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The Dalitz plot analysis technique is used to study the resonantsubstructures of $B^{-} \to D^{+} \pi^{-} \pi^{-}$ decays in a data samplecorresponding to 3.0 ${\rm fb}^{-1}$ of $pp$ collision data recorded by theLHCb experiment during 2011 and 2012. A model-independent analysis of theangular moments demonstrates the presence of resonances with spins 1, 2 and 3at high $D^{+}\pi^{-}$ mass. The data are fitted with an amplitude modelcomposed 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 togetherwith the branching fractions for their production in $B^{-} \to D^{+} \pi^{-}\pi^{-}$ decays. The $D^{+}\pi^{-}$ S-wave has phase motion consistent withthat expected due to the presence of the $D^{*}_{0}(2400)^{0}$ state. Theseresults constitute the first observations of the $D^{*}_{3}(2760)^{0}$ and$D^{*}_{2}(3000)^{0}$ resonances.

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