From triply charmed dibaryons to pentaquark states: A model-independent way to determine the spins of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4440</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi>P</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4457</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:math>
Y. Pan, Ming-Zhu Liu, Fang‐Zheng Peng, Mario Sánchez Sánchez, Li‐Sheng Geng, Manuel Pavón Valderrama
Abstract
The LHCb Collaboration has recently observed three narrow pentaquark states---the ${P}_{c}(4312)$, ${P}_{c}(4440)$, and ${P}_{c}(4457)$---that are located close to the $\overline{D}{\mathrm{\ensuremath{\Sigma}}}_{c}$ and ${\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ thresholds. Among the so-far proposed theoretical interpretations for these pentaquarks, the molecular hypothesis seems to be the preferred one. Nevertheless, in the molecular picture, the spins of the ${P}_{c}(4440)$ and ${P}_{c}(4457)$ have not been unambiguously determined yet. In this paper, we point out that heavy-antiquark-diquark symmetry induces a model-independent relation between the spin splitting in the masses of the ${P}_{c}(4440)$ and ${P}_{c}(4457){\overline{D}}^{*}{\mathrm{\ensuremath{\Sigma}}}_{c}$ pentaquarks and the corresponding splitting for the ${0}^{+}$ and ${1}^{+}$ ${\mathrm{\ensuremath{\Xi}}}_{cc}{\mathrm{\ensuremath{\Sigma}}}_{c}$ triply charmed dibaryons. This is particularly relevant owing to a recent lattice-QCD prediction of the ${1}^{+}$ triply charmed dibaryon, which suggests that a calculation of the mass of its ${0}^{+}$ partner might be within reach. This, in turn, would reveal the spins of the ${P}_{c}(4440)$ and ${P}_{c}(4457)$ pentaquarks, providing a highly nontrivial test of heavy-quark symmetry and the molecular nature of the pentaquarks. Furthermore, the molecular interpretation of the hidden-charm pentaquarks implies the existence of a total of ten triply charmed dibaryons as ${\mathrm{\ensuremath{\Xi}}}_{cc}^{(*)}{\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}$ molecules, which, if confirmed in the lattice, will largely expand our understanding of the nonperturbative strong interaction in the heavy-quark sector.