$P_c$ pentaquarks with chiral tensor and quark dynamics

We investigate the hidden-charm pentaquarks as superpositions of ${\mathrm{\Lambda }}_c{\overline{D}}^{(*)}$ and ${\mathrm{\Sigma }}_c^{(*)}{\overline{D}}^{(*)}$ (isospin $I=1/2$) meson-baryon channels coupled to a $uudc\overline{c}$ compact core by employing an interaction satisfying the heavy quark and chiral symmetries. Our model can consistently explain the masses and decay widths of $P_c^{+}(4312)$, $P_c^{+}(4440)$ and $P_c^{+}(4457)$ with the dominant components of ${\mathrm{\Sigma }}_c\overline{D}$ and ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ with spin-parity assignments $J^P=1/2^{-}$, $3/2^{-}$ and $1/2^{-}$, respectively. We analyze basic properties of the $P_c$’s such as masses and decay widths, and find that the mass ordering is dominantly determined by the quark dynamics while the decay widths by the tensor force of the one-pion exchange.

Figure 1

Experimental data (EXP) [1, 34] and our results of masses and widths for various $P_c$ states. The horizontal dashed lines show the thresholds for corresponding channels and values in the right axis are isospin averaged ones in units of MeV. The centers of the bars are located at the central values of pentaquark masses while their lengths correspond to the pentaquark widths with the exception of $P_c(4380)$ width.

Figure 2

Comparing the results with and without the tensor force of the OPEP for the states around the ${\mathrm{\Sigma }}_c{\overline{D}}^{*}$ and ${\mathrm{\Sigma }}_c^{*}{\overline{D}}^{*}$ thresholds. The label “without T” stands for the result without the OPEP tensor force, while the label “with T” stands that with the OPEP tensor force. The same convention is adopted as in Fig. 1.