$\mu$-$e$ conversion in nuclei and Z${}^{\prime }$ physics

Abstract

Together with the existence of new neutral gauge bosons, models based on extended gauge groups (rank $>4$) often predict also new charged fermions. A mixing of the known fermions with new states with {\it exotic} weak-isospin assignments (left-handed singlets and right-handed doublets) will induce tree level flavour changing neutral interactions mediated by $Z$ exchange, while if the mixing is only with new states with {\it ordinary} weak-isospin assignments, the flavour changing neutral currents are mainly due to the exchange of the lightest new neutral gauge boson $Z^{\prime }$. We show that the present experimental limits on $\mu -e$ conversion in nuclei give a nuclear-model-independent bound on the $Z$-$e$-$\mu$ vertex which is twice as strong as that obtained from $\mu \to eee$. In the case of E${}_6$ models these limits provide quite stringent constraints on the $Z^{\prime }$ mass and on the $Z-Z^{\prime }$ mixing angle. We point out that the proposed experiments to search for $\mu -e$ conversion in nuclei have good chances to find evidence of lepton flavour violation, either in the case that new exotic fermions are present at the electroweak scale, or if a new neutral gauge boson $Z^{\prime }$ of E${}_6$ origin lighter than a few TeV exists.

Plain Tex, 24 pages, + 2 PostScript figure appended after \bye (and available upon request), UM-TH 93--08, FTUV 93-14

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