Oscillations and CP Violation in Neutral Mesons

Two-state Hamiltonian in the Meson Rest Frame

• Discuss the most general Hamiltonian H for a meson-antimeson system; What constraint does CPT implies? What is the phase-independent condition for CP conservation? Recapitulate eigenvalues and eigenvectors for H.
• Derive the expression for the ratio between right-sign and wrong-sign decays of a neutral meson (and a neutral antimeson). Discuss the possible sources of CP violation.
• What are analogies and differences between the K and B systems, as far as the mixing properties are concerned? The CP violating asymmetry in semileptonic K decays and the mass difference in the B system are both controlled by the 12 matrix element of the mass matrix. Analyze the dipendence of this matrix element on the SM parameters.
• Sketch the computation of the box diagram. Why is the total amplitude convergent despite the divergent behaviour of the individual contributions? Describe the difference in the box diagram between the K and the B systems.