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The resonant substructures of $B^0 \to \overline{D}^0 \pi^+\pi^-$ decays arestudied with the Dalitz plot technique. In this study a data samplecorresponding to an integrated luminosity of 3.0 fb$^{-1}$ of $pp$ collisionscollected by the LHCb detector is used. The branching fraction of the $B^0 \to\overline{D}^0 \pi^+\pi^-$ decay in the region $m(\overline{D}^0\pi^{\pm})>2.1$GeV$/c^2$ is measured to be $(8.46 \pm 0.14 \pm 0.29 \pm 0.40) \times 10^{-4}$,where the first uncertainty is statistical, the second is systematic and thelast arises from the normalisation channel $B^0 \to D^*(2010)^-\pi^+$. The$\pi^+\pi^-$ S-wave components are modelled with the Isobar and K-matrixformalisms. Results of the Dalitz plot analyses using both models arepresented. A resonant structure at $m(\overline{D}^0\pi^-) \approx 2.8$GeV$/c^{2}$ is confirmed and its spin-parity is determined for the first timeas $J^P = 3^-$. The branching fraction, mass and width of this structure aredetermined together with those of the $D^*_0(2400)^-$ and $D^*_2(2460)^-$resonances. The branching fractions of other $B^0 \to \overline{D}^0 h^0$ decaycomponents with $h^0 \to \pi^+\pi^-$ are also reported. Many of these branchingfraction measurements are the most precise to date. The first observation ofthe decays $B^0 \to \overline{D}^0 f_0(500)$, $B^0 \to \overline{D}^0f_0(980)$, $B^0 \to \overline{D}^0 \rho(1450)$, $B^0 \to D_3^*(2760)^- \pi^+$and the first evidence of $B^0 \to \overline{D}^0 f_0(2020)$ are presented.

Dalitz plot analysis of $B^0 \to \overline{D}^0 \pi^+\pi^-$ decays