There is some theoretical uncertainty in the predictions for CP-violating hadronic asymmetries in neutral-^ decays to CP eigenstates due to the existence of penguin diagrams. Using isospin relations, we show that it is possible to remove this uncertainty for the decays B^-* nn, PACS numbers: 13.25.-l-m, llJO.Er, 14.40.JzOne of the few remaining problems confronting the standard model of the weak and electromagnetic interactions is whether or not the Cabibbo-Kobayashi-Maskawa (CKM) matrix is the correct explanation of CP violation. Probably the best method of verifying this is by measuring CP-violating asymmetries in the B system J The most promising of these^involves a hadronic final state_to which both B^ and B^ can decay. Because of B^-B^ mixing, a state which at time t =0 was a B^ (or a B^) will evolve in time into a mixture of B^ and B^. CP violation then occurs due to the interference between the decay chains B^-^f and B^^ B^-^f. If the final state is a CP eigenstate, then the time-dependent asymmetry a(r) = nB%t)--f)-riB%)-^f)

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The decays B → P P , where P denotes a pseudoscalar meson, are analyzed, with emphasis on charmless final states. Numerous triangle relations for amplitudes hold within SU(3) symmetry, relating (for example) the decays B + → π + π 0 , π 0 K + , and π + K 0 . Such relations can improve the possibilities for early detection of CP -violating asymmetries. Within the context of a graphical analysis of decays, relations are analyzed among SU(3) amplitudes which hold if some graphs are neglected. One application is that measurements of the rates for the above three B + decays and their charge-conjugates can be used to determine a weak CKM phase. With measurements of the remaining rates for B decays to ππ, πK, and KK, one can obtain two CKM phases and several differences of strong phase shifts.

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We discuss the role of electroweak penguins in B decays to two light pseudoscalar mesons. We confirm that the extraction of the weak phase α through the isospin analysis involving B → ππ decays is largely unaffected by such operators. However, the methods proposed to obtain weak and strong phases by relating B → ππ, B → πK and B → KK decays through flavor SU(3) will be invalidated if electroweak penguins are large. We show that, although the introduction of electroweak penguin contributions introduces no new amplitudes of flavor SU(3), there are a number of ways to experimentally measure the size of such effects. Finally, using SU(3) amplitude relations we present a new way of measuring the weak angle γ which holds even in the presence of electroweak penguins.

The theory of CP violation based on phases in weak couplings in the Cabibbo-Kobayashi-Maskawa (CKM) matrix requires the phase γ ≡ Arg V *

In the Standard Model (SM) the photon in radiativeB 0 andB s decays is predominantly left-handed. Thus, mixing induced CP asymmetries in b → sγ and b → dγ are suppressed by m s /m b and m d /m b , respectively, and are very small. In many extensions of the SM, such as the left-right symmetric model (LRSM), SU(2) × U(1) models with exotic fermions and SUSY, the amplitude of right-handed photons grows proportional to the virtual heavy fermion mass, which can lead to large asymmetries. As an example, in the LRSM, asymmetries larger than 50% are possible even when radiative decay rate measurements agree with SM predictions.