QCD sum rule analysis of local meson-meson currents for the $K(1690)$ state

TL;DR

This study uses QCD sum rules to analyze local meson-meson currents for the $K(1690)$, finding that the observed state is unlikely to be described by such currents and suggesting a multiquark structure instead.

Contribution

It provides a systematic QCD sum rule analysis of various local meson-meson currents for the $K(1690)$, concluding these do not match the experimental mass, implying a different internal structure.

Findings

Extracted masses around 2 GeV or higher, above the $K(1690)$ mass.

Analysis stable across different currents and QCD parameters.

Disfavors local meson-meson currents as the $K(1690)$'s dominant structure.

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 $J^P=0^-$, 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 $J^P=0^-$, covering the representative Dirac structures $0^- \otimes 0^+$, $0^+ \otimes 0^-$, $1^- \otimes 1^+$, $1^+ \otimes 1^-$, 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 $2~\mathrm{GeV}$ 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.