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

Abstract

An angular analysis of the decay $B_s^0\to K^{\ast 0}\bar{K}{}^{\ast 0}$ 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 $B_s^0\to K^{\ast }(892{)}^0\bar{K}{}^{\ast }(892{)}^0$ decay. A large scalar contribution from the $K_0^{\ast }(1430)$ and $K_0^{\ast }(800)$ 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 $\mathcal{B}(B_s^0\to K^{\ast }(892{)}^0\bar{K}{}^{\ast }(892{)}^0)$ is measured to be $(10.8\pm 2.1(stat.)\pm 1.4(syst.)\pm 0.6(f_d/f_s))\times 10^{-6}$.