Electron-muon conversion in nuclei and rare decays induced by LFV dark photon

TL;DR

This work investigates lepton-flavor violation (LFV) mediated by a sub-GeV dark photon in two contexts: e−μ conversion in nuclei and rare decays of the η and η′ mesons to γμe. It develops a quantum-field framework with a Stueckelberg dark photon, including diagonal and off-diagonal couplings, and analyzes three portal scenarios (general, hadrophilic, leptophilic) to derive bounds on LFV couplings as a function of the dark-photon mass $m_{A'}$. The authors compute μ→eγ and μ→3e widths and e−μ conversion cross sections, and relate η, η′→γμe decays to the dark-photon couplings via vector-meson mixing and the chiral anomaly, obtaining upper limits on the corresponding branching ratios. They find that current fixed-target e-beam searches are subdominant to μ-decay constraints, but η/η′ decays can provide competitive or complementary bounds in the resonance window $m_{A'}<m_{η,η'}$, highlighting the potential of high-luminosity η factories such as REDTOP to probe LFV vector portals.

Abstract

We study lepton-flavor violation (LFV) effects occurring in the $e-μ$ conversion in nuclei and in the rare radiative decays $η(η') \to γμe$ of the $η$ and $η'$ mesons with a special impact of the sub-GeV mass vector mediator (dark photon). In the case of the lepton conversion, we make estimates for running and future experiments operating with electron beams at fixed target. Obtained results are implemented in analysis of the LFV decays $η(η') \to γμe$.

Figures (5)

• Figure 1: Gauge-invariant set of Feynman diagrams induced by dark photon mediator and contributing to the $\mu \to e \gamma$ decay
• Figure 2: Diagram contributing to the $\mu \to 3e$ decay generated by the dark photon mediator due to its nondiagonal coupling with SM leptons.
• Figure 3: Diagrams contributed to the lepton $e - \mu$ conversion in nuclei due to LFV dark photon: diagram induced by mixing of QED and dark photon (left); (b) diagram induced by form factor relevant for the $\mu \to e \gamma$ transition (right). Dashed triangle blob in right diagram represents the vertex function $\Gamma_\nu(k_1,k_2)$.
• Figure 4: $m_{A'}$ dependence of bounds for the products of diagonal and nondiagonal couplings of dark photon with SM fermions. Shaded region corresponds to available data from limits on rare muon LFV decays and for current statistics of the NA64 experiment. Dashed lines correspond to estimates of future beam dump experiments with electron beams. Parameters used here are presented in Table \ref{['ParamTable']}.
• Figure 5: Feynman diagrams that show vertices of decay pseudoscalar meson into two photons (a) or one photon and a dark photon in different scenarios: (b) general, (c) hadrophilic, and (d) leptophilic.