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The present study is devoted for an improved analysis of theself-interference contribution of the electromagnetic dipole operator O_7 tothe double differential decay width $d\Gamma/(ds_1 ds_2)$ for the inclusive$\bar{B} \to X_s \gamma \gamma$ process, where the kinematical variables s_1and s_2 are defined as s_i=(p_b - q_i)^2/m_b^2 with p_b, q_1, q_2 being themomenta of the b-quark and two photons. This calculation completes the NLL QCDprediction of the numerically important self-interference contribution of O_7by keeping the full dependence on the strange-quark mass m_s, which isintroduced to control possible collinear configurations of one of the photonswith the strange quark. Our results are given for exact m_s, in contrast to anearlier work where only logarithmic and constant terms in m_s were retained.This improved NLL result for the (O_7, O_7)-interference contribution showsthat finite m_s effects are only sizable near the kinematical endpoints of thespectrum $d\Gamma/(ds_1 ds_2)$. At the level of the branching ratio, in thephase-space region considered in this paper, it is observed that $Br[\bar{B}\to X_s \gamma \gamma]$ does not develop a sizable m_s dependence: the impacton this branching ratio is less than 5% when m_s is varied between 400-600 MeV.For the same phase-space region finite strange quark mass effects for thebranching ratio are less than 7%.

Improved analysis of the (O_7, O_7) contribution to $\bar{B} \rightarrow X_s \gamma \gamma$ at $O(\alpha_s)$