The resonant structure of the reaction $overline{B}^0rightarrow J/psi pi^+pi^-$ 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 $pi^+pi^-$ pair and three decay angular distributions are used to determine the fractions of the resonant and non-resonant 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 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 $qoverline{q}$ 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.
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