We show that, if a fourth generation is discovered at the Tevatron or LHC, one could study CP violation in b ′ → s decays. Asymmetries could reach 30% for b ′ → sZ for m b ′ < ∼ 350 GeV, while it could be greater than 50% for b ′ → sγ and extend to higher m b ′. Branching ratios are 10 −3-10 −5 , and CPV measurement requires tagging. Once measured, however, the CPV phase can be extracted with little theoretical uncertainty. PACS numbers: 11.30.Er, 12.15.Ff, 12.15.Lk, 12.15.Mm Measurements of the phase angle sin 2β/φ 1 ≡ sin 2Φ B d in B d → J/ψK 0 and other decays are in good agreement [1] with the Kobayashi-Maskawa (KM) model [2]. This Standard Model (SM) with 3 generations predicts sin 2Φ SM Bs ≃ −0.04 [1] for time-dependent CP violation (TCPV) in B s → J/ψφ mode, which is beyond the sensitivities at the Tevatron, and accessible only by the LHCb experiment. Any indication for a finite value at the Teva-tron implies physics beyond SM (BSM). Interestingly, both the CDF and D∅ experiments reported [3] recently a large and negative value for sin 2Φ Bs. Though not yet significant, the central value echoes the predictions [4] based on a fourth generation explanation of the direct CPV (DCPV) difference, ∆A Kπ ≡ A B + →K + π 0 − A B 0 →K + π − ∼ +15% [1, 5], observed by the B factories. By correlations of the b → s Z-penguin and b¯ s ↔ s ¯ b box diagrams, a sizable 4th geneation contribution to ∆A Kπ would imply prominent CPV in B s → J/ψφ. With B s mixing observed by CDF in 2006, a stronger prediction was made. New results on sin 2Φ Bs (≡ − sin 2β s of CDF) are eagerly awaited. To up the ante, a 4th generation could enhance the invariant CPV measure of Jarlskog [6] by a factor of 10 15 [7], and perhaps could satisfy the CPV part of the Sakharov conditions [8] for baryogenesis in the early Universe. The 4th generation is troubled by the electroweak precision test (EWPT) S parameter [9]. However, this severe constraint [1] is softened when one allows some t ′-b ′ mass splitting that contributes to T parameter [10, 11]. With the LHC, we finally have a machine that can discover or rule out the 4th generation once and for all by direct search [12]. There is in fact renewed interest at the Tevatron. CDF has recently searched for t ′ → qW (no b-tagging) using 2.8 fb −1 , and for same sign dilep-tons [13] in b ′¯ b ′ → t ¯ tW − W + [12] based on 2.7 fb −1 data, setting the 95% C.L. limits of m t ′ > 311 GeV [14] and m b ′ > 325 GeV [15], respectively. Note that these limits assume predominance of the search mode. The t ′ and especially the b ′ decays could be richer. Motivated by the BSM source of CPV, and with heightened direct search activity, we ask: What can the direct discovery of the b ′ and t ′ quarks do for the quest of CPV? We find the best case to be flavor changing neutral current (FCNC) b ′ → s decays, with b ′ around and above the tW threshold (see Fig. 1). The study of CPV in b ′ → s transitions complements the traditional agenda of BSM CPV search in the flavor sector, such as B s → J/ψφ, K L → π 0 ¯ νν, or D 0 ...

We study J/ production at photon-photon colliders, which can be realized with Compton scattering of laser photons at e ϩ e Ϫ colliders. We find that the production rate through the color-octet channel is comparable to that through the color-singlet channel. Experimentally the two mechanisms can be studied separately because the processes have different signals. ͓S0556-2821͑98͒04301-X͔

We study CP violation in J/ψ → ΛΛ decay. This decay provides a good place to look for CP violation. Some observables are very sensitive to the Λ electric dipole moment d Λ and therefore can be used to improve the experimental upper bound on d Λ . CP violations in the lepton pair decays of J/ψ and Υ are also discussed.

We study CP violation in fermion pair decays of Higgs boson. We identify some CP odd observables related to the tree level decay amplitude. We find that a few thousand Higgs boson decay events can already provide important information about CP violation. If the Higgs boson is produced, such an analysis could be carried out at the SSC, LHC and NLC.

We consider the ~ossibility of searching for C P nonconservation in the process e+e-+ ZH. The simplest strategy is to measure the forward-backward asymmetry of the Z boson, a nonzero value of which signals C P violation. The effects of C P violation are calculated in the two Higgs doublet model. We show here that a choice of optimal observables can improve the chances of observing the effect. Although the number of events produced is expected not to be large, useful information about CP-violating parameters can be extracted.