Abstract
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 $(10.8 \pm 2.1 {\ \rm (stat.)} \pm 1.4 {\ \rm (syst.)} \pm 0.6 \ (f_d/f_s) ) \times 10^{-6}$.
Highlights
Form q · ( 1 × 2) where q is the momentum of one of the final vector mesons and 1 and 2 are their respective polarisations
Remarkably low longitudinal polarisation fraction was observed, compatible with that found for the similar decay Bs0 → φφ [9], and at variance with that observed in the mirror channel B0 → K∗0K∗0 [10] and with some predictions from QCD factorisation [7, 11]
In the analysis presented in this paper, only the time-integrated asymmetries
Summary
Considering only the S-wave (J1,2 = 0) and P-wave (J1,2 = 1) production of the Kπ pairs, with J1,2 the angular momentum of the respective Kπ combination, the decay Bs0 → (K+π−)J1(K−π+)J2 can be described in terms of six helicity decay amplitudes. Each amplitude corresponds to a different helicity (Lz = 0, +1, −1) of the vector mesons in the final state with respect to their relative momentum direction, H0, H+ and H−. Kπ pairs need to be taken into account within the mass window indicated above The amplitudes describing this S-wave configuration are AVS, ASV and ASS, corresponding to the following decays. It is possible to write the full decay amplitude in terms of CP -odd and CP -even amplitudes (the SS final configuration is a CP eigenstate with ηSS = 1) by defining
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