Can discovery of hidden charm strange pentaquark states help determine the spins of <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>?
Ming-Zhu Liu, Y. Pan, Li‐Sheng Geng
Abstract
The pentaquark states ${P}_{c}(4312)$, ${P}_{c}(4440)$, and ${P}_{c}(4457)$ could be nicely arranged into a multiplet of seven molecules of ${\overline{D}}^{(*)}{\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}$ dictated by heavy quark spin symmetry. However, the spins of ${P}_{c}(4440)$ and ${P}_{c}(4457)$ are not yet fully determined. We employ the contact-range effective field theory to investigate the SU(3)-flavor counterparts of ${\overline{D}}^{(*)}{\mathrm{\ensuremath{\Sigma}}}_{c}^{(*)}$ and study the possibility of whether their discovery could help determine the spins of ${P}_{c}(4457)$ and ${P}_{c}(4440)$. We find the existence of a complete hidden charm strange multiplet of ${\overline{D}}^{(*)}{\mathrm{\ensuremath{\Xi}}}_{c}^{(\ensuremath{'})*}$ molecules, irrespective of the spins of ${P}_{c}(4440)$ and ${P}_{c}(4457)$. On the other hand, we find that although molecules of ${\overline{D}}^{(*)}{\mathrm{\ensuremath{\Xi}}}_{c}$ are also likely, depending on the realization of the underlying dynamics, their discovery could be more useful for determining the spins of ${P}_{c}(4440)$ and ${P}_{c}(4457)$ and for telling us how heavy quark and light quark interactions depend on the spin of the light quark pair.