Measurement of $CP$ asymmetries and polarisation fractions in $B_s^0 \rightarrow K^{*0}\bar{K}{}^{*0}$ decays

An angular analysis of the decay $B_s^0 rightarrow K^{*0}bar{K}{}^{*0}$ is performed using $pp$ collisions corresponding to an integrated luminosity of $1.0$ ${fb}^{-1}$ collected by the LHCb experiment at a centre-of-mass energy $sqrt{s} = 7$ TeV. A combined angular and mass analysis separates six helicity amplitudes and allows the measurement of the longitudinal polarisation fraction $f_L = 0.201 pm 0.057 {(stat.)} pm 0.040{(syst.)}$ for the $B_s^0 rightarrow K^*(892)^0 bar{K}{}^*(892)^0$ decay. A large scalar contribution from the $K^{*}_{0}(1430)$ and $K^{*}_{0}(800)$ resonances is found, allowing the determination of additional $CP$ asymmetries. Triple product and direct $CP$ asymmetries are determined to be compatible with the Standard Model expectations. The branching fraction $mathcal{B}(B_s^0 rightarrow K^*(892)^0 bar{K}{}^*(892)^0)$ is measured to be $(10.8 pm 2.1 { rm (stat.)} pm 1.4 { rm (syst.)} pm 0.6 (f_d/f_s) ) times 10^{-6}$.