Present status of inclusive rare $B$ decays

Most inclusive rare $B$ decays are important modes of flavor physics due to the small hadronic uncertainties. In this article, the author gives a status report on such decays, highlighting recent developments and open problems. The focus is on the decay modes $\overrightarrow{B}{X}_{s,d}\gamma ,$ $\overrightarrow{B}{X}_s{\mathcal{l}}^{+}{\mathcal{l}}^{-},$ and $\overrightarrow{B}{X}_s\nu \overline{\nu }$ and on their role as laboratories in the search for new physics. The experimental data already available from CLEO and the $B$ factories BABAR and BELLE are collected and discussed. The article then reviews the next-to-leading-log (NLL) and next-to-next-to-leading log (NNLL) QCD calculations of the inclusive decay rates that were recently completed and discusses future prospects, especially the issue of the charm-mass-scheme ambiguity. The phenomenological impact of these decay modes, in particular, on the CKM phenomenology and on the indirect search for supersymmetry, is analyzed. Direct $\mathrm{CP}$ violation in inclusive rare $B$ decays is briefly treated, as are the rare kaon decays $K^{+}\to {\pi }^{+}\nu \overline{\nu }$ and $K_L\to {\pi }^0\nu \overline{\nu },$ which offer complementary, theoretically clean information.