Connection between near the $D_s^{+}{D}_s^{-}$ threshold enhancement in $B^{+}\to D_s^{+}{D}_s^{-}{K}^{+}$ and conventional charmonium ${\chi }_{c0}(2P)$

Abstract

Focusing on recent measurement of $B^{+}\to D_s^{+}{D}_s^{-}{K}^{+}$ process given by the LHCb Collaboration, we propose that this newly observed near the $D_s^{+}{D}_s^{-}$ threshold enhancement can be due to the contribution of the ${\chi }_{c0}(2P)$, which is a $P$-wave charmonium below the $D_s^{+}{D}_s^{-}$ threshold. By performing a combined fit to the measured $D_s^{+}{D}_s^{-}$, $D_s^{+}{K}^{+}$, and $D_s^{-}{K}^{+}$ invariant mass spectra, introducing the ${\chi }_{c0}(2P)$ can well reproduce the near threshold enhancement in the $D_s^{+}{D}_s^{-}$ invariant mass spectrum. When depicting the whole $D_s^{+}{D}_s^{-}$ invariant mass spectrum, the contributions from higher charmonium $\psi (4230)$ and charmoniumlike state $X_0(4140)$ are obvious. In addition, a charmed meson $D^{\ast }(3^3{S}_1)$ with mass around 3015 MeV is found to be important to depict the $D_s^{-}{K}^{+}$ invariant mass spectrum well. Especially, the importance of node effect of the spatial wave function of the ${\chi }_{c0}(2P)$ is revealed, by which the anomaly of the ratio $\Gamma (X\to D^{+}{D}^{-})/\Gamma (X\to D_s^{+}{D}_s^{-})$ indicated by LHCb can be explained well. Finally, our scenario of the newly observed enhancement structure resulted from the ${\chi }_{c0}(2P)$ is enforced.

arXiv comment8 pages, 5 figures and 2 tables

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• Molecular Interpretation of $X(3960)$ as $D_s^{+}{D}_s^{-}$ State
• Understanding the $0^{++}$ and $2^{++}$ charmonium(-like) states near 3.9 GeV
• Charmonium ${\chi }_{c0}$ and ${\chi }_{c2}$ resonances in coupled-channel scattering from lattice QCD
• Resonance $X(3960)$ as a hidden charm-strange scalar tetraquark
• On the nature of X(3960)
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• Near-threshold structures in the $D_s^{+}{D}_s^{-}$ mass distribution of the decay $B^{+}\to D_s^{+}{D}_s^{-}{K}^{+}$