Exploring $b\rightarrow s$ electroweak penguin decays at LHCb

The angular distribution of $B^{0} \to K^{*0} \mu^+ \mu^-$ was studied using 1.0$\mathrm{fb}^{-1}$ of $pp$ collisions recorded at the LHCb detector at the LHC. Angular observables are measured in five independent bins of the di-muon invariant mass squared, $q^2$, and the theoretically interesting region from $1 < q^{2} < 6~\mathrm{GeV}^{2}/c^{4}$. The results are in good agreement with Standard Model predictions. The contribution from a $K\pi$ S-wave is included in the angular distribution of $B^{0} \to K^{+}\pi^{-}\mu^+ \mu^-$. The $K\pi$ S-wave is shown to have an overall dilution effect on measurements of the $B^{0} \to K^{+}\pi^{-}\mu^+ \mu^-$ angular observables. For an S-wave contribution of $7\%$ between a $K\pi$ invariant mass squared of $0.64<p^{2} <1.0~\mathrm{GeV}^{2}/c^{4}$, there is a significant bias on the angular observables for dataset of over 500 events. It is possible to remove this bias by incorporating the S-wave into the angular distribution and by fitting the $K\pi$ mass spectrum. The fraction of the S-wave in $B^{0} \to K^{*0} \mu^+ \mu^-$, $F_S$, was analysed in seven bins of $q^2$ using $1.0\mathrm{fb}^{-1}$ of data from LHCb. The value of $F_S$ in the region from $1 < q^{2} < 6~\mathrm{GeV}^{2}/c^{4}$ and from $0.64<p^{2}<1.0~\mathrm{GeV}^{2}/c^{4}$ was found to be