Top-quark decay via R-parity violating interactions at the Tevatron

We consider the top-quark decay $t\to \tilde{\tau }b$ and $t\to \tau b \tilde{\chi}^0_1$ via explicit R-parity violating interactions in SUSY theories. We discuss the observability of those channels at the Fermilab Tevatron collider. The existing Tevatron data indicate a 95% confidence level upper bound on the coupling to be less than 0.94(0.63) for a long-lived (short-lived) ${\tilde{\chi }}_1^0$ with $m_{\tilde{\tau }}=70$ GeV. At Tevatron Run II with an integrated luminosity of 2 (10) fb${}^{-1}$, one can obtain a 2$\sigma$ constraint as 0.38 (0.24) for a long-lived ${\tilde{\chi }}_1^0$ and 0.29(0.19) for a short-lived ${\tilde{\chi }}_1^0$, beyond the current indirect limit.