Is a high $P_T$ muon of the $e^+p \to \mu^+ X$ event observed at HERA a   signature of the stop?
  We investigate the $e^+p \to \mu^+ X$ event with high transverse momenta observed at HERA (H1) and show that this event could be interpreted as a signature of the single production of the scalar top quark in a supersymmetric model with $R$-parity breaking interactions. The event topology of the H1 event is rather characteristic and in fact it can be simulated by our specific scenario if we reasonably choose our model parameters to be ({\romannumeral 1}) $m_{{\widetilde{d}},{\widetilde{b}}, {\widetilde{\nu}}}$ ${{\stackrel{>}{\sim}}}$ $1$TeV [$0.8$TeV] for ${\lambda'_{131}}$ $=$ $0.1$ [$0.05$] and ({\romannumeral 2}) $m_{{\widetilde{W}}_{1}}$ ${{\stackrel{<}{\sim}}}$ $150$GeV, $100$GeV ${{\stackrel{<}{\sim}}}$ $m_{{\widetilde{t}}_1}$ ${{\stackrel{<}{\sim}}}$ $200$GeV and ${\lambda'_{131}}$ ${{\stackrel{>}{\sim}}}$ $0.05$. 
T. Kon, T. Kobayashi and S. Kitamura