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 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 independent local color-singlet meson-meson interpolating currents with $J^P=0^{-}$ and analyze their QCD sum rules. For the currents that admit reliable Borel windows, the extracted effective mass scales are consistently in the range of $2.0$--$2.3\mathrm{GeV}$, significantly above the experimental mass of the $K(1690)$. Within the standard pole-plus-continuum framework, none of the selected local currents yields a separately resolved low-lying pole compatible with the COMPASS signal. These results indicate that the selected local color-singlet meson-meson currents do not isolate the $K(1690)$ signal within the present framework, while leaving open the possibility of more extended molecular dynamics and other configurations beyond the present analysis.

Accepted by CPC