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

Abstract

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 $\nu_\ell$ and $\tilde{\nu}_\ell$, $\ell = e,\mu,\tau$ 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 $\mu^-\rightarrow e^-$ 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 $\mu^- \rightarrow e^-$ experiments, to put stringent constraints on the parameters of NSI Lagrangians.