Spectrum of the molecular pentaquarks

We investigate the mass spectrum of the molecular pentaquarks composed of a baryon and a meson. We establish the underlying relations among the near-threshold interactions of the molecular tetraquark and pentaquark systems. We find the existence of the molecule candidates in the ${\mathrm{\Sigma }}_c{\overline{D}}^{(*)}$, $D{D}^{*}$, and $D{\overline{D}}^{*}$ systems indicates a substantial presence of the hadronic molecules in the heavy baryon plus heavy meson systems (heavy refers to the hadrons with the $c$ and/or $s$ quarks). We make an exhaustive prediction of the possible bound/virtual molecular states in the systems: ${\mathrm{\Sigma }}_c^{(*)}{\overline{D}}^{(*)}$, ${\mathrm{\Sigma }}_c^{(*)}{D}^{(*)}$, ${\mathrm{\Xi }}_c^{(\prime ,*)}{\overline{D}}^{(*)}$, ${\mathrm{\Xi }}_c^{(\prime ,*)}{D}^{(*)}$, ${\mathrm{\Sigma }}_c^{(*)}{K}^{*}$, ${\mathrm{\Sigma }}_c^{(*)}{\overline{K}}^{*}$, ${\mathrm{\Xi }}_c^{(\prime ,*)}{K}^{*}$, ${\mathrm{\Xi }}_c^{(\prime ,*)}{\overline{K}}^{*}$, ${\mathrm{\Xi }}_{cc}^{(*)}{\overline{D}}^{(*)}$, ${\mathrm{\Xi }}_{cc}^{(*)}{D}^{(*)}$, ${\mathrm{\Xi }}_{cc}^{(*)}{K}^{*}$, ${\mathrm{\Xi }}_{cc}^{(*)}{\overline{K}}^{*}$, ${\mathrm{\Sigma }}^{(*)}{\overline{D}}^{(*)}$, ${\mathrm{\Sigma }}^{(*)}{D}^{(*)}$, ${\mathrm{\Xi }}^{(*)}{\overline{D}}^{(*)}$, ${\mathrm{\Xi }}^{(*)}{D}^{(*)}$, ${\mathrm{\Sigma }}^{(*)}{K}^{*}$, ${\mathrm{\Sigma }}^{(*)}{\overline{K}}^{*}$, ${\mathrm{\Xi }}^{(*)}{K}^{*}$, ${\mathrm{\Xi }}^{(*)}{\overline{K}}^{*}$. Hunting for the predicted states in experiments will significantly deepen our understanding of the formation mechanism of the hadronic molecules, and shed light on the manifestation of flavor symmetry in the low-energy residual strong interactions.

Figure 1

The correspondences among the systems in Table 1 under the heavy ($c$ and $s$) quark symmetry.

Figure 2

Spectrum of the molecular pentaquarks with a charmed baryon. The $x$- and $y$-axes represent the $I(J^P)$ quantum numbers and the masses (in units of MeV), respectively. The corresponding dihadron systems are marked in each subfigure. We use the red, blue and black rectangles to denote the bound states, virtual states and the possibly nonexistent states, respectively, while the red (blue) rectangles with blue (red) edges means that the states can also be the near-threshold virtual (bound) states. The dark gray rectangles represent the experimental data. We stress that only the vertical widthes of red rectangles qualitatively reflect the corresponding mass ranges. The corresponding thresholds are denoted with the horizontal dashed lines. The experimental data for $P_{\psi }^N$ and $P_{\psi s}^{\mathrm{\Lambda }}$ states are taken from Refs. [14, 41, 42], where the results with two-peak hypothesis for $P_{\psi s}^{\mathrm{\Lambda }}(4459)$ [41] are quoted.

Figure 3

Spectrum of the molecular pentaquarks with a double-charm baryon. The horizontal bands with light gray represent the uncertainties of ${\mathrm{\Xi }}_{cc}^{*}$ mass. Other notations are the same as those in Fig. 2.

Figure 4

Spectrum of the molecular pentaquarks with a hyperon ${\mathrm{\Sigma }}^{(*)}$ or ${\mathrm{\Xi }}^{(*)}$. The corresponding dihadron systems are marked in each subfigure. The notations are the same as those in Fig. 2.