Lepton mixing and charged lepton flavour violation from inverse seesaw with non-degenerate heavy states

Abstract

We analyse an inverse seesaw scenario with 3+3 gauge singlets. The flavour structure is determined by a flavour symmetry, Delta (3 n^2) or Delta (6 n^2), n integer, and CP and their residual groups among charged leptons and the neutral states. For the latter, the Dirac mass matrix of the gauge singlets carries all non-trivial flavour structure. Consequently, the heavy sterile states form three pseudo-Dirac pairs which have in general distinct masses. We discuss the signal strength of different charged lepton flavour violating processes. Ensuring that the lepton mixing angles can be accommodated at the 3 sigma level or better, we find that the current bounds on the branching ratios of mu -> e gamma, mu -> 3 e, tau -> l gamma and tau -> 3 l, l=e, mu, as well as the rate of mu-e conversion in nuclei do not strongly constrain the considered parameter space, while the limits expected from the upcoming experiments Mu3E, COMET and Mu2e will have a relevant impact.

Figures (13)

• Figure 1: Masses $m_{4,...,9}$ of the heavy sterile states in GeV as function of the lightest neutrino mass $m_0$ in eV. In the left plot we display the results for light neutrino masses with NO and in the right plot for IO light neutrino masses. For concreteness, we fix $y_0=0.1$ and $\mu_0=3 \, \mathrm{keV}$ and use the best-fit values of the solar and the atmospheric mass squared differences from Esteban:2024eli. Note that the four masses $m_{4}$, $m_{5}$, $m_{7}$ and $m_{8}$ are almost degenerate in the case of an IO light neutrino mass spectrum, compare also eq. (\ref{['eq:miratiosIOm0large']}).
• Figure 2: Case 1). Results for $\mathrm{BR} (\mu\to e \, \gamma)$, $\mathrm{BR} (\mu\to 3 \,e)$ and $\mathrm{CR} (\mu-e, \mathrm{Al})$ in the upper, middle and lower row, respectively. These results are for $n=26$ and $s=1$, and six different values of the angle $\theta_S$, shown in different colours. In the left plot we display the results for light neutrino masses with NO and $m_0=0.03 \, \mathrm{eV}$ and in the right plot for IO light neutrino masses with $m_0=0.015 \, \mathrm{eV}$. For concreteness, we fix $\mu_0=3 \, \mathrm{keV}$ and use the best-fit values of the solar and the atmospheric mass squared differences and the reactor mixing angle Esteban:2024eli. The dotted lines indicate that at least one of the heavy sterile states has a mass lower than $150 \, \mathrm{GeV}$.
• Figure 3: Case 1). Results of numerical scan for $\mathrm{BR} (\mu\to e \, \gamma)$, $\mathrm{BR} (\mu\to 3 \,e)$ and $\mathrm{CR} (\mu-e, \mathrm{Al})$ varying $y_0$, $\mu_0$ and $\theta_S$ in the ranges in eqs. (\ref{['eq:y0range']}), (\ref{['eq:mu0range']}) and (\ref{['eq:thetaSrange']}), respectively. The parameters $n$ and $s$ are the same as in fig. \ref{['fig:Case1mu0fixedNOIO']}. The light neutrino mass ordering is fixed to NO and $m_0$ to $m_0=0.03 \, \mathrm{eV}$. Points in grey, orange and red are excluded by different (current/future) experimental bounds, see text for details. Points in other colours correspond to a certain value of the lightest mass of the heavy sterile states, see colour bar, and pass all the imposed limits.
• Figure 4: Case 2). Results of numerical scan for $\mathrm{BR} (\mu\to e \, \gamma)$, $\mathrm{BR} (\mu\to 3 \,e)$ and $\mathrm{CR} (\mu-e, \mathrm{Al})$ varying $y_0$, $\mu_0$ and $\theta_S$ in the ranges in eqs. (\ref{['eq:y0range']}), (\ref{['eq:mu0range']}) and (\ref{['eq:thetaSrange']}), respectively. The parameters $n$, $s$ and $t$ are set to $n=14$, $s=1$ and $t=2$ corresponding to $u=0$ (and $v=6$). The light neutrino mass ordering is fixed to NO and $m_0$ to $m_0=0.03 \, \mathrm{eV}$. The colour-coding of the data points is the same as in fig. \ref{['fig:Case1n26s1NOm0003']}.
• Figure 5: Case 2). Results of numerical scan for $\mathrm{BR} (\mu\to e \, \gamma)$, $\mathrm{BR} (\mu\to 3 \,e)$ and $\mathrm{CR} (\mu-e, \mathrm{Al})$ varying $y_0$, $\mu_0$ and $\theta_S$ in the ranges in eqs. (\ref{['eq:y0range']}), (\ref{['eq:mu0range']}) and (\ref{['eq:thetaSrange']}), respectively. The parameters $n$, $s$ and $t$ are set to $n=14$, $s=1$ and $t=1$ corresponding to $u=1$ (and $v=3$). The light neutrino mass ordering is fixed to NO and $m_0$ to $m_0=0.03 \, \mathrm{eV}$. The colour-coding of the data points is the same as in fig. \ref{['fig:Case1n26s1NOm0003']}.