Spin-3/2 Pentaquark in QCD Sum Rules

TL;DR

This paper applies QCD sum rules to investigate the spin-3/2 pentaquark with strangeness +1, providing evidence for a positive parity state around 1.4 GeV and explaining its narrow width.

Contribution

The study formulates QCD sum rules for the spin-3/2 pentaquark, emphasizing the importance of a wide Borel window and using correlator differences to improve reliability.

Findings

Evidence for a positive parity spin-3/2 pentaquark at ~1.4 GeV

No evidence found for negative parity state

Method improves sum rule stability and reliability

Abstract

The QCD sum rule method is formulated for the strangeness +1 pentaquark baryon with isospin I=0 and spin-parity J^P = 3/2^\pm. The spin-3/2 states are considered to be narrower than the spin-1/2 ones, and thus may provide a natural explanation for the experimentally observed narrow width of \Theta^+. In order to obtain reliable results in QCD sum rule calculations, we stress the importance of establishing a wide Borel window, where convergence of the operator product expansion and sufficient low-mass strength of the spectral function are guaranteed. To this end, we employ the difference of two independent correlators so that the high-energy continuum contribution is suppressed. The stability of the physical quantities against the Borel mass is confirmed within the Borel window. It is found that the sum rule gives positive evidence for the (I, J^P) = (0, 3/2^+) state with a mass of about 1.4 \pm 0.2 GeV, while we cannot extract any evidence for the (0, 3/2^-) state.