First Study for the Pentaquark Potential in SU(3) Lattice QCD

Abstract

The static penta-quark (5Q) potential $V_{\rm 5Q}$ is studied in SU(3) lattice QCD with $16^3\times 32$ and $β$=6.0 at the quenched level. From the 5Q Wilson loop, $V_{\rm 5Q}$ is calculated in a gauge-invariant manner, with the smearing method to enhance the ground-state component. $V_{\rm 5Q}$ is well described by the OGE plus multi-Y Ansatz: a sum of the OGE Coulomb term and the multi-Y-type linear term proportional to the minimal total length of the flux-tube linking the five quarks. Comparing with ${\rm Q \bar Q}$ and 3Q potentials, we find a universality of the string tension, $σ_{\rm Q \bar Q} \simeq σ_{\rm 3Q} \simeq σ_{\rm 5Q}$, and the OGE result for Coulomb coefficients.