Three-body molecules <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover><mml:msup><mml:mrow><mml:mover accent="true"><mml:mrow><mml:mi>D</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">¯</mml:mo></mml:mrow></mml:mover></mml:mrow><mml:mrow><mml:mo>*</mml:mo></mml:mrow></mml:msup><mml:msub><mml:mrow><mml:mi mathvariant="normal">Σ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>: Understanding the nature of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>T</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>c</mml:mi></mml:mrow></mml:msub></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>P</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4312</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>P</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4440</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>, and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>P</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4457</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>
Y. Pan, Tian-Wei Wu, Ming-Zhu Liu, Li‐Sheng Geng
Abstract
The nature of the three pentaquark states, ${P}_{c}(4312)$, ${P}_{c}(4440)$, and ${P}_{c}(4457)$, discovered by the LHCb Collaboration in 2019, is still under debate, although the ${\overline{D}}^{(*)}{\mathrm{\ensuremath{\Sigma}}}_{c}$ molecular interpretation seems to be the most popular. In this work, by adding a $\overline{D}$ meson into the ${\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ pair, we investigate the mass and decay width of the three-body molecules $\overline{D}{\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ and explore the correlation between the existence of the $\overline{D}{\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ molecules with the existence of ${\overline{D}}^{(*)}{\mathrm{\ensuremath{\Sigma}}}_{c}$ and ${\overline{D}}^{*}\overline{D}$ two-body molecules. The latter can be identified with the doubly charmed tetraquark state ${T}_{cc}$ recently discovered by the LHCb Collaboration. Based on the molecular nature of ${P}_{c}(4312)$, ${P}_{c}(4440)$, ${P}_{c}(4457)$, and ${T}_{cc}$, our results indicate that there exist two three-body bound states of $\overline{D}{\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ with $I({J}^{P})=1(1/{2}^{+})$ and $I({J}^{P})=1(3/{2}^{+})$, and binding energies 37.24 MeV and 29.63 MeV below the $\overline{D}{\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ mass threshold. In addition, we find that the mass splitting of these two three-body molecules are correlated to the mass splitting of ${P}_{c}(4440)$ and ${P}_{c}(4457)$, which offers a nontrivial way to reveal the molecular nature of these states. The partial widths of two $\overline{D}{\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ molecules decaying into $J/\ensuremath{\psi}p\overline{D}$ and $J/\ensuremath{\psi}p{\overline{D}}^{*}$ are found to be several MeV. We recommend the experimental searches for the $\overline{D}{\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ molecules in the $J/\ensuremath{\psi}p\overline{D}$ and $J/\ensuremath{\psi}p{\overline{D}}^{*}$ invariant mass distributions.