Methods for Angular Analyses of $B \to J/\psi X$

This note describes a Monte Carlo based method to take angular efficiencies in angular analyses into account, in particular for the Bs->JpsiPhi and Bd->JpsiK*channels. We describe the theory behind the method of ‘angular efficiency weights’, extending it for general values of DeltaGamma_s and showing it can be used together with proper time efficiencies. Also a qualitative description of the relation between angular and proper time efficiencies is given. We perform toy Monte Carlo studies to validate and demonstrate the robustness of the method and determine the amount of statistics needed. We present a method to visualize the fit results while using the efficiency weights. After that we study when angular resolution effects can be neglected. Furthermore we propose an alternative parameterization of the strong phases in the fit, which makes the estimate better and the fit more stable. Finally we perform a sensitivity study with the most recent full Monte Carlo based settings, using the angular efficiency correction method and studying the parameterization of the strong phases. We find that the efficiency correction method and the alternative parameterization of the strong phases do not introduce losses of sensitivities. In particular the sensitivity to −2beta_s is (0.030 ± 0.001) radians for a nominal year of LHCb operation.