Weakened Constraints from b to s γ on Supersymmetry Flavor Mixing Due to Next-To-Leading-Order Corrections

We examine the process $B \to X_s \gamma$ in minimal supersymmetry (SUSY) with general squark flavor mixings. We include all relevant next--to--leading order (NLO) QCD corrections and dominant NLO SUSY effects from the gluino. We find that gluino--squark corrections to down--type quark masses induce large NLO corrections to the dominant Wilson coefficients whose size is often similar to those at LO, especially at large $\tan\beta$. For $\mu>0$, destructive interference, and suppression by the renormalization group running lead to a ``focusing effect'' of reducing the size of gluino corrections to the branching ratio, and also of reducing the LO sensitivity to flavor mixings among squarks. Constraints from $B(B \to X_s \gamma)$ on the SUSY--breaking scale can become significantly weakened relative to the minimal flavor violation case, even, at large $\tan\beta$, for small flavor mixings. The case of $\mu<0$ can also becomes allowed.