Coupled-channel effects of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:msubsup><mml:mi mathvariant="normal">Σ</mml:mi><mml:mi>c</mml:mi><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:mover accent="true"><mml:mi>D</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover><mml:mrow><mml:mo stretchy="false">(</mml:mo><mml:mo>*</mml:mo><mml:mo stretchy="false">)</mml:mo></mml:mrow></mml:msup><mml:mo>−</mml:mo><mml:msub><mml:mi mathvariant="normal">Λ</mml:mi><mml:mi>c</mml:mi></mml:msub><mml:mo stretchy="false">(</mml:mo><mml:mn>2595</mml:mn><mml:mo stretchy="false">)</mml:mo><mml:mover accent="true"><mml:mi>D</mml:mi><mml:mo stretchy="false">¯</mml:mo></mml:mover></mml:math> system and molecular nature of the <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:math> pentaquark states from one-boson exchange model

Abstract

The effects of the ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}\ensuremath{-}{\mathrm{\ensuremath{\Lambda}}}_{c}(2595)\overline{D}$ coupled-channel dynamics and various one-boson-exchange (OBE) forces for the LHCb pentaquark states, ${P}_{c}(4440)$ and ${P}_{c}(4457)$, are reinvestigated. Both the pion and $\ensuremath{\rho}$-meson exchanges are considered for the ${\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}\text{\ensuremath{-}}{\mathrm{\ensuremath{\Lambda}}}_{c}(2595)\overline{D}$ coupled-channel dynamics. It is found that the role of the ${\mathrm{\ensuremath{\Lambda}}}_{c}(2595)\overline{D}$ channel in the descriptions of the ${P}_{c}(4440)$ and ${P}_{c}(4457)$ states is not significant with the OBE parameters constrained by other experimental sources. The naive OBE models with the short-distance $\ensuremath{\delta}(\stackrel{\ensuremath{\rightarrow}}{r})$ term of the one-pion exchange (OPE) keep failing to reproduce the ${P}_{c}(4440)$ and ${P}_{c}(4457)$ states simultaneously. The OPE potential with the full $\ensuremath{\delta}(\stackrel{\ensuremath{\rightarrow}}{r})$ term results in a too large mass splitting for the ${J}^{P}=1/{2}^{\ensuremath{-}}$ and $3/{2}^{\ensuremath{-}}\text{ }\text{ }{\mathrm{\ensuremath{\Sigma}}}_{c}{\overline{D}}^{*}$ bound states with total isospin $I=1/2$. The OBE model with only the OPE $\ensuremath{\delta}(\stackrel{\ensuremath{\rightarrow}}{r})$ term dropped may fit the splitting much better but somewhat underestimates the splitting. Since the $\ensuremath{\delta}(\stackrel{\ensuremath{\rightarrow}}{r})$ potential is from short-distance physics, which also contains contributions from the exchange of mesons heavier than those considered explicitly, we vary the strength of the $\ensuremath{\delta}(\stackrel{\ensuremath{\rightarrow}}{r})$ potential and find that the masses of the ${P}_{c}(4312)$, ${P}_{c}(4440)$, and ${P}_{c}(4457)$ can be reproduced simultaneously with the $\ensuremath{\delta}(\stackrel{\ensuremath{\rightarrow}}{r})$ term in the OBE model reduced by about 80%. While two different spin assignments are possible to produce their masses, in the preferred description, the spin parities of the ${P}_{c}(4440)$ and ${P}_{c}(4457)$ are $3/{2}^{\ensuremath{-}}$ and $1/{2}^{\ensuremath{-}}$, respectively.

Topics & Concepts