– 1 – Polarization in B Decays

We review the notation used in polarization measurements of B decays and discuss CP -violating observables in polarization measurements. We look at several examples of vector-vector B meson decays, while more details about the theory and experimental results in B decays can be found in a separate mini-review [1] in this Review. The angular distribution of the B meson decay to two vector mesons with the sequential decay of each vector meson is of special interest because it reflects both weakand strong-interaction dynamics. Using the helicity formalism [2], this distribution can be expressed as a function of three helicity angles which describe the flight direction of the vector meson daughters in the decay chain. An equivalent set of transversity angles can be used to reparameterize the angular distribution [3]. While the function of the angles depends on the quantum numbers of the vector mesons daughters, the differential decay width has three complex amplitudes Aλ corresponding to the vector meson helicity λ = 0 or ±1 [4], where the last two can be expressed in terms of parity-even and parity-odd amplitudes A‖,⊥ = (A+1 ±A−1)/ √ 2. The angular distribution involves the terms proportional to the absolute values squared of the three amplitudes, plus the interference terms Im(A⊥A‖), Re(A‖A∗0), and Im(A⊥A∗0). Therefore, spin alignment in the vector-vector decay can be expressed with the parameters fL = |A0|/Σ|Aλ|, f⊥ = |A⊥|/Σ|Aλ|, and the relative phases φ‖ = arg(A‖/A0), φ⊥ = arg(A⊥/A0). Moreover, CP -violation can be tested in the angular distribution of the decay as the difference between the B and B̄. This includes the vector triple-product asymmetries, directCP asymmetries in the amplitudes, and mixing-induced CP asymmetries in the time evolution. Overall, six non-trivial CP violating parameters can be constructed from the Āλ and Aλ amplitudes [4]. Three parameters are equivalent to the three direct CP violating quantities, and in Ref. 5 they are chosen as