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

Abstract

The resonant substructures of $B^0\to {\overline{D}}^0{\pi }^{+}{\pi }^{-}$ decays are studied with the Dalitz plot technique. In this study a data sample corresponding to an integrated luminosity of 3.0 fb${}^{-1}$ of $pp$ collisions collected 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 the last arises from the normalisation channel $B^0\to D^{\ast }(2010{)}^{-}{\pi }^{+}$. The ${\pi }^{+}{\pi }^{-}$ S-wave components are modelled with the Isobar and K-matrix formalisms. Results of the Dalitz plot analyses using both models are presented. 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 time as $J^P=3^{-}$. The branching fraction, mass and width of this structure are determined together with those of the $D_0^{\ast }(2400{)}^{-}$ and $D_2^{\ast }(2460{)}^{-}$ resonances. The branching fractions of other $B^0\to {\overline{D}}^0{h}^0$ decay components with $h^0\to {\pi }^{+}{\pi }^{-}$ are also reported. Many of these branching fraction measurements are the most precise to date. The first observation of the decays $B^0\to {\overline{D}}^0{f}_0(500)$, $B^0\to {\overline{D}}^0{f}_0(980)$, $B^0\to {\overline{D}}^0\rho (1450)$, $B^0\to D_3^{\ast }(2760{)}^{-}{\pi }^{+}$ and the first evidence of $B^0\to {\overline{D}}^0{f}_0(2020)$ are presented.

64 pages, 17 figures

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