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.