1-loop SQCD corrections to the decay of top-squarks to charm and neutralino in the generic MSSM

In this article we calculate the 1-loop supersymmetric QCD (SQCD) corrections to the decay $\tilde u_1\to c \tilde\chi^0_1$ in the MSSM with generic flavour structure. This decay mode is phenomenologically important if the mass difference between the lightest squark $\tilde u_1$ (which is assumed to be mainly stop-like) and the neutralino LSP $\tilde \chi^0_1$ is smaller than the top mass. In such a scenario $\tilde u_1\to t \tilde\chi^0_1$ is kinematically not allowed and searches for $\tilde u_1\to W b \tilde\chi^0_1$ and $\tilde u_1\to c \tilde\chi^0_1$ are performed. A large decay rate for $\tilde u_1\to c \tilde\chi^0_1$ can weaken the LHC bounds from $\tilde u_1\to W b \chi^0_1$ which are usually obtained under the assumption ${\rm Br}[\tilde u_1\to W b \chi^0_1]=100\%$. We find the SQCD corrections enhance $\Gamma[\tilde u_1\to c \tilde\chi^0_1]$ by approximately 10\% if the flavour-violation originates from bilinear terms. If flavour-violation originates from trilinear terms, the effect can be $\pm 50\%$ or more, depending on the sign of $A^t$. We note that connecting a theory of SUSY breaking to LHC observables, the shift from the $\overline{\rm DR}$ to the on-shell mass is numerically very important for light stop decays.