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A four-body amplitude analysis of the $B^- \to D^{*+} \pi^- \pi^-$ decay isperformed, where fractions and relative phases of the various resonancescontributing to the decay are measured. Several quasi-model-independentanalyses are performed aimed at searching for the presence of new states andestablishing the quantum numbers of previously observed charmed mesonresonances. In particular the resonance parameters and quantum numbers aredetermined for the $D_1(2420)$, $D_1(2430)$, $D_0(2550)$, $D^*_1(2600)$,$D_2(2740)$ and $D^*_3(2750)$ states. The mixing between the $D_1(2420)$ and$D_1(2430)$ resonances is studied and the mixing parameters are measured. Thedataset corresponds to an integrated luminosity of 4.7 $fb^{-1}$, collected inproton-proton collisions at center-of-mass energies of 7, 8 and 13 TeV with theLHCb detector.

Determination of quantum numbers for several excited charmed mesons observed in $B^- \to D^{*+} \pi^- \pi^-$ decays