$\overline{K}\overline{D}N$ molecular state as a “$uuds\overline{c}$ pentaquark” in a three-body calculation

We predict a new three-body hadronic molecule composed of antikaon $\overline{K}$, anticharm meson $\overline{D}$, and nucleon $N$ with spin-parity $J^P=1/2^{+}$ and isospin $I=1/2$. This state behaves like an explicit pentaquark state because its minimal quark configuration is $uuds\overline{c}$ or $udds\overline{c}$. Owing to the attraction between every pair of two hadrons, in particular the $\overline{K}\overline{D}$ attraction which dynamically generates $D_{s0}{\left(2317\right)}^{-}$ and $\overline{K}N$ attraction which dynamically generates $\mathrm{\Lambda }\left(1405\right)$, the $\overline{K}\overline{D}N$ system is bound, and the real (imaginary) part of its eigenenergy is calculated as $3253\text{MeV}$ (minus a few MeV) in a nonrelativistic three-body potential model. We discuss properties of this $\overline{K}\overline{D}N$ quasibound state which emerge uniquely in three-body dynamics.

Figure 1

Density distributions for the $\overline{K}\overline{D}$ system in the $D_{s0}\left(2317\right)$ (solid line) and for the $\overline{D}N$ system in the $\overline{D}N$ bound state (dashed line).

Figure 2

Real parts of the effective local potentials with the energies at the respective thresholds.

Figure 3

Three types of Jacobi coordinates.

Figure 4

Eigenenergy $E_{\mathrm{pole}}$ as a function of the number of the Gaussian expansion $N$ (open circles using option A and open squares using option B) from $N=4$ to $N=10$ in intervals of 2. We also plot the branch points for the $\mathrm{\Lambda }\left(1405\right)+\overline{D}, D_{s0}\left(2317\right)+N$, and $\overline{K}+\overline{D}+N$ as filled symbols.

Figure 5

Diagrams for the decay of the $\overline{K}\overline{D}N$ quasibound state. Open circles represent hadron-hadron interactions. While we take into account the direct process (a) in the effective potentials, we do not include the meson exchange processes (b) and (c) in our three-body calculation.

Figure 6

Density distributions for the $\overline{K}N, \overline{K}\overline{D}$, and $\overline{D}N$ subsystems in the $\overline{K}\overline{D}N$ quasibound state using options A (top panel) and B (bottom panel).