The decay property of the $X(3842)$ as the $\psi_{_3}(1^3D_{_3})$ state

Wei Li; Su-Yan Pei; Tianhong Wang; Tai-Fu Feng; Guo-Li Wang

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arXiv · 2308.02280

The decay property of the $X(3842)$ as the $\psi_{_3}(1^3D_{_3})$ state

Wei Li·Su-Yan Pei·Tianhong Wang·Tai-Fu Feng·Guo-Li Wang

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Abstract

In this paper, the new particle $X(3842)$ discovered by the LHCb Collaboration is identified to be the $\psi_{_3}(1^3D_{_3})$ state. We study its strong decays with the combination of the Bethe-Salpeter method and the $^3P_{_0}$ model. Its electromagnetic (EM) decay is also calculated by the Bethe-Salpeter method within Mandelstam formalism. The strong decay widths are {$\Gamma[X(3842)\rightarrow D^{0}\bar{D}^{0}]=1.28$ MeV}, $\Gamma[X(3823)\rightarrow D^{+}D^{-}]=1.08$ MeV, and the ratio ${\cal B}[X(3842)\rightarrow D^{+}D^{-}]/{\cal B}[X(3823)\rightarrow D^{0}\bar{D}^{0}]=0.84$. The EM decay width is $\Gamma[X(3842)\rightarrow\chi_{_{c2}}\gamma]=0.29$ MeV. We also estimate the total width to be 2.87 MeV, which is in good agreement with the experimental data $2.79^{+0.86}_{-0.86}$ MeV. Since the used relativistic wave functions include different partial waves, we also study the contributions of different partial waves in electromagnetic decay.

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Wei Li, Su-Yan Pei, Tianhong Wang, Tai-Fu Feng, Guo-Li Wang. 2023-08-04. The decay property of the $X(3842)$ as the $\psi_{_3}(1^3D_{_3})$ state. https://arxiv.org/abs/2308.02280

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