Probing Lepton Flavor Violation Signal Induced by R-violating Minimal Supersymmetric Standard Model at a Linear Collider

The lepton-flavor violation (LFV) effect at an $e^+e^-$ linear collider (LC), in the frame of R-parity violating minimal supersymmetric standard model is studied. We take the R-parity violating processes $e^+e^-\to e^{\mp}\mu^{\pm}$ as signal, and define the summation of the two processes as ``experiment'' observable. We find that the cross-section summation can reach $\cal{O}$$(10^1)fb$ in the parameter space without sneutrino resonance effect($\sqrt{s} \sim m_{\tilde{\nu}}$). The summation treatment manifests uniform differential distribution on $\cos\theta$, where $\theta$ denotes the polar angles of both outgoing $e^+/e^-$ respectively to incoming electron beam in two signal processes. The uniform feature together with $e\mu$ collinearity would help to reduce the SM background dramatically. Consequently we conclude that at a $500 GeV$ LC with $480 fb^{-1}$ annual luminosity, it's either possible to detect the distinctive R-violating LFV $e\mu$ signal, or exclude sneutrino to $m_{\tilde{\nu}}>1.1 TeV$ at 95% CL in the machine's biennial runtime interval.