First measurement of the CP-violating phase ϕsdd¯ $$ {\phi}_s^{d\overline{d}} $$ in Bs0 → (K+π−)(K−π+) decays

A flavour-tagged decay-time-dependent amplitude analysis of B 0  → (K+π−)(K−π+) decays is presented in the K±π∓ mass range from 750 to 1600MeV/c2. 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 0 * (800)0 and K 0 * (1430)0, the K*(892)0 and the K 2 * (1430)0 resonances, respectively. The longitudinal polarisation fraction for the $$ {B}_s^0\to {K}^{\ast }(892){}^{\circ}{\overline{K}}^{\ast }{(892)}^0 $$ decay is measured as fL = 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 $$ b\to d\overline{d}s $$ transitions is performed, yielding a value of $$ {\phi}_s^{d\overline{d}}=-0.10\pm 0.13\left(\mathrm{stat}\right)\pm 0.14 $$ (syst) rad.