A Search for R-Parity Violated Scalar Tau-neutrino ($\widetilde{\nu_{\tau}}$) at the Future Circular Collider.

Future Circular Collider is one of the next generation energy-frontier proton-proton colliders with 100 TeV center of mass energy and promising very high luminosity. FCC will be an extraordinary machine for searching Beyond the Standard Model physics because of its very high center of mass energy and luminosity. Searching supersymmetric particles via R-parity violated interactions could be listed in promising BSM physics at the FCC. Scalar tau neutrino is one of the most interesting predictions. A search for $\widetilde{\nu}_{\tau}$ neutrino decaying into $e\mu$ final state via R-parity violated interactions has been conducted at the FCC-pp. It is seen from this research that FCC-pp will be able to discover $\widetilde{\nu}_{\tau}$ up to 28.8 TeV, observe 32.0 TeV and exclude 34.5 TeV mass values by taking $\lambda_{311}^{\prime}=0.11$ and $\lambda_{312}=\lambda_{321}=0.07$ at $\mathcal{L}_{int}=17500\,fb^{-1}$. FCC-pp, also, will allow to examine very low values of the Yukawa coupling constants which cause R-parity violation interactions. It is obviously seen that FCC-pp will give an opportunity for detailed research on scalar tau neutrino production and decay via R-parity violated interactions.