Role of the short-range dynamics in simultaneous interpretation of $P_{cs}$ pentaqurks via $Ξ_c^{(\prime,*)}\bar{D}^{(*)}$ molecules

TL;DR

This work addresses the origin of hidden-charm pentaquarks with strangeness by modeling $\\Xi_c^{(\\prime,*)}\\bar{D}^{(*)}$ interactions as hadronic molecules within an one-boson-exchange framework. It introduces a short-range regulator $a$ and a cutoff $\\Lambda$ to control contact-like contributions, and solves coupled-channel Schrödinger equations to map near-threshold states, identifying $P_{cs}(4459)$ and $P_{cs}(4472)$ as a $3/2^-$ and a $1/2^-$ isoscalar pair arising from $\\Xi_c^{\\prime}\\bar{D}-\\Xi_c\\bar{D}^*$ dynamics. The analysis predicts additional $I=0$ molecular candidates in the $4.3-4.7$ GeV range and examines the roles of $\\Lambda\\eta_c$ and $\\Lambda J/\\psi$ decay channels, which mainly affect pole widths and production pathways. The results highlight the crucial interplay of short-range dynamics and coupled-channel effects in explaining hidden-charm pentaquarks as hadronic molecules and provide guidance for future experimental searches.

Abstract

We investigate hidden-charm molecular states in $Ξ_c^{(\prime,*)}\bar{D}^{(*)}$ systems using the one-boson exchange model. By regulating the short-range interactions with parameter $a$ and cutoff $Λ$, we found ten bound states in isoscalar systems. Our analysis reveals that if the LHCb Collaboration's $P_{cs}(4459)$ and Belle Collaboration's $P_{cs}(4472)$ pentaqurks are indeed distinct states, their mass splitting can be resolved through $Ξ_c^{\prime}\bar{D}$-$Ξ_c\bar{D}^*$ coupled channel dynamics using consistent model parameters. This framework assigns $3/2^-$ and $1/2^-$ spin-parity quantum numbers to $P_{cs}(4459)$ and $P_{cs}(4472)$, respectively. With this consistent model parameter, we predict several new molecular candidates in the $4.3-4.7$ GeV mass region, demonstrating the crucial interplay between coupled channel effects and short-range dynamics in understanding hidden-charm pentaquarks as hadronic molecules. Additionally, we investigate the effects of $Λη_c$ and $ΛJ/ψ$ decay channels on the predicted molecular states, showing how these channels influence pole positions and provide insights into the detectability of these states through different production mechanisms.

Figures (7)

• Figure 1: The $S$-wave OBE potentials of isoscalar systems for the $J^P=1/2^-, 3/2^-, 5/2^-$ states with $\Lambda= 1.2$ GeV. The solid and dashed curves are corresponding to the cases with $a=0$ and $1$, respectively.
• Figure 2: Plots similar to Fig. \ref{['V(r)_I=0']} for isovector system.
• Figure 3: Masses of the bound states with $I=0$ and $J^P=1/2^-, 3/2^-, 5/2^-$ quantum numbers in $\Xi_c^{(\prime,*)}\bar{D}^{(*)}$ systems . For curves of the same color, the solid(dashed) lines represent the $a=0(1)$ case. Curves for the $1/2^-$ and $3/2^-$ bound states in $\Xi_c\bar{D}^*$ channel are overlapped.
• Figure 4: Bound state wave function for the $(1/2^-,3/2^-) \Xi_{c}\bar{D}^{*}$ system with $I=0$ when the cutoff $\Lambda$=2.12 GeV.
• Figure 5: Plots analogous to Fig. \ref{['E(I=0)']} are shown for the $I=1$ system.