Vacuum Stability Constraints on Flavor Mixing Parameters and Their Effect on Gluino Decays

In this article, we study the two body gluino decays $\tilde{g} \rightarrow \tilde{u}_i \bar{u}_g$, $\tilde{g} \rightarrow \tilde{d}_i \bar{d}_g$ with $i=1,2,...6$ and $g=1,2,3$ in the Minimal Supersymmetric Standard Model (MSSM) with quark flavour violation (QFV). At the outset, constraints on QFV parameters $\delta _{ij}^{U/D(LR)}$ and $\delta _{ij}^{U/D(RL)}$ with $i,j=1,2,3$ and $(i\neq j)$ are calculated for a specific set of MSSM parameters using charge and color breaking minima (CCB) and unbounded from below minima (UFB) conditions. These constraints are more stringent compared to the constraints coming from B-physics observables (BPO), that are already available in literature. In the second step, we re-calculate the partial decay widths of $\tilde{g} \rightarrow \tilde{u}_i \bar{u}_g$, $\tilde{g} \rightarrow \tilde{d}_i \bar{d}_g$ for the allowed range of QFV parameters. The partial decay widths can reach upto 120 GeV in the RR sector of the squarks mass matrices while in the LL sector it can be $\approx 90$ GeV. The QFV in the LR/RL sector is usually ignored due to stringent CCB andd UFB constraints, however, our analysis reveals that this mixing can contribute upto $\approx 12$ GeV for some parameter points and should not be ignored. We hope that these results will prove helpful for the experimental searches of gluinos at the current and future colliders.