QCD sum rule analysis of local meson-meson currents for the K(1690) state
Abstract
The nature of the recently observed K(1690) state, reported by the COMPASS Collaboration as a candidate for a strange crypto-exotic meson with JP=0-, remains unclear. In this work, we investigate whether it can be described by local meson-meson currents within the framework of QCD sum rules. We construct a set of local meson-meson-type interpolating currents with JP=0-, covering the representative Dirac structures 0- 0+, 0+ 0-, 1- 1+, 1+ 1-, as well as tensor configurations. For all these currents, we perform a systematic operator product expansion up to dimension-eight condensates and carry out a detailed analysis of Borel stability, continuum threshold dependence, and pole contributions. We find that the extracted masses are consistently located around 2~GeV or higher, significantly above the experimental mass of the K(1690). This behavior is highly stable against variations of QCD parameters and the choice of interpolating currents, and is observed universally across all the considered configurations. The absence of any low-lying pole compatible with the COMPASS signal therefore disfavors interpreting the K(1690) as a state predominantly coupled to these local meson-meson currents within the QCD sum rule framework. Our results thus make a compact multiquark configuration a more plausible explanation for this state.