $m_0=100$ GeV, $m_0=300$ GeV and $m_0=500$ GeV.
• Figure 4: The same as Fig. 3, but for $\tan \beta=10$.
• Figure 5: The same as Fig.3 (lower plot) using a logarithmic scale for $\hat{\theta}_1$.