## Measurement of Open Charm Decays

Since 2003 a variety of charmonium-like structures ($$X$$, $$Y$$, $$Z$$ states) have been detected, but their nature has not been understood so far. On the one hand, exotic forms of hadronic matter, such as tetraquarks, hybrids and meson-meson molecules, are considered as possible explanatory models. On the other hand, it can not be ruled out that some of the structures (in particular $$Z_{c}$$) are purely kinematic effects. Also, it is not yet known if all the known $$X$$, $$Y$$, $$Z$$ structures have the same physical cause.
It is important to note that for a consistent description, for example, it is not sufficient to identify a single state as presumably tetraquark-like. Rather, in the example given, the postulation of a tetraquark is followed by the existence of a whole class of these states, which must also be detectable experimentally. So far, none of the models mentioned above can consistently describe all $$X$$, $$Y$$ and $$Z$$ states.

One possible way to better understand these exotic, charmonium-like structures is to study open-charm final states. Dominant are topologies of the form $$e^{+} e^{-} \to D\bar{D}, \, \pi D \bar{D}, \, \pi D \bar{D}^{*}$$, $$D^{*} \bar{D}^{*}$$ and $$\pi D^{*} \bar{D}^{*}$$.
Their importance lies in the fact that many of the well-known $$X$$, $$Y$$ and $$Z$$ states are close to the production threshold of open-charm final states. So the mass of the $$X(3872)$$ is almost identical to the $$D^{0} \bar{D}^{* 0}$$ threshold, while $$Z_{c}(3900)^{+}/Z_{c}(3885)^{+}$$ and $$Z_{c}(4020)^{+}$$ just above the $$\bar{D}^{0} D^{*+}$$ or $$\bar{D}^{*0} D^{*+}$$ threshold.
In addition, the $$Y$$ states show a weak coupling to open-charm final states, while conventional charmonia such as the $$\psi(4415)$$, which is identified as $$4{}^{3}\mathrm{S}_{1}$$ state, strongly decay into such states.

The high integrated luminosity of the BESIII datasets allows precise measurement of the open-charm production cross sections in the energy range $$\sqrt{s} = 4$$-$$4\text{,} 6\,\mathrm{GeV}$$.
Through a coupled analysis that also has knowledge of hidden-charm cross sections such as $$\pi^{+} \pi^{-} J/\psi$$ and $$\pi^{+} \pi^{-} h_{c}$$, it is possible to compare models for the inner structure of the various $$X$$, $$Y$$ and $$Z$$ states.
Of particular interest here is the analysis of multibody final states such as $$e^{+} e^{-} \to \pi^{+} D^{0} D^{*-}$$. Although in positron-electron reactions it is not possible to generate the charged $$Z_{c}$$ states in formation ($$e^{+} e^{-} \nrightarrow Z_{c}^{\pm}$$) , these appear for example in the reaction $$e^{+} e^{-} \to \pi^{+} Z_{c}^{-} \to \pi^{+} (D^{0} D^{*-})$$ as intermediate resonances.
With the method of partial wave analysis, it is therefore possible to examine their properties in more detail.

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