Molecular nature of <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> and its heavy quark spin partners

Abstract

Inspired by the observation of the ${P}_{cs}(4459)$ state by LHCb recently, we reexamine the results of the interaction of the $J/\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}}$ channel with its coupled channels, exploiting the coupled channel unitary approach combined with heavy quark spin and local hidden gauge symmetries. By tuning the only free parameter, we find a pole of $(4459.07+i6.89)\text{ }\text{ }\mathrm{MeV}$ below the ${\overline{D}}^{*}{\mathrm{\ensuremath{\Xi}}}_{c}$ threshold, which was consistent with the mass and width of the ${P}_{cs}(4459)$ state. Thus, we assume the ${P}_{cs}(4459)$ state to be a ${\overline{D}}^{*}{\mathrm{\ensuremath{\Xi}}}_{c}$ bound state with the possible degeneracy of ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$ and ${J}^{P}={\frac{3}{2}}^{\ensuremath{-}}$. According to this degeneracy, it would have a two-pole structure, like ${P}_{c}(4450)$ before. There is another pole in the ${J}^{P}={\frac{1}{2}}^{\ensuremath{-}}$ sector, $(4310.53+i8.23)\text{ }\text{ }\mathrm{MeV}$, corresponding to a deep bound state of $\overline{D}{\mathrm{\ensuremath{\Xi}}}_{c}$. Furthermore, the previously predicted loosely bound states $\overline{D}{\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}$, ${\overline{D}}^{*}{\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}$, ${\overline{D}}^{*}{\mathrm{\ensuremath{\Xi}}}_{c}^{*}$ with $J=1/2,I=0$ and ${\overline{D}}^{*}{\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}$, $\overline{D}{\mathrm{\ensuremath{\Xi}}}_{c}^{*}$, ${\overline{D}}^{*}{\mathrm{\ensuremath{\Xi}}}_{c}^{*}$ with $J=3/2,I=0$ may exist as either bound states or unbound virtual states. We hope that future experiments can search for the ${\overline{D}}^{(*)}{\mathrm{\ensuremath{\Xi}}}_{c}$ molecular states not only in their dominant decay channels ${\overline{D}}_{s}^{(*)}{\mathrm{\ensuremath{\Lambda}}}_{c}$, but also in the channels $J/\ensuremath{\psi}\mathrm{\ensuremath{\Lambda}}$ and ${\ensuremath{\eta}}_{c}\mathrm{\ensuremath{\Lambda}}$ in order to reveal their different natures.

Topics & Concepts