First measurement of the CP -violating phase $ {\phi}_s^{d\overline{d}} $ in B s o → (K + π – )(K – π + ) decays
A flavour-tagged decay-time-dependent amplitude analysis of B s o → (K + π – )(K – π + ) decays is presented in the K ± π ∓ mass range from 750 to 1600MeV/c 2 . The analysis uses pp collision data collected with the LHCb detector at centre-of-mass energies of 7 and 8 TeV, corresponding to an integrated luminosity of 3.0 fb –1 . Several quasi-two-body decay modes are considered, corresponding to K ± π ∓ combinations with spin 0, 1 and 2, which are dominated by the K o * (800)0 and K o * (1430) o , the K*(892) o and the K 2 * (1430) o resonances, respectively. The longitudinal polarisation fraction for the B 0 s → K*(892)°K¯*(892) 0 decay is measured as f L = 0.208 ± 0.032 ± 0.046, where the first uncertainty is statistical and the second is systematic. The first measurement of the mixing-induced CP -violating phase, $ {\phi}_s^{d\overline{d}} $, in b → dd¯s transitions is performed, yielding a value of $ {\phi}_s^{d\overline{d}} $ = –0.10 ± 0.13 (stat) ± 0.14 (syst) rad.