Abstract
We discuss charged lepton flavour violating processes occurring in the presence of muonic atoms, such as muon-electron conversion in nuclei $\text{CR}(\mu -e, \text{ N})$, the (Coulomb enhanced) decay of muonic atoms into a pair of electrons BR($\mu^- e^- \to e^- e^-$, N), as well as Muonium conversion and decay, $\text{Mu}-\bar{\text{Mu}}$ and $\text{Mu}\to e^+ e^-$. Any experimental signal of these observables calls for scenarios of physics beyond the Standard Model. In this work, we consider minimal extensions of the Standard Model via the addition of sterile fermions, providing the corresponding complete analytical expressions for all the considered observables. We first consider an "ad hoc" extension with a single sterile fermion state, and investigate its impact on the above observables. Two well motivated mechanisms of neutrino mass generation are then considered: the Inverse Seesaw embedded into the Standard Model, and the $\nu$MSM. Our study reveals that, depending on their mass range and on the active-sterile mixing angles, sterile neutrinos can give significant contributions to the above mentioned observables, some of them even lying within present and future sensitivity of dedicated cLFV experiments. We complete the analysis by confronting our results to other (direct and indirect) searches for sterile fermions.
Highlights
By construction, lepton flavour violation (LFV) is forbidden in the SM
We investigate the cLFV observables presented in the previous section, for different classes of SM extensions: we first carry a detailed analysis for a simple toy model (“3+1”), and highlight the most important points emerging from the study of two well motivated NP models, the Inverse Seesaw (ISS) and the νMSM
We have considered an inverted mass hierarchy (IH) spectrum for the light neutrino spectrum, finding that this leads to similar results concerning the cLFV observables
Summary
Sterile fermions, such as RH neutrinos (or other fermions which are singlets under the SM gauge group) appear as building blocks of many SM extensions aiming at accounting for neutrino masses and their mixings. In addition to possibly generating Dirac and/or Majorana masses for the light neutrinos, the sterile states can have a non-negligible impact for a number of processes: due to the mixing with the light (mostly active) neutrinos, the sterile fermions induce modifications to the SM charged and neutral currents. If the new sterile states are not excessively heavy, and have sizeable mixings to the light neutrinos, their phenomenological imprint can be important — many observables will be sensitive to the active-sterile mixing couplings, and their current experimental values (or bounds) will constrain such SM extensions
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