Angular analysis of a B decaying into tensor, vector and scalar modes

Abstract

This thesis studies the decays B ---> J/{\`Psi}T, B ---> J /{`Psi}V and B ---> J /{`Psi}S, where T, V and S are tensor (J^P = 2^+), vector (J^P = 1^-) and scalar (J^P = 0^+) mesons respectively. The Present study is inspired by the recent observation of the decays B ---> J/{`Psi}K^*base X(1430), where X = 0,2. There exist two mesons, a tensor meson K^*base2(1430) and a scalar meson K^*base0(1430) at the same mass of 1430 MeV, making it difficult to measure the branching fraction for B ---> K^*base2(1430), without including contributions from B ---> K^*base0(1430). There also exists a vector meson resonances, at 1410 MeV, K^*(1410), that is close enough to overlap with the wide K^*baseX(1430)resonances. Since, all of these decay modes contribute to the same final state B ---> K{`Pi}l^+ l^-, contributions from the various decay channels cannot be separated by cuts on the kinematics. It is shown in detail how angular analysis could be used to separate contributions from each of the decay modes. The most general effective matrix elements for each of the decay channels is written using Lorenz invariance and current conservation. The decay spectrum for the final state B ---> K{`Pi}l^+ l^-, is calculated. The K^*baseX(1430) and K^*(1410) are considered to decay to K{`Pi} and J/{`Psi} to l^+ l^- . The angular distribution of the K in the K{`Pi} center of mass(c.m.) frame and l^- in the l^+ l^- c.m. frame, are studied; Also the correlation between the K{`Pi} decay plane and the l^+ l^- decay frame are studied. The formulation developed here could be applied to include any scalar, vector or tensor meson, in addition to K^*base X (1430) and K^*(1410). The study performed in this thesis finds immediate application in the analysis of data collected by the B factories running at KEK Japan ans SLAC USA.