A Cosmic Amplification for Muon-to-Positron Conversion in Nuclei

Abstract: We present an analysis of the lepton-number and lepton-flavour-violating process of muon-to-positron conversion $\mu^- + N \rightarrow e^+ + N'$, in the presence of an ultralight scalar dark matter (ULSDM) field which couples to neutrinos. The ULSDM contributes to the effective off-diagonal Majorana mass $ m_{\mu e}$, therefore amplifying the rate of muon-to-positron conversion to experimentally observable levels. Using existing bounds from SINDRUM II, COMET, and Mu2e experiments, we derive constraints on the flavour-off-diagonal couplings of neutrinos to ULSDM for the first time. Our work reveals that upcoming experiments can provide stronger sensitivity to these new couplings than bounds arising from cosmological surveys and terrestrial experiments.