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Nuclear aspects of neutral current non-standard $ν$-nucleus reactions and the role of the exotic $μ^-\to e^{-}$ transitions experimental limits

The nuclear aspects of flavour changing neutral current (FCNC) processes, predicted by various new-physics models to occur in the presence of nuclei, are examined by computing the relevant nuclear matrix elements within the context of the quasi-particle RPA using realistic strong two-body forces. One of our aims is to explore the role of the non-standard interactions (NSI) in the leptonic sector and specifically: (i) in lepton flavour violating (LFV) processes involving the neutral particles $ν_\ell$ and $\tildeν_\ell$, $\ell = e,μ,τ$ and (ii) in charged lepton flavour violating (cLFV) processes involving the charged leptons $\ell^-$ or $\ell^+$. As concrete nuclear systems we have chosen the stopping targets of $μ^-\rightarrow e^-$ conversion experiments, i.e. the $^{48}\mathrm{Ti}$ nucleus of the PRIME/PRISM experiment at J-PARC and the $^{27}\mathrm{Al}$ of the COMET at J-PARC as well as of the Mu2e at Fermilab. These experiments have been designed to reduce the single event sensitivity down to $10^{-16}$--$10^{-18}$ in searching for charged lepton mixing events. Our goal is, by taking advantage of our detailed nuclear structure calculations and using the present limits or the sensitivity of the aforementioned exotic $μ^- \rightarrow e^-$ experiments, to put stringent constraints on the parameters of NSI Lagrangians.