Measurement of Charmless B → V V decays at BABAR

A vector-vector or vector-axial vector B-meson decay can be characterised by three complex helicity amplitudes, A+, A0 and A−, corresponding to meson helicity states λ = +1, 0 and −1, respectively. The A0 amplitude is expected to dominate due to the (V −A) nature of weak interactions and helicity conservation in strong interactions [1]. Most B decays that arise from tree level b → c transitions follow an amplitude heirachy of |A0| > |A+| > |A−|. The B meson decays to heavy vector particles with charm such as B → J/ΨK show a substantial fraction of the amplitude with transverse polarisation of the mesons (A±). This is because the larger the meson mass, the weaker the amplitude heirachy. Therefore the amplitude heirachy |A0| > |A+| > |A−| is expected to be more significant in B decays to light vector particles in both penguin [2–4] and tree-level [1] transitions. In the tree-level b → u transitions, such as B → ρρ [5], B → ρρ [6], and B → ωρ [7], the dominance of longitudinal polarisation has been confirmed by the BABAR and Belle experiments. However a large fraction of transverse polarisation was first observed by BABAR and confirmed by Belle for the decays B → φK and B → ρK, which is a significant departure from the expected dominance of the longitudinal amplitude. This polarisation anomaly in the vector-vector decays B → φK and B → ρK suggests other contributions to the amplitude, that were previously neglected. This possibility has generated great interest in vector-vector decays, motivating a number of proposed contributions from physics beyond the standard model [8]. In addition there are mechanisms within the standard model which have been proposed to explain the anomaly such as annihilation penguin [4, 9] or electroweak penguin, or QCD rescattering [10]. The key to understanding this anomaly could be obtained by studying other vector-vector and vector-axial vector decays such as B → φV , B → KK, B → ρb1, B → Ka1 and comparing experimental results with theory.