Probing R-parity violation in the production of \(t \bar c\)\((c \bar{t})\) at lepton colliders

We studied the process \(e^{+}e^{-} \rightarrow t\bar c+c\bar{t}\) in a \(R_{p}\)-violating supersymmetric model with effects from both B- andL-violating interactions. The calculation shows that it is possible to either detect the \(R_{p}\)-violating signal at the Next Linear Collider or get more stringent constraints on the heavy-flavor \(\rlap/R_{p}\) couplings. A comparison with results from \(\gamma\gamma \rightarrow t\bar c+ c\bar{t}\) may allow one to distinguish between B- and L-violating interactions. For very clean background conditions and \(R_{p}\)-violating parameters close to the present limits, the future detection of B-violating interactions should be possible. The process of \(\mu ^{+} \mu ^{-} \rightarrow t \bar c+c\bar{t}\) is also considered.