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

The hidden-charmed pentaquark P-c (4450)and the charmonium-like state Y (4274)are investigated as a (D) over bar Sigma(c) and a D-s(D) over bar (s0) (2317) molecular state, respectively. The spin parities of these two states cannot be well understood if only S-wave (D) over bar*Sigma(c)and D-s(D) over bar (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 +/- 4i and 4392 +/- 46i MeV are produced from the (D) over bar*Sigma(c) interaction coupled with the J /(sic)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/(sic)p invariant mass spectrum. The D-s(D) over bar (s0) (2317) interaction coupled with the J/(sic)phi channel is studied and a pole at 4275 +/- 11i MeV is produced in J(P) = 1(+) wave, which corresponds to P-wave D-s(D) over bar (s0) (2317) interaction. The pole from S-wave D-s(D) over bar (s0) (2317) interaction is far below that from P-wave interaction even the J/(sic)phi threshold, so cannot be observed in the J/(sic)phi 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.