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Light tetraquark states with $J^{P C} = 1^{- -}$ from QCD sum rules

Yi-Wei Jiang^1,*, Hua-Xing Chen^1,†, Er-Liang Cui ^2,‡, Ding-Kun Lian ^1,§, Wen-Ying Liu^3,4,5,6,∥, and Niu Su^7,¶

¹School of Physics, Southeast University, Nanjing 210094, China
²College of Science, Northwest A&F University, Yangling 712100, China
³School of Physical Science and Technology, Lanzhou University, Lanzhou 730000, China
⁴Lanzhou Center for Theoretical Physics, Key Laboratory of Theoretical Physics of Gansu Province, Key Laboratory of Quantum Theory and Applications of MoE, Gansu Provincial Research Center for Basic Disciplines of Quantum Physics, Lanzhou University, Lanzhou 730000, China
⁵MoE Frontiers Science Center for Rare Isotopes, Lanzhou University, Lanzhou 730000, China
⁶Research Center for Hadron and CSR Physics, Lanzhou University and Institute of Modern Physics of CAS, Lanzhou 730000, China
⁷College of Physics and Optoelectronic Engineering, Taiyuan University of Technology, Taiyuan 030024, China

^*Contact author: yiweijiang@seu.edu.cn
^†Contact author: hxchen@seu.edu.cn
^‡Contact author: erliang.cui@nwafu.edu.cn
^§Contact author: liandk@seu.edu.cn
^∥Contact author: liuwenying@lzu.edu.cn
^¶Contact author: suniu@tyut.edu.cn

Phys. Rev. D 114, 074028 – Published 13 October, 2026

DOI: https://doi.org/10.1103/rpd1-1xvb

Abstract

We perform a systematic QCD sum rule study of light tetraquark states with $J^{P C} = 1^{- -}$ in the diquark-antidiquark picture. A complete set of local interpolating currents is constructed and projected onto six flavor-isospin configurations ( $q = u / d$ ): the isoscalar $q q \bar{q} \bar{q}$ , $q s \bar{q} \bar{s}$ , and $s s \bar{s} \bar{s}$ sectors, the isovector $q q \bar{q} \bar{q}$ and $q s \bar{q} \bar{s}$ sectors, and the isotensor $q q \bar{q} \bar{q}$ sector. From the nonderivative currents studied in the present work, the extracted masses of the $q q \bar{q} \bar{q}$ , $q s \bar{q} \bar{s}$ , and $s s \bar{s} \bar{s}$ configurations lie in the ranges 1.53–2.37 GeV, 1.86–2.51 GeV, and 2.46–2.60 GeV, respectively. For the $s s \bar{s} \bar{s}$ vector sector, we also quote the previous derivative-current result ${2.34}_{- 0.30}^{+ 0.23} GeV$ as a complementary benchmark. We further compare the present $1^{- -}$ tetraquark spectrum with previous QCD sum rule results for the $1^{- +}$ tetraquark and hybrid states [N. Su, E.-L. Cui, Y.-W. Jiang, and H.-X. Chen, Eur. Phys. J. C 86, 724 (2026).], aiming to provide useful information for distinguishing tetraquark and hybrid configurations in the light hadron spectrum. As an additional improvement, we complete the previously missing isotensor $1^{- +}$ tetraquark entry and obtain its lowest mass to be $M = 2.1 9_{- 0.24}^{+ 0.26} GeV$ , which is included in the spectral comparison.

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Phys. Rev. D 114, 074028– Published 13 October, 2026

Vol. 114, Iss. 7 — 1 October 2026

Received 17 July 2026
Revised 6 September 2026
Accepted 21 September 2026

DOI: https://doi.org/10.1103/rpd1-1xvb

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP³.

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Light tetraquark states with $J^{P C} = 1^{- -}$ from QCD sum rules

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Light tetraquark states with JPC=1−− from QCD sum rules

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Light tetraquark states with $J^{P C} = 1^{- -}$ from QCD sum rules