Comparison between the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>P</mml:mi><mml:mi>ψ</mml:mi><mml:mi>N</mml:mi></mml:msubsup></mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi>P</mml:mi><mml:mrow><mml:mi>ψ</mml:mi><mml:mi>s</mml:mi></mml:mrow><mml:mi mathvariant="normal">Λ</mml:mi></mml:msubsup></mml:math> systems
Kan Chen, Zi-Yang Lin, Shi-Lin Zhu
Abstract
We construct the effective potentials of the ${P}_{\ensuremath{\psi}}^{N}$ and ${P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}$ states based on the ${\mathrm{SU}(3)}_{\mathrm{f}}$ symmetry and heavy quark symmetry. Then we perform the coupled-channel analysis of the lowest-isospin ${P}_{\ensuremath{\psi}}^{N}$ and ${P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}$ systems. The coupled-channel effects play different roles in the ${P}_{\ensuremath{\psi}}^{N}$ and ${P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}$ systems. In the ${P}_{\ensuremath{\psi}}^{N}$ systems, this effect gives minor corrections to the masses of the ${P}_{\ensuremath{\psi}}^{N}$ states. In the ${P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}$ system, the ${\mathrm{\ensuremath{\Lambda}}}_{c}{\overline{D}}_{s}\ensuremath{-}{\mathrm{\ensuremath{\Xi}}}_{c}\overline{D}$ coupling will shift the mass of the ${P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}(4338{)}^{0}$ close to the ${\mathrm{\ensuremath{\Xi}}}_{c}\overline{D}$ threshold. The ${\mathrm{\ensuremath{\Lambda}}}_{c}{\overline{D}}_{s}^{(*)}\ensuremath{-}{\mathrm{\ensuremath{\Xi}}}_{c}{\overline{D}}^{(*)}$ coupling will also produce extra ${P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}$ states. We discuss the correspondence between the ${P}_{\ensuremath{\psi}}^{N}$ and ${P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}$ states. Our results prefer that the SU(3) partners of the observed ${P}_{\ensuremath{\psi}}^{N}(4312{)}^{+}$, ${P}_{\ensuremath{\psi}}^{N}(4440{)}^{+}$, and ${P}_{\ensuremath{\psi}}^{N}(4457{)}^{+}$ in the ${P}_{\ensuremath{\psi}s}^{\mathrm{\ensuremath{\Lambda}}}$ system not have been found yet.