Insights into the nature of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msub><mml:mi>P</mml:mi><mml:mrow><mml:mi>c</mml:mi><mml:mi>s</mml:mi></mml:mrow></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>4459</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>
Meng-Lin Du, Zhi-Hui Guo, J. A. Oller
Abstract
We study the nature of the recently observed ${P}_{cs}(4459)$ by the LHCb collaboration by employing three methods based on the elastic effective-range expansion and the resulting size of the effective-range, the saturation of the compositeness relation and width of the resonance, and a direct fit to data involving the channels $J/\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}}$, ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}\overline{D}$, and ${\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{*}$. We have also considered the addition of a Castillejo-Dalitz-Dyson (CDD) pole but this scenario can be discarded. Our different analyses clearly indicate the molecular nature of the ${P}_{cs}(4459)$ with a clear ${\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{*}$ dominant component. In relation with heavy-quark-spin symmetry our results also favor the actual existence of two resonances with $J=1/2$ (the lighter one) and $3/2$ (the heavier one) in the energy region of the ${P}_{cs}(4459)$. In the scenario of two-resonance for the ${P}_{cs}(4459)$, the inclusion of the ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}\overline{D}$ channel is required for their mass splitting and it allows one to determine the spin structures of the two resonances.