QCD sum rule analysis of hidden strange $1^{++}$ tetraquark masses and radial excitations

Abstract: We revisit the light tetraquark states with quantum numbers $J<sup>{PC}=1<sup>{++}$ using QCD sum rules, focusing on a complete set of derivative-free diquark-antidiquark interpolating currents. By calculating the operator product expansion up to dimension-eight condensates, we extract the ground-state mass of the hidden-strange $us\bar{u}\bar{s}$ tetraquark from both Laplace sum rules (LSR) and finite-energy sum rules (FESR). Our combined analysis yields $M_{us\bar{u}\bar{s}} = 1.45\pm0.11$~GeV, which agrees well with the mass of the $a_1(1420)$ resonance and supports its tetraquark interpretation. Furthermore, we perform Gaussian sum rule (GSR) analyses to probe radial excitations, adopting a two-resonance narrow-width model. The GSR fit reveals a heavier state with mass $m_2 = 1.86\pm0.12$~GeV and a relative coupling $r = 0.15\pm0.03$ for the lighter state, indicating that the $a_1(1930)$ is a promising candidate for a compact $1<sup>{++}$ tetraquark. We also discuss the dominant decay modes of these tetraquark candidates, emphasizing hidden-strange channels such as $K<sup>*K$ and $f_0(980)π$, which can be tested in future experiments.