Understanding spin parity of $P_c(4450)$ and $Y(4274)$ in a hadronic molecular state picture

Abstract

The hidden-charmed pentaquark $P_c(4450)$ and the charmonium-like state $Y(4274)$ are investigated as a ${\bar{D}}^{\ast }{\Sigma }_c$ and a $D_s{\bar{D}}_{s0}(2317)$ molecular state, respectively. The spin parities of these two states cannot be well understood if only S-wave ${\bar{D}}^{\ast }{\Sigma }_c$ and $D_s{\bar{D}}_{s0}(2317)$ interactions are considered. In this work, the interactions are studied in a quasipotential Bethe-Salpeter equation approach with a partial wave decomposition on spin parity $J^P$, and the contributions of different partial waves are studied in a two-channel scattering model including a generating channel and an observation channel. Two poles at $4447\pm 4i$ and $4392\pm 46i$ MeV are produced from the ${\bar{D}}^{\ast }{\Sigma }_c$ interaction coupled with the $J/\psi p$ channel in $3/2^{-}$ wave and $5/2^{+}$ wave, respectively. The peak for the $5/2^{+}$ state has a comparable height as that of the $3/2^{-}$ state in the $J/\psi p$ invariant mass spectrum. The $D_s{\bar{D}}_{s0}(2317)$ interaction coupled with the $J/\psi \varphi$ channel is studied and a pole at $4275\pm 11i$ MeV is produced in $J^P=1^{+}$ wave, which corresponds to P-wave $D_s{\bar{D}}_{s0}(2317)$ interaction. The pole from S-wave $D_s{\bar{D}}_{s0}(2317)$ interaction is far below that from P-wave interaction even the $J/\psi \varphi$ threshold, so cannot be observed in the $J/\psi \varphi$ channel. The result suggests that in these cases a state carrying a spin parity corresponding to P-wave interaction should be taken as seriously as these carrying a spin parity corresponding to S-wave interaction in the hadronic molecular state picture.

Comments: 7 pages, 5 figures. published version