A Time Dependent Angular Analysis of the Rare Decay $\bar{B}^0_s, B^0_s \to \phi(\to K^+K^-)\mu^+\mu^-$

This report presents both a time-independent and a time-dependent angular analysis study of the rare decay mode $\bar{B}^0_s, B^0_s \to \phi(\to K^+K^-)\mu^+\mu^-$. The time-independent PDF was studied in terms of four CP-averages and four CP-asymmetries of this decay. One-dimensional projections of the helicity angles were plotted and fitted using a maximum-log likelihood fit method. High-statistical toys were generated in order to explore whether the simulated data was unbiased and free from large errors before studying the time-dependent decay scenario. An analytical calculation of the time-dependent PDF was conducted, with a new basis defined analogous to the time-independent case. The time-dependent PDF included new observables with respect to the time-independent case, which could point to a new avenue in which to explore New Physics scenarios. New high-statistical toys were generated and the four one-dimensional projections were plotted and compared to the time-independent results.