Absence of evidence for pentaquarks on the lattice

We study the question of whether or not QCD predicts a pentaquark state ${\Theta }^{+}$. We use the improved, fixed point lattice QCD action which has very little sensitivity to the lattice spacing and also allows us to reach light quark masses. The analysis was performed on a single volume of size $(1.8\mathrm{fm}{)}^3\times 3.6\mathrm{fm}$ with lattice spacing of $a=0.102\mathrm{fm}$. We use the correlation matrix method to identify the ground and excited states in the isospin 0, negative parity channel. In the quenched approximation where dynamical quark effects are omitted, we do not find any evidence for a pentaquark resonance in QCD.

Figure 1

The effective mass of the optimized pentaquark ground state correlator. The optimal effective mass as defined in Ref. [27] is also shown with diamond symbols.

Figure 2

The effective mass of the optimized pentaquark first excited state correlator. The optimal effective mass as defined in Ref. [27] is also shown with diamond symbols.

Figure 3

Single- and two-exponential fits to the ground state diagonal component of the optimized correlation matrix. For the single-exponential fit, the fit could only be done starting at large time separations.

Figure 4

The fitted energies for the pentaquark ground and first excited states and the quality of the fits as a function of $t_{\min }$, the smallest time separation included in the fit range. The horizontal solid lines are the kaon-nucleon threshold (including the error) and the horizontal dashed lines are the energy levels of kaon-nucleon scattering states.

Figure 5

The fitted pentaquark ground and first excited state energies as a function of the sum of the nucleon and pseudoscalar meson mass. The degenerate quark mass data are the dark circles, the nondegenerate quark mass data the light squares. The hollow symbols are the three lowest kaon-nucleon scattering state energies. The dashed lines indicate the physical values of $M_{\mathrm{K}}+M_{\mathrm{N}}$.