2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/184156The 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 $e^+e^-\to e^{\mp}μ^{\pm}$ 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($\sqrt{s} \sim m_{\tildeν}$). The summation treatment manifests uniform differential distribution on $\cosθ$, where $θ$ denotes the polar angles of both outgoing $e^+/e^-$ respectively to incoming electron beam in two signal processes. The uniform feature together with $eμ$ 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 $eμ$ signal, or exclude sneutrino to $m_{\tildeν}>1.1 TeV$ at 95% CL in the machine's biennial runtime interval.14 pages, 9 figuresHigh Energy Physics - Phenomenologytext