First measurement of the CP-violating phase ${\phi}_s^{d\overline{d}}$ in B ⁰ _s  → (K⁺π⁻)(K⁻π⁺) decays

Abstract

A flavour-tagged decay-time-dependent amplitude analysis of B ⁰ _s  → (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 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 $b\to d\overline{d}s$ 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.