Study of the penguin-dominated decay $B_s^0 \rightarrow K^{*0} \overline{K}{}^{*0}$ at LHCb

This thesis is devoted to the search for and subsequent analysis of the decay channel $B_s^0 \rightarrow K^{*0} \overline{K}{}^{*0}$, using the first data acquired by LHCb during 2010 and 2011 from the LHC proton-proton collisions at a centre-of-mass energy $\sqrt{s}=7\;{\rm TeV}$, corresponding to an integrated luminosity of $37\;{\rm pb}^{-1}$ and $1.0\;{\rm fb}^{-1}$ respectively. As a result of the work presented here, the first observation of the $B_s^0 \rightarrow K^{*0} \overline{K}{}^{*0}$ decay was performed. With the extended data sample collected in 2011, a combined angular and mass analysis was carried out, in order to assess the longitudinal polarisation fractions of the $K^{*0}$, obtaining $f_L = 0.201 \pm 0.057{\rm (stat.)} \pm 0.040{\rm (syst.)}$. The branching fraction for this decay was also measured to be $\mathcal{B}({B_s^0 \rightarrow K^{*0} \overline{K}{}^{*0}}) =$ (10.6 $\pm$ 1.8(stat.) $\pm$ 1.0(syst.) $\pm$ 0.6 $(f_d/f_s)$) $\times 10^{−6}$, in agreement with the Standard Model prediction. All of the triple product and $CP$ direct asymmetries measurable in the time-integrated and flavour-untagged analysis of $B_s^0 \rightarrow (K^+ \pi^-) (K^- \pi^+)$ were also determined. No signs of $CP$ violation were found, in agreement with the Standard Model expectation.