Role of the short-range dynamics in simultaneous interpretation of $P_{cs}$ pentaqurks via $Ξ_c^{(\prime,*)}\bar{D}^{(*)}$ 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's $P_{cs}(4459)$ and Belle'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.