First measurement of the $CP$-violating phase ${\varphi }_s^{d\overline{d}}$ in $B_s^0\to (K^{+}{\pi }^{-})(K^{-}{\pi }^{+})$ decays

Abstract

A flavour-tagged decay-time-dependent amplitude analysis of $B_s^0\to (K^{+}{\pi }^{-})(K^{-}{\pi }^{+})$ decays is presented in the $K^{\pm }{\pi }^{\mp }$ mass range from 750 to 1600 MeV$/c^2$. 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 $K^{\pm }{\pi }^{\mp }$ combinations with spin 0, 1 and 2, which are dominated by the $K_0^{\ast }(800{)}^0$ and $K_0^{\ast }(1430{)}^0$, the $K^{\ast }(892{)}^0$ and the $K_2^{\ast }(1430{)}^0$ resonances, respectively. The longitudinal polarisation fraction for the $B_s^0\to K^{\ast }(892{)}^0{\overline{K}}^{\ast }(892{)}^0$ decay is measured as $f_L=0.208\pm 0.032\pm 0.046$, where the first uncertainty is statistical and the second is systematic. The first measurement of the mixing-induced $CP$-violating phase, ${\varphi }_s^{d\overline{d}}$, in $b\to d\overline{d}s$ transitions is performed, yielding a value of ${\varphi }_s^{d\overline{d}}=-0.10$ $\pm$ $0.13$ (stat) $\pm$ $0.14$ (syst) rad.

All figures and tables, along with any supplementary material and additional information, are available at https://cern.ch/lhcbproject/Publications/p/LHCb-PAPER-2017-048.html