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Major new experimental efforts on detecting CP violation in $B$ decays will very soon go on the air. Recent developments suggest that final state interaction phases in exclusive decays of $B$ are unlikely to be small indicating the possibility of observable direct CP asymmetries in these channels. CLEO results on charmless hadronic modes suggest penguin amplitudes are rather big implying that the extraction of $alpha$ from $B^0$-$bar B^0$ alone will be difficult, thus necessitating also information from direct CP ull. Importance of $B(B_s)$ decays to two vectors for model independent tests of electroweak penguins and for extraction of $alpha(gamma)$ is emphasized. Inclusive $bto sg^ast$ and related modes, e.g. $Bto eta^prime X_s$, are very good probes of CP-odd phase(s) due to beyond the standard model physics. On the other hand, $bto dg^ast$ and related modes, e.g. $Bto eta^prime X_d$ are more suitable for CP violation due to the CKM phase. Two body $b$-quark decays: $bto Mq_f$ leading to semi-inclusive, $B$ decays, $Bto MX$ (with $2lsim E_Mlsim2.8$ GeV), are very interesting and important. Their theory is relatively clean; partial rate asymmetries may be large in several cases (e.g. $M=K^ast, K, rho, pi...$) and a few cases provide very good probe of electroweak penguins.
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The recently observed CP violation in B decay and $B$-$ovar{B}$ mixing data put constraints on the mass of $W_R$ and the parameters of the right-handed current quark mixing matrix $V^R$ in $SU(2)_L times SU(2)_Rtimes U(1)$ gauge model. It is shown that the allowed region of parameters are severely restricted for light $W_R$ with mass on the order of 1 TeV. There exist sets of parameters which can accommodate large CP violation as measured by Belle, $sin2phi_1|_{exp}simeq 1$, for $M_{W_R}=1 sim 10$ TeV.
We study the determination of gamma from CP-violating observables in B -> pi+ pi- and B -> psi K_S. This determination requires theoretical input to one combination of hadronic parameters. We show that a mild assumption about this quantity may allow bounds to be placed on gamma, but we stress the pernicious effects that an eightfold discrete ambiguity has on such an analysis. The bounds are discussed as a function of the direct (C) and interference (S) CP-violating observables obtained from time-dependent B -> pi+ pi- decays, and their behavior in the presence of new physics effects in B-Bbar mixing is studied. (V2: Misprints corrected. Slightly improved discussion.)
Contributions to B - bar B mixing from physics beyond the standard model may be detected from CP-violating asymmetries in B decays. There exists the possibility of large new contributions that cannot be detected by first generation experiments because of a discrete ambiguity. Some possible strategies for resolving this are discussed.
We point out that, given the current experimental status of radiative kaon decays, a subclass of the ${cal O} (p^4)$ counterterms of the weak chiral lagrangian can be determined in closed form. This involves in a decisive way the decay $K^pm to pi ^pm pi ^0 l^+ l^-$, currently being measured at CERN by the NA48/2 and NA62 collaborations. We show that consistency with other radiative kaon decay measurements leads to a rather clean prediction for the ${cal{O}}(p^4)$ weak couplings entering this decay mode. This results in a characteristic pattern for the interference Dalitz plot, susceptible to be tested already with the limited statistics available at NA48/2. We also provide the first analysis of $K_Sto pi^+pi^-gamma^*$, which will be measured by LHCb and will help reduce (together with the related $K_L$ decay) the experimental uncertainty on the radiative weak chiral couplings. A precise experimental determination of the ${cal{O}}(p^4)$ weak couplings is important in order to assess the validity of the existing theoretical models in a conclusive way. We briefly comment on the current theoretical situation and discuss the merits of the different theoretical approaches.
U-spin symmetry predicts equal CP rate asymmetries with opposite signs in pairs of $Delta S=0$ and $Delta S=1$ $B$ meson decays in which initial and final states are related by U-spin reflection. Of particular interest are six decay modes to final states with pairs of charged pions or kaons, including $B_s to pi^+K^-$ and $B_sto K^+K^-$ for which asymmetries have been reported recently by the LHCb collaboration. After reviewing the current status of these predictions, highlighted by the precision of a relation between asymmetries in $B_s to pi^+K^-$ and $B^0to K^+pi^-$, we perform a perturbative study of U-spin breaking corrections, searching for relations for combined asymmetries which hold to first order. No such relation is found in these six decays, in two-body decays involving a neutral kaon, and in three-body $B^+$ decays to charged pions and kaons.
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