The resonant structure of the reaction ${\overline{B}}^0\to J/\psi {\pi }^{+}{\pi }^{-}$ is studied using data from $3{\mathrm{fb}}^{-1}$ 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 ${\pi }^{+}{\pi }^{-}$ pair and three decay angular distributions are used to determine the fractions of the resonant and nonresonant components. Six interfering ${\pi }^{+}{\pi }^{-}$ states, $\rho (770)$, $f_0(500)$, $f_2(1270)$, $\rho (1450)$, $\omega (782)$ and $\rho (1700)$, are required to give a good description of invariant mass spectra and decay angular distributions. The positive and negative charge parity 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 where these scalar mesons are formed from two quarks and two antiquarks (tetraquarks) 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° at 90% confidence level.

• Received 22 April 2014

DOI:https://doi.org/10.1103/PhysRevD.90.012003

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© 2014 CERN, for the LHCb collaboration