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

Abstract

We investigate hidden-charm molecular states in ${\Xi }_c^{(\prime ,\ast )}{\bar{D}}^{(\ast )}$ 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 ${\Xi }_c^{\prime }\bar{D}$-${\Xi }_c{\bar{D}}^{\ast }$ 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.

Comments: 17 pages, 7 figures, 9 tables