Effect of fourth generation CP phase on $b\to s$ transitions

Abstract

We study the effect of a sequential fourth generation on b\to s gamma, B_s mixing, B\to K^{(*)}\ell^+\ell^-, X_s\ell^+\ell^- and \phi K_S, taking into account the presence of a new CP phase in quark mixing. We find that the effects via electromagnetic and strong penguins, such as in b\to s gamma or CP violation in B\to \phi K_S, are rather mild, but impact via box or Z penguins is quite significant. Not only can one have much larger than expected B_s mixing, even if it is measured near the present limit, mixing dependent CP violation could become maximal. For electroweak penguin modes, the fourth generation can provide the enhancement that perhaps may be needed, while the m_{\ell^+\ell^-} dependence of the forward-backward asymmetry in B\to K^{*}\ell^+\ell^- can further probe for the fourth generation. These effects can be studied in detail at the B factories and the Tevatron.