The volume dependence of spectral weights and the pentaquark state

Abstract

Before studying the pentaquark system we examine the spectral weights of the two lowest scattering states in the two-pion system in the isospin I=2 channel on lattices of size $16^3\times 32$, $24^3 \times 32$ and $32^3 \times 64$ at $β=6.0$ in the quenched theory. We find that the spectral weights scale with the volume for large time separations. Therefore very accurate data are necessary in order that the spectral weights determined on different volumes yield a ratio that is precise enough to distinguish a scattering state from a single particle state. The pentaquark system is studied on the same lattices and scaling of the spectral weights of the low lying state is investigated. The accuracy of the results obtained for the scaling of spectral weights do not allow us to exclude a pentaquark resonance.