Observation of the decay ${\overline{B}}_s^0\to \ddot{I}ˆ(2S)K^{+}\ddot{I}{€}^{-}$

Abstract

The decay ${\overline{B}}_s^0\to \ddot{I}ˆ(2S)K^{+}\ddot{I}{€}^{-}$ is observed using a data set corresponding to an integrated luminosity of $3.0f{b}^{-1}$ collected by the LHCb experiment in $pp$ collisions at centre-of-mass energies of 7 and 8 TeV. The branching fraction relative to the $B^0\to \ddot{I}ˆ(2S)K^{+}\ddot{I}{€}^{-}$ decay mode is measured to be \begin{equation} \frac{{\cal B}(\overline{B}^0_s \rightarrow ψ(2S) K^+ π^-)}{{\cal B}(B^0 \rightarrow ψ(2S) K^+ π^-)} = 5.38 \pm 0.36 (stat) \pm 0.22 (syst) \pm 0.31 \, (f_s/f_d) \, \%,\nonumber \end{equation} where $f_s/f_d$ indicates the uncertainty due to the ratio of probabilities for a $b$ quark to hadronise into a $B_s^0$ or $B^0$ meson. Using an amplitude analysis, the fraction of decays proceeding via an intermediate $K^{\ast }(892{)}^0$ meson is measured to be $0.645\pm 0.049(stat)\pm 0.049(syst)$ and its longitudinal polarisation fraction is $0.524\pm 0.056(stat)\pm 0.029(syst)$. The relative branching fraction for this component is determined to be \begin{equation} \frac{{\cal B}(\overline{B}^0_s \rightarrow ψ(2S) K^*(892)^0)}{{\cal B}(B^0 \rightarrow ψ(2S) K^*(892)^0)} = 5.58 \pm 0.57 (stat) \pm 0.40 (syst) \pm 0.32 \, (f_s/f_d) \, \%. \nonumber \end{equation} In addition, the mass splitting between the $B_s^0$ and $B^0$ mesons is measured as \begin{equation} M(B^0_s) - M(B^0) = 87.45 \pm 0.44 (stat) \pm 0.07 (syst) MeV/c^2. \nonumber \end{equation}

15 pages, 7 figures. v2 updated with published version. All figures and tables, along with any supplementary material and additional information, are available at https://lhcbproject.web.cern.ch/lhcbproject/Publications/LHCbProjectPublic/LHCb-PAPER-2015-010.html