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

Abstract

We investigate hidden-charm molecular states in $\Xi_c^{(\prime,*)}\bar{D}^{(*)}$ systems using the one-boson exchange model. By regulating the short-range interactions with parameter $a$ and cutoff $\Lambda$, 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 $\Xi_c^{\prime}\bar{D}$-$\Xi_c\bar{D}^*$ 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 $\Lambda\eta_c$ and $\Lambda J/\psi$ 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.