(μ^-, μ⁺) conversion in nuclei as a probe of new physics

We present a detailed analysis of the muonic analogue of neutrinoless double beta decay (μ¹, μ⁺) conversion. We study several lepton number violating (LNV) mechanisms potentially triggering this process: ex-change by light and heavy Majorana neutrinos as well as exchange by supersymmetric particles participating in R-parity violating interactions. The nuclear structure is taken into account within the renormalized quasi-particle random phase approximation method. This is the first realistic treatment of nuclear structure aspects of the (μ^-, μ⁺) conversion. We estimate the rate of this process utilizing the existing experimental constraints on the parameters of the underlying LNV interactions and conclude that the (μ^-, μ⁺) conversion will hardly be detectable in the near future experiments.