Study of $\hat{I}\cdot -\hat{I}{\cdot }^{\prime }$ mixing from measurement of $B_{(s)}^0\to J/\ddot{I}ˆ\hat{I}{\cdot }^{(\prime )}$~decay rates

Abstract

A study of $B^0$~and $B_s^0$ meson decays into $J/\ddot{I}ˆ\hat{I}\cdot$~and $J/\ddot{I}ˆ\hat{I}{\cdot }^{\prime }$ final states is performed using a data set of proton-proton collisions at centre-of-mass energies of 7 and 8TeV, collected by the LHCb experiment and corresponding to 3.0fb${}^{-1}$ of integrated luminosity. The decay $B^0\to J/\ddot{I}ˆ\hat{I}{\cdot }^{\prime }$ is observed for thefirst time. The following ratios of branching fractions are measured: $$\frac{\mathcal{B}(B^0\to J/\ddot{I}ˆ\hat{I}{\cdot }^{\prime })}{\mathcal{B}(B_s^0\to J/\ddot{I}ˆ\hat{I}{\cdot }^{\prime })}=(2.28\pm 0.65(stat)\pm 0.10(syst)\pm 0.13(f_s/f_d))\times 10^{-2},$$ $$\frac{\mathcal{B}(B^0\to J/\ddot{I}ˆ\hat{I}\cdot )}{\mathcal{B}(B_s^0\to J/\ddot{I}ˆ\hat{I}\cdot )}=(1.85\pm 0.61(stat)\pm 0.09(syst)\pm 0.11(f_s/f_d))\times 10^{-2},$$ where the third uncertainty is related to the present knowledge of $f_s/f_d$, the ratio between the probabilities for a $b$ quark to form a $B_s^0$ or $B^0$ meson. The branching fraction ratios are used to determine the parameters of $\hat{I}\cdot -\hat{I}{\cdot }^{\prime }$ meson mixing. In addition, the first evidence for the decay $B_s^0\to \ddot{I}ˆ(2S)\hat{I}{\cdot }^{\prime }$ is reported, and the relative branching fraction is measured, $$\frac{\mathcal{B}(B_s^0\to \ddot{I}ˆ(2S)\hat{I}{\cdot }^{\prime })}{\mathcal{B}(B_s^0\to J/\ddot{I}ˆ\hat{I}{\cdot }^{\prime })}=(38.7\pm 9.0(stat)\pm 1.3(syst)\pm 0.9(\mathcal{B}))\times 10^{-2},$$ where the third uncertainty is due to the limited knowledge of the branching fractions of $J/\ddot{I}ˆ$ and $\ddot{I}ˆ(2S)$~mesons.

26 pages, 7 figures