<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 other possible molecular states from <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">Ξ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msubsup><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 stretchy="false">(</mml:mo><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msubsup><mml:mrow><mml:mi mathvariant="normal">Ξ</mml:mi></mml:mrow><mml:mrow><mml:mi>c</mml:mi></mml:mrow><mml:mrow><mml:mo>′</mml:mo></mml:mrow></mml:msubsup><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 stretchy="false">(</mml:mo><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup></mml:mrow></mml:math> interactions
J. Zhu, Lin-Qing Song, Jun He
Abstract
Recently, the LHCb Collaboration reported a new structure ${P}_{cs}(4459)$ with a mass of 19 MeV below the ${\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{*}$ threshold. It may be a candidate of molecular state from the ${\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{*}$ interaction. In the current work, we perform a coupled-channel study of the ${\mathrm{\ensuremath{\Xi}}}_{c}^{*}{\overline{D}}^{*}$, ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}{\overline{D}}^{*}$, ${\mathrm{\ensuremath{\Xi}}}_{c}^{*}\overline{D}$, ${\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{*}$, ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}\overline{D}$, and ${\mathrm{\ensuremath{\Xi}}}_{c}\overline{D}$ interactions in the quasipotential Bethe-Salpeter equation approach. With the help of the heavy quark chiral effective Lagrangian, the potential is constructed by light meson exchanges. Two ${\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{*}$ molecular states are produced with spin parities ${J}^{P}=1/{2}^{\ensuremath{-}}$ and $3/{2}^{\ensuremath{-}}$. The lower state with $3/{2}^{\ensuremath{-}}$ can be related to the observed ${P}_{cs}(4450)$ while two-peak structure cannot be excluded. Within the same model, other strange hidden-charm pentaquarks are also predicted. Two states with spin parities $1/{2}^{\ensuremath{-}}$ and a state with $3/{2}^{\ensuremath{-}}$ are predicted near the ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}\overline{D}$, ${\mathrm{\ensuremath{\Xi}}}_{c}\overline{D}$, and ${\mathrm{\ensuremath{\Xi}}}_{c}^{*}\overline{D}$ thresholds, respectively. As two states near ${\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{*}$ threshold, two states are produced with $1/{2}^{\ensuremath{-}}$ and $3/{2}^{\ensuremath{-}}$ near the ${\mathrm{\ensuremath{\Xi}}}_{c}^{\ensuremath{'}}{\overline{D}}^{*}$ threshold. The couplings of the molecular states to the considered channels are also discussed. The experimental research of those states are helpful to understand the origin and internal structure of the ${P}_{cs}$ and ${P}_{c}$ states.