Possible quantum numbers of Θ⁺ (1540) in QCD sum rules

Using the QCD sum rule method, various pentaquark states with strangeness S = +1 are investigated. In order to find a region in the Borel mass, where the the operator product expansion (OPE) is thought to converge and the sum rule is dominated by the resonance pole, we calculate the OPE up to dimension 14 and employ the difference of two independent correlators to construct the sum rules, by which the constributions of the higher-energy continuum states are strongly suppressed. As a result of this investigation, we find stable Borel mass curves for the quantum numbers I J^π = 1/2^-, 1 1/2^-, 0 3/2⁺,1 3/2⁺, suggesting the existence of resonance poles in these channels. As the width of the J^π = 1/2^- states is likely to be very broad, and Θ⁺ ( 1540) is thought to be an isosinglet state, we conclude that the most probable candidate for Θ⁺(1540) is the state with quantum numbers I J^π = 3/2⁺.