Technicolor corrections on $B_{s,d} \to \gamma\gamma$ decays in QCD factorization

Within the framework of the Top-color-assisted Technicolor (TC2) model, we calculate the new physics contributions to the branching ratios $\calb(B_{s,d} \to \gamma \gamma)$ and CP violating asymmetries $\rcpm(B_{s,d} \to \gamma \gamma)$ in the QCD factorization based on the heavy-quark limit $m_b \gg \Lambda_{QCD}$. Using the considered parameter space, we find that (a) for both $B_s\to \gamma \gamma$ and $B_d \to \gamma \gamma$ decays, the new physics contribution can provide a factor of two to six enhancement to their branching ratios, (b) for the $B_s \to \gamma \gamma$ decay, its direct CP violation is very small in both the SM and TC2 model, and (c) the CP violating asymmetry $\rcpm(B_d \to \gamma \gamma)$ is around the ten percent level in both the SM and TC2 model, but the sign of CP asymmetry in the TC2 model is different from that in the SM.