Spin-3/2pentaquark in the QCD sum rule approach

Abstract

We study $I{J}^{P}=0{\frac{3}{2}}^{\ifmmode\pm\else\textpm\fi{}}$ and $1{\frac{3}{2}}^{\ifmmode\pm\else\textpm\fi{}}$ pentaquark states with $S=+1$ in the QCD sum rule approach. The QCD sum rule for positive parity states and that for negative parity are independently derived. The sum rule suggests that there exist the $0{\frac{3}{2}}^{\ensuremath{-}}$ and the $1{\frac{3}{2}}^{\ensuremath{-}}$ states. These states may be observed as extremely narrow peaks since they can be much below the $S$-wave threshold and since the only allowed decay channels are $NK$ in $D$ wave, whose centrifugal barriers are so large that the widths are strongly suppressed. The $0{\frac{3}{2}}^{\ensuremath{-}}$ state may be assigned to the observed ${\ensuremath{\Theta}}^{+}(1540)$ and the $1{\frac{3}{2}}^{\ensuremath{-}}$ state can be a candidate for ${\ensuremath{\Theta}}^{++}$.