Unraveling $K(1690)$ as a pseudoscalar $ud\bar{d}\bar{s}$ tetraquark state

TL;DR

This study uses QCD sum rules to investigate whether the $K(1690)$ resonance can be interpreted as a pseudoscalar $ud\bar{d}\bar{s}$ tetraquark state, providing theoretical support for its exotic nature.

Contribution

It systematically calculates the masses of $ud\bar{d}\bar{s}$ tetraquark states using QCD sum rules, including comprehensive tri-gluon condensate contributions, supporting the $K(1690)$ as a tetraquark.

Findings

Supports $K(1690)$ as a $ud\bar{d}\bar{s}$ tetraquark.

Highlights the importance of tri-gluon condensate contributions.

Demonstrates IR safety in sum-rule analysis.

Abstract

The recent observed $K (1690)$ has been identified as a supernumerary pseudoscalar resonance signal in the strange-meson spectrum predicted by quark model calculations. It is the best candidate of a strange crypto-exotic state. In this work, we systematically study the hadron masses of $ud\bar{d}\bar{s}$ tetraquark states with $J^P = 0^-$ in the method of QCD sum rules (QCDSR). For ten interpolating currents, we calculate the correlation functions up to dimension-8 nonperturbative condensates. To calculate the tri-gluon condensate, we comprehensively consider the contributions from different operators with and without covariant derivatives. The infrared (IR) safety can be guaranteed for the completely calculated tri-gluon condensate by properly addressing the IR divergences in Feynman diagrams. It is demonstrated that the tri-gluon condensate provides significant contributions to the sum-rule analyses in these light tetraquark systems. Our results support the interpretation of $K (1690)$ resonance to be a pseudoscalar $ud\bar{d}\bar{s}$ tetraquark state.