CP Violation in the $B_s^0$ system

Abstract

We review experimental and theoretical aspects of CP violation in the $B_s^0$-system. In that respect we present updates for the mixing parameters of the $B_s^0$ mesons expected in the Standard Model (SM): the mass difference $\Delta M_s^{\mathrm{SM}}=(18.3\pm 2.7)$ ps${}^{-1}$, the decay rate difference $\Delta {\Gamma }_s^{\mathrm{SM}}=(0.085\pm 0.015)$ ps${}^{-1}$, the flavour specific CP asymmetry $a_{\mathrm{fs}}^{s,\mathrm{SM}}=(2.22\pm 0.27)\cdot 10^{-5}$ and the equivalent quantities in the $B^0$-sector. The experimental measurements of $\Delta M_s$ and $\Delta {\Gamma }_s$ are more precise and agree very well with theoretica predictions, which can also be viewed as a proof of theoretical tools, like the Heavy Quark Expansion (HQE). CP violating studies in the $B_s^0$ system provide essential information to test the SM expectations. Mixing quantities can be used to study model independent bounds on new physics (NP) effects, yielding the familiar picture: the standard model (SM) gives the dominant contribution, while there is still some sizable space for NP effects. In the case of $\Delta M_s$ effects of the order of $15\%$ are not excluded. In the CP phase ${\varphi }_s$ due to CP violation in the interference of decays and mixing $\mathcal{O}(100\%)$ effects are still possible. The semi-leptonic CP asymmetry $a_{\mathrm{sl}}^s$, which is due to CP violation in mixing, could still be a factor of 250 larger than its robust SM expectation and thus provides a very clean observable for NP searches. We comment in detail on theoretical improvements that are necessary to make full use of the experimental precision.

51 pages, 30 figures, to appear in Reviews of Modern Physics; v2 matches journal version plus corrected typo in Eq. 48

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