Minimal Flavor Violation in the Lepton Sector

TL;DR

This paper extends the Minimal Flavor Violation (MFV) framework to the lepton sector, proposing a symmetry-based EFT in which lepton-flavor violation (LFV) in charged leptons is tied to the neutrino mass/mixing structure. It analyzes two minimal realizations: (i) minimal field content without right-handed neutrinos, where LFV arises from spurions $\lambda_e$ and $g_\nu$ with lepton-number violation at $\Lambda_{\rm LN}$; and (ii) an extended field content with three right-handed neutrinos, where LFV is driven by Yukawas and a heavy Majorana mass $M_\nu$, with $\Lambda_{\rm LN}$ identified with $M_\nu$. The authors construct a basis of dimension-6 LFV operators and derive explicit expressions for the LFV couplings $\Delta$ (or $\lambda_\nu^\dagger\lambda_\nu$) in terms of neutrino masses and the PMNS matrix, showing that observable LFV requires a sizable hierarchy $\Lambda_{\rm LN} \gg \Lambda_{\rm LFV}$. They provide model-independent predictions for ratios of LFV rates, such as $B_{\tau\to\mu\gamma}$ to $B_{\mu\to e\gamma}$, and discuss how future experiments probing $\mu\to e\gamma$ and $\mu \to e$ conversion can test or falsify the MLFV framework, with distinct predictions depending on the normal or inverted hierarchy and on CP phases.

Abstract

We extend the notion of Minimal Flavor Violation to the lepton sector. We introduce a symmetry principle which allows us to express lepton flavor violation in the charged lepton sector in terms of neutrino masses and mixing angles. We explore the dependence of the rates for flavor changing radiative charged lepton decays (ell(i) -> ell(j) + gamma) and mu-to-e conversion in nuclei on the scales for total lepton number violation, lepton flavor violation and the neutrino masses and mixing angles. Measurable rates are obtained when the scale for total lepton number violation is much larger than the scale for lepton flavor violation.

Figures (5)

• Figure 1: Ratios $R_{i}$ defined in Eq. (\ref{['eq:Ri']}) as a function of $s_{13}$ for $c^{(3)}_{LL} = c^{(2)}_{RL} = 1$ and all other $c^{(i)} = 0$. The shaded bands correspond to variation of the phase $\delta$ between $0$ and $\pi$.
• Figure 2: Ratios $B_{\mu \to e \gamma} /B_{\tau \to \mu \gamma}$ (left) and $B_{\mu \to e \gamma} /B_{\tau \to e \gamma}$ (right) as a function of $s_{13}$ for different values of the CP violating phase $\delta$ in the normal hierarchy case. The uncertainty due to the first 3 entries in table \ref{['tab:inputs']} is not shown.
• Figure 3: $B_{\tau \to \mu \gamma}$ and $B_{\mu \to e \gamma}$ as a function of $s_{13}$, for ${\Lambda_{\rm LN}}/{\Lambda_{\rm LFV}} = 10^{10}$ and $c^{(2)}_{RL} - c^{(1)}_{RL}= 1$. The shading corresponds to different values of the phase $\delta$ and the normal/inverted spectrum. The uncertainty due to the first 3 entries in table \ref{['tab:inputs']} is not shown.
• Figure 4: Ratios $\widehat{R}_{i}$ defined in Eq. (\ref{['eq:Ri2']}) as a function of $s_{13}$ for $c^{(3)}_{LL} = c^{(2)}_{RL} = 1$, all other $c^{(i)} = 0$, normal spectrum and $\delta=0$.
• Figure 5: $B_{\tau \to \mu \gamma}$ and $B_{\mu \to e \gamma}$ as a function of $s_{13}$, for $(v M_\nu) /{\Lambda^2_{\rm LFV}} = 5 \times 10^{7}$ and $c^{(2)}_{RL}-c^{(1)}_{RL}=1$. The shading corresponds to different values of the lightest neutrino mass, ranging between 0 and 0.02 eV. The two choices of $\delta$ correspond to the $\pm$ sign in Eq. (\ref{['eq:bij']}).