Variational Monte Carlo Study of Pentaquark States

Accurate numerical solution of the five-body Schrödinger equation is effected via variational Monte Carlo calculations. The spectrum is assumed to exhibit a narrow resonance with strangeness $S=+1$. A fully antisymmetrized and pair-correlated five-quark wave function is obtained for the assumed nonrelativistic Hamiltonian, which has spin, isospin, and color dependent pair interactions and many-body confining terms, which are fixed by the nonexotic spectra. Gauge field dynamics are modeled via flux-tube exchange factors. The energy determined for the ground states with $J^{\pi }={\frac{1}{2}}^{-}({\frac{1}{2}}^{+})$ is 2.22 (2.50) GeV. A lower energy negative parity state is consistent with recent lattice results. The short-range structure of the state is analyzed via its diquark content.

Figure 1

Topological configurations of flux tubes. In general, configurations of quarks do not lie in the plane.

Figure 2

Radial diquark-diquark pair distributions in the state $|1;1^{+}⟩$.