Measurement of the resonant and CP components in ${\overline{B}}^0\to J/\ddot{I}ˆ\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ decays

Abstract

The resonant structure of the reaction ${\overline{B}}^0\to J/\ddot{I}ˆ\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ is studied using data from 3 fb${}^{-1}$ of integrated luminosity collected by the LHCb experiment, one-third at 7 Tev center-of-mass energy and the remainder at 8 Tev. The invariant mass of the $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ pair and three decay angular distributions are used to determine the fractions of the resonant and non-resonant components. Six interfering $\ddot{I}{€}^{+}\ddot{I}{€}^{-}$ states: $\ddot{I}(770)$, $f_0(500)$, $f_2(1270)$, $\ddot{I}(1450)$, $\ddot{I}‰(782)$ and $\ddot{I}(1700)$ are required to give a good description of invariant mass spectra and decay angular distributions. The positive and negative CP fractions of each of the resonant final states are determined. The $f_0(980)$ meson is not seen and the upper limit on its presence, compared with the observed $f_0(500)$ rate, is inconsistent with a model of tetraquark substructure for these scalar mesons at the eight standard deviation level. In the $q\overline{q}$ model, the absolute value of the mixing angle between the $f_0(980)$ and the $f_0(500)$ scalar mesons is limited to be less than $17^{\circ }$ at 90% confidence level.

28 pages 14 figures