Experimental Study of Heavy Charged Leptons and Search for Scalar Partners of Muons at PETRA ($12 \mathrm{GeV}<~E_{\mathrm{c}.\mathrm{m}.\mathrm{}}<~36.7 \mathrm{GeV}$)

Data from the MARK-J detector on the reactions $e^{+}{e}^{-}\to {\mu }^{+}{\mu }^{-}$, ${\tau }^{+}{\tau }^{-}$ in the center-of-mass energy range from 12 to 36.7 GeV are presented. The $\mu$, $\tau$ radii are shown to be <${10}^{-16\mathrm{}}$ cm. A search has been made for the production of a new heavy lepton and for the production of spin-0 supersymmetric partners of the muon. 95%-confidence-level lower limits of 16 GeV for the mass of a new charged heavy lepton and 15 GeV for the mass of the scalar partners of the muon are obtained.