CP Violation and the Role of Electroweak Penguins in Non-leptonic B Decays

The phenomenon of CP violation in the B system and strategies for extracting CKM phases are reviewed. We focus both on general aspects and on some recent developments including CP-violating asymmetries in Bd decays, the Bs system in light of a possible width difference ∆Γs, charged B decays, and SU(3) relations among certain transition amplitudes. In order to describe the relevant non-leptonic B decays, low energy effective Hamiltonians calculated beyond the leading logarithmic approximation are used. Special emphasis is given to the role of electroweak penguin operators in such transitions. These effects are analyzed both within a general framework and more specifically in view of the theoretical cleanliness of methods to determine CKM phases. Strategies for obtaining insights into the world of electroweak penguins are discussed. To appear in International Journal of Modern Physics A Internet: [email protected] International Journal of Modern Physics A, f c World Scientific Publishing Company CP VIOLATION AND THE ROLE OF ELECTROWEAK PENGUINS IN NON-LEPTONIC B DECAYS ROBERT FLEISCHER Institut für Theoretische Teilchenphysik, Universität Karlsruhe D–76128 Karlsruhe, Germany Received (received date) Revised (revised date) The phenomenon of CP violation in the B system and strategies for extracting CKM phases are reviewed. We focus both on general aspects and on some recent developments including CP-violating asymmetries in Bd decays, the Bs system in light of a possible width difference ∆Γs, charged B decays, and SU(3) relations among certain transition amplitudes. In order to describe the relevant non-leptonic B decays, low energy effective Hamiltonians calculated beyond the leading logarithmic approximation are used. Special emphasis is given to the role of electroweak penguin operators in such transitions. These effects are analyzed both within a general framework and more specifically in view of the theoretical cleanliness of methods to determine CKM phases. Strategies for obtaining insights into the world of electroweak penguins are discussed. 1. Setting the Scene Although the experimental discovery of CP violation by Christenson, Cronin, Fitch and Turlay goes back to the year 1964, the non-conservation of the CP symmetry still remains one of the unsolved mysteries in particle physics. 1.1. CP Violation in the K-System So far CP violation has been observed only within the neutral K-meson system, where it is described by two complex quantities called ε and ε which are defined by the following ratios of decay amplitudes: A(KL → ππ) A(KS → π+π−) = ε+ ε, A(KL → ππ) A(KS → π0π0) = ε− 2ε. (1) While ε = (2.26± 0.02) · eiπ4 · 10 parametrizes “indirect” CP violation originating from the fact that the mass eigenstates of the neutral K-meson system are not eigenstates of the CP operator, the quantity Re(ε/ε) provides a measure of “direct” CP violation in K → ππ transitions. Unfortunately the experimental situation concerning Re(ε/ε), which has been subject of very involved experiments performed both at CERN and Fermilab by the the NA31 and E731 collaborations, respectively, is unclear at present. Whereas NA31 finds Re(ε/ε) = (23 ± 7) · 10 indicating already direct CP violation, the result Re(ε/ε) = (7.4±5.9) ·10−4 of the Fermilab