Amplitude analysis of $B^- \to D^+ \pi^- \pi^-$ decays

The Dalitz plot analysis technique is used to study the resonant substructures of $B^- \to D^+ \pi^- \pi^-$ decays in a data sample corresponding to 3.0 fb$^-1$ of $pp$ collision data recorded by the LHCb experiment during 2011 and 2012. A model-independent analysis of the angular moments demonstrates the presence of resonances with spins 1, 2 and 3 at high $D^+\pi^-$ mass. The data are fitted with an amplitude model composed of a quasi-model-independent function to describe the $D^+\pi^-$ S-wave together with virtual contributions from the $D^*(2007)^{0}$ and $B^{*0}$ states, and components corresponding to the $D^*_2(2460)^{0}$, $D^*_1(2680)^{0}$, $D^*_3(2760)^{0}$ and $D^*_2(3000)^{0}$ resonances. The masses and widths of these resonances are determined together with the branching fractions for their production in $B^- \to D^+ \pi^- \pi^-$ decays. The $D^+\pi^-$ S-wave has phase motion consistent with that expected due to the presence of the $D^*_0(2400)^{0}$ state. These results constitute the first observations of the $D^*_3(2760)^{0}$ and $D^*_2(3000)^{0}$ resonances.