A new look at the $P_{cs}$ states from a molecular perspective

Abstract

We have a look at the $P_{cs}$ states generated from the interaction of ${\bar{D}}^{(\ast )}{\Xi }_c^{(\prime \ast )}$ coupled channels. We consider the blocks of pseudoscalar-baryon $({\frac{1}{2}}^{+},{\frac{3}{2}}^{+})$ and vector-baryon $({\frac{1}{2}}^{+},{\frac{3}{2}}^{+})$, and find $10$ resonant states coupling mostly to $\bar{D}{\Xi }_c,{\bar{D}}^{\ast }{\Xi }_c,\bar{D}{\Xi }_c^{\prime },{\bar{D}}^{\ast }{\Xi }_c^{\prime },\bar{D}{\Xi }_c^{\ast }$ and ${\bar{D}}^{\ast }{\Xi }_c^{\ast }$. A novel aspect of the work is the realization that the $\bar{D}{\Xi }_c,{\bar{D}}_s{\Lambda }_c$ or ${\bar{D}}^{\ast }{\Xi }_c,{\bar{D}}_s^{\ast }{\Lambda }_c$ channels, with a strong transition potential, collaborate to produce a larger attraction than the corresponding states $\bar{D}{\Sigma }_c,\bar{D}{\Lambda }_c$ or ${\bar{D}}^{\ast }{\Sigma }_c,{\bar{D}}^{\ast }{\Lambda }_c$ appearing in the generation of the strangenessless $P_c$ states, since in the latter case the transition potential between those channels is zero. The extra attraction obtained in the $\bar{D}{\Xi }_c,{\bar{D}}^{\ast }{\Xi }_c$ pairs preclude the association of these channels to the $P_{cs}(4338)$ and $P_{cs}(4459)$ states respectively. Then we find a natural association of the $P_{cs}(4338)$ state coupling mostly to ${\bar{D}}^{\ast }{\Xi }_c$ while the $P_{cs}(4459)$ is associated to the state found that couples mostly to $\bar{D}{\Xi }_c^{\prime }$. Four more states appear, like in other molecular pictures, and some of the states are degenerate in spin. Counting different spin states we find $10$ states, which we hope can be observed in the near future.

8 pages, 4 figures, accepted for publication in Physics Letters B

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