Effect of Supersymmetric phases on the Direct CP Asymmetry of B -> X_d γ

We investigate the effect of supersymmetric CP violating phases on the inclusive decay B\to X_d\gamma. Although such a decay contains a large background from B\to X_s\gamma, if isolated it may exhibit sizeable CP violation, both in the Standard Model (SM) and in the context of models beyond the SM. With unconstrained supersymmetric CP violating phases we show that the direct CP asymmetry (A_CP) lies in the region -40% \le A_CP \le 40%, where a positive asymmetry would constitute a clear signal of physics beyond the SM. Even if a direct measurement of B\to X_d\gamma proves too dif ficult experimentally, its asymmetry contributes non-negligibly to the measurements of A_CP for B\to X_s\gamma, and thus should be included in future analyses. We show t hat there may be both constructive and destructive interference between A^d\gamma_CP and A^s\gamma_CP.