Can the ${\pi }^{+}{\chi }_{c1}$ resonance structures be $D^{\ast }{\bar{D}}^{\ast }$ and $D_1\bar{D}$ molecules?

Abstract

We use QCD sum rules to study the recently observed resonance-like structures in the ${\pi }^{+}{\chi }_{c1}$ mass distribution, $Z_1^{+}(4050)$ and $Z_2^{+}(4250)$, considered as $D^{\ast +}{\bar{D}}^{\ast 0}$ and $D_1^{+}{\bar{D}}^0+D^{+}{\bar{D}}_1^0$ molecules with the quantum number $J^P=0^{+}$ and $J^P=1^{-}$ respectively. We consider the contributions of condensates up to dimension eight and work at leading order in ${\alpha }_s$. We obtain $m_{D^*D^*}=(4.15\pm0.12) \GeV$, around 100 MeV above the $D^{\ast }{D}^{\ast }$ threshold, and $m_{D_1D}=(4.19\pm 0.22) \GeV$, around 100 MeV below the $D_{1}D$ threshold. We conclude that the $D^{\ast +}{\bar{D}}^{\ast 0}$ state is probably a virtual state that is not related with the $Z_1^{+}(4050)$ resonance-like structure. In the case of the $D_{1}D$ molecular state, considering the errors, its mass is consistent with both $Z_1^{+}(4050)$ and $Z_2^{+}(4250)$ resonance-like structures. Therefore, we conclude that no definite conclusion can be drawn for this state from the present analysis.

revised version accepted for publication in Nucl. Phys. A

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