Can the $\pi^+\chi_{c1}$ resonance structures be $D^*\bar{D}^*$ and $D_1\bar{D}$ molecules?

TL;DR

This study uses QCD sum rules to analyze whether the observed $Z_1^+(4050)$ and $Z_2^+(4250)$ structures can be interpreted as molecular states of $D^*ar{D}^*$ and $D_1ar{D}$, finding that the $D^*ar{D}^*$ state is likely virtual and the $D_1ar{D}$ state could be related to the observed structures.

Contribution

The paper applies QCD sum rules with condensates up to dimension eight to investigate the molecular nature of the $Z_1^+(4050)$ and $Z_2^+(4250)$ resonances.

Findings

The $D^*ar{D}^*$ state is probably a virtual state, not related to $Z_1^+(4050)$.

The $D_1ar{D}$ molecular state's mass is consistent with the observed resonances.

No definitive conclusion on the nature of the states can be drawn from the current analysis.

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 $D^{*+}\bar{D}^{*0}$ 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 $D^*D^*$ threshold, and $m_{D_1D}=(4.19\pm 0.22) \GeV$, around 100 MeV below the $D_1D$ threshold. We conclude that the $D^{*+}\bar{D}^{*0}$ state is probably a virtual state that is not related with the $Z_1^+(4050)$ resonance-like structure. In the case of the $D_1D$ 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.