Modified Godfrey-Isgur mass predictions \cite{Godfrey:1985xj}. The figure shows the $c\bar{u}$ spectrum in which the masses have been scaled such that the ground state coincides with the $D^0$ mass. The $2^-$ states, not shown in the original publication, have been inserted following the splitting structure of the 1P states.

Invariant mass distribution for (a) $ D ^+ \rightarrow K^-\pi^+\pi^+$, (b) $ D ^0 \rightarrow K^-\pi^+$, and (c) $ D ^{*+} \rightarrow D ^0 \pi ^+ $ decays. The solid lines are the results from the fits described in the text. The vertical dashed lines indicate the signal regions.

Invariant mass distribution for (a) $ D ^+ \pi ^- $, (b) $ D ^0 \pi ^+ $ and (c) $ D ^{*+} \pi ^- $ candidates (points). The full line histograms (in red) show the wrong-sign mass spectra for (a) $ D ^+ \pi ^+ $, (b) $ D ^0 \pi ^- $ and (c) $ D ^{*+} \pi ^+ $ normalized to the same yield at high $D^{(*)}\pi$ masses.

Fit to the $ D ^{*+} \pi ^- $ mass spectrum, {\it enhanced unnatural parity sample}, as defined in Table ???. The dashed (blue) line shows the fitted background, the dotted (red) line the $ D_1(2420)^0$ contribution. The inset displays the $ D ^{*+} \pi ^- $ mass spectrum after subtracting the fitted background. The full line curves (blue) show the contributions from $ D_{J}(2580)^0$ , $ D_{J}(2740)^0$ , and $ D_{J}(3000)^0$ states. The top window displays the pull distribution where the horizontal lines indicate $\pm 3 \sigma$. The pull is defined as $(N_{\rm data} - N_{\rm fit})/\sqrt{N_{\rm data}}$.

Fit to the {\it natural parity sample} $ D ^{*+} \pi ^- $ mass spectrum. The dashed (blue) line shows the fitted background, the dotted lines the $ D_1(2420)^0$ (red) and $ {D}^*_2(2460)^0$ (blue) contributions. The inset displays the $ D ^{*+} \pi ^- $ mass spectrum after subtracting the fitted background. The full line curves (red) show the contributions from $ D_{J}(2580)^0$ , $ D_{J}(2740)^0$ , and $ D_{J}(3000)^0$ . The dotted (blue) lines display the $ D^*_{J}(2650)^0$ and $ D^*_{J}(2760)^0$ contributions. The top window shows the pull distribution where the horizontal lines indicate $\pm 3 \sigma$.

Fit to the {\it unnatural parity sample} $ D ^{*+} \pi ^- $ mass spectrum. The dashed (blue) line shows the fitted background, the dotted lines the $ D_1(2420)^0$ (red) and $ {D}^*_2(2460)^0$ (blue) contributions. The inset displays the $ D ^{*+} \pi ^- $ mass spectrum after subtracting the fitted background. The full line curves (red) show the contributions from $ D_{J}(2580)^0$ , $ D_{J}(2740)^0$ , and $ D_{J}(3000)^0$ states. The dotted (blue) lines display the $ D^*_{J}(2650)^0$ and $ D^*_{J}(2760)^0$ contributions. The top window shows the pull distribution where the horizontal lines indicate $\pm 3 \sigma$.

Fit to the total $ D ^{*+} \pi ^- $ sample. The dashed (blue) line shows the fitted background, the dotted lines the $ D_1(2420)^0$ (red) and $ {D}^*_2(2460)^0$ (blue) contributions. The inset displays the $ D ^{*+} \pi ^- $ mass spectrum after subtracting the fitted background. The full line curves (red) show the contributions from $ D_{J}(2580)^0$ , $ D_{J}(2740)^0$ , and $ D_{J}(3000)^0$ states. The dotted (blue) lines display the $ D^*_{J}(2650)^0$ and $ D^*_{J}(2760)^0$ contributions. The top window shows the pull distribution where the horizontal lines indicate $\pm 3 \sigma$.

Distributions of (a) $ D_1(2420)^0$ and (b) $ {D}^*_2(2460)^0$ candidates as functions of the helicity angle $\cos\theta_{\rm H}$ . The distributions are fitted with unnatural and natural parity functions, respectively.

Distributions of (a) $ D^*_{J}(2650)^0$ and (b) $ D^*_{J}(2760)^0$ candidates as functions of the helicity angle $\cos\theta_{\rm H}$ . The distributions are fitted with natural parity (black continuous), unnatural parity (red, dashed) and $J^P=0^-$ (blue, dotted) functions.

Distributions of (a) $ D_{J}(2580)^0$ , (b) $ D_{J}(2740)^0$ and (c) $ D_{J}(3000)^0$ candidates as functions of the helicity angle $\cos\theta_{\rm H}$ . The distributions are fitted with natural parity (black continuous) and unnatural parity (red, dashed) functions. In (a) the $J^P=0^-$ (blue, dotted) hypothesis is also tested.

Fit to the $ D ^+ \pi ^- $ mass spectrum. The filled histogram (in red) shows the estimated cross-feeds from the high mass $ D ^* \pi$ resonances. The dashed (blue) line displays the fitted background. The dotted (blue) line shows the $ {D}^*_2(2460)^0$ contribution. The inset displays the mass spectrum after the fitted background subtraction. The full (blue) curves show the $ D^*_{J}(2760)^0$ and $ D^*_{J}(3000)^0$ contributions. The top window displays the pull distribution where the horizontal lines indicate $\pm 3 \sigma$.

Fit to the $ D ^0 \pi ^+ $ mass spectrum. The filled histogram (in red) shows the estimated cross-feeds from the high mass $ D ^* \pi$ resonances. The dashed (blue) line displays the fitted background. The dotted (blue) line shows the $ {D}^*_2(2460)^+$ contribution. The inset displays the mass spectrum after the fitted background subtraction. The full (blue) curves show the $ D^*_{J}(2760)^+$ and $ D^*_{J}(3000)^+$ contributions. The top window displays the pull distribution where the horizontal lines indicate $\pm 3 \sigma$.

Animated gif made out of all figures.

Breit-Wigner parameters describing the cross-feed from $ D_1(2420)$ and $ D^*_2(2460)$ in the $ D ^+ \pi ^- $ and $ D ^0 \pi ^+ $ final states.

Definition of the categories selected by different ranges of $\cos\theta_{\rm H}$ , and fraction of the total natural parity contribution.

Mass intervals, number of bins, yields, and $\chi^2/{\rm ndf}$ in the fits to the different mass spectra.

Resonance parameters, yields and statistical significances. The first uncertainty is statistical, the second systematic. Significances are evaluated using the method described in the text.

Results from the fits to the $\cos\theta_{\rm H} $ angular distributions for the resonances observed in the $ D ^{*+} \pi ^- $ mass spectrum. The resulting $\chi^2/{\rm ndf}$ for different spin-parity assignments are reported. For each resonance, the expected angular distributions are indicated, where $h$ is a free parameter. The favoured spin-parity assignment is indicated in bold font.