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arXiv · 2412.11144

Study on the structure of the $Z_{c}(3900)$ state

Yan Ma·De-Shun Zhang·Cheng-Qun Pang·Zhi-Feng Sun
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Abstract

In this work, we studied the $Z_{c}(3900)$ state within the framework of effective field theory. We firstly show the construction of the Lagrangian describing meson-meson-meson and meson-diquark-diquark interactions. By using the Feynman rule, we calculate the effective potentials corresponding to the coupled channels of $D\bar{D}^{*}/D^{*}\bar{D}$ and $S_{cq}\bar{A}_{cq}/A_{cq}\bar{S}_{cq}$ with $S_{cq}$ ($A_{cq}$) the scalar (axial vector) diquark composed of $c$ and $q$ quarks. After solving the Bethe-Salpeter equation of the on-shell parametrized form and compare our numerical results with the experimental mass and width of $Z_{c}(3900)$, we find that the $Z_{c}(3900)$ state can be explained as the mixture of $D\bar{D}^{*}/D^{*}\bar{D}$ and $S_{cq}\bar{A}_{cq}/A_{cq}\bar{S}_{cq}$ components.

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Yan Ma, De-Shun Zhang, Cheng-Qun Pang, Zhi-Feng Sun. 2024-12-15. Study on the structure of the $Z_{c}(3900)$ state. https://arxiv.org/abs/2412.11144

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