SM with four generations: Selected implications for rare B and K decays

Abstract

We extend our recent work and study implications of the Standard Model with four generations (SM4) for rare B and K decays. We again take seriously the several 2-3 $\sigma$ anomalies seen in B, $B_s$ decays and interpret them in the context of this simple extension of the SM. SM4 is also of course of considerable interest for its potential relevance to dynamical electroweak symmetry breaking and to baryogenesis. Using experimental information from processes such as $B\to X_s\gamma$, $B_d$ and $B_s$ mixings, indirect CP-violation from $K_L\to \pi \pi$ etc along with oblique corrections, we constrain the relevant parameter space of the SM4, and find $m_{t^{\prime }}$ of about 400-600 GeV with a mixing angle $|V_{t^{\prime }b}^{\ast }{V}_{t^{\prime }s}|$ in the range of about (0.05 to 1.4)$\times 10^{-2}$ and with an appreciable CP-odd associated phase, are favored by the current data. Given the unique role of the CP asymmetry in $B_s\to \psi \varphi$ due to its gold-plated nature, correlation of that with many other interesting observables, including the semileptonic asymmetry ($A_{SL}$) are studied in SM4. We also identify several processes, such as $B\to X_s\nu \bar{\nu }$, $K_L\to {\pi }^0\nu \bar{\nu }$ etc, that are significantly different in SM4 from the SM. Experimentally the very distinctive process $B_s\to {\mu }^{+}{\mu }^{-}$ is also discussed; the branching ratio can be larger or smaller than in SM, $(3.2\to 4.2)\times 10^{-9}$, by a factor of $\mathcal{O}(3)$.

v2: 49 pages, 20 eps figures, Corrected some typos, added few references and minor changes with regard to direct CP in K pi. Also some added information to facilitate direct comparison with Buras et al, arXiv:1002.2126.

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