The low-lying light tetraquark states with quantum numbers $J^{P}=0^{+ }$, $1^{+}$ and $2^{+}$

TL;DR

This paper analyzes low-lying light tetraquark states in a non-relativistic quark model that includes pseudoscalar meson exchange, two confinement schemes (Cornell and linear), and an instanton-induced interaction as a residual spin-dependent force. By constructing eight symmetric color–spin–flavor configurations and solving a Gaussian-basis generalized eigenvalue problem, the authors obtain masses for $nn\bar{n}\bar{n}$, $ns\bar{n}\bar{s}$, $ss\bar{s}\bar{s}$, $nn\bar{n}\bar{s}$, and $ns\bar{s}\bar{s}$ states, finding several low-lying levels that align with light-meson resonances such as $f_{0}(500)$, $f_{0}(1370)$, $f_{0}(1500)$, $h_{1}(1170)$, $h_{1}(1595)$, $h_{1}(1965)$, $f_{2}(1430)$, $f_{2}(1810)$, $a_{0}(980)$, $a_{1}(1260)$, $a_{2}(1700)$, and kaon states like $K^{*}_{0}(1430)$, $K_{1}(1270)$, and $K^{*}_{2}(1980)$. The results highlight the role of instanton-induced interactions in producing isospin-dependent mass shifts and suggest significant mixing between $q\bar{q}$ and $qq\bar{q}\bar{q}$ components. Overall, the work provides a spectrum-theory framework that connects compact tetraquark components to observed light mesons and offers guidance for experimental searches of tetraquarks in the light-quark sector.

Abstract

The low-lying light tetraquark states are investigated in the non-relativistic quark model (NRQM) including the pseudoscalar meson exchange, where two different confinement potential schemes, the Cornell potential and the linear potential, are employed, along with the instanton-induced interaction serving as the residual spin-dependent interaction. The numerical results show agreement with masses of $f_{0}(500)$, $f_{0}(1370)$, $f_{0}(1500)$, $f_{0}(2020)$, $f_{0}(2200)$, $h_{1}(1170)$, $h_{1}(1595)$, $h_{1}(1900)$, $h_{1}(1965)$, $h_{1}(2215)$, $f_{2}(1430)$, $f_{2}(1640)$, $f_{2}(1810)$, $f_{2}(2010)$, $f_{2}(2150)$, $a_{0}(980)$, $a_{0}(1450)$, $a_{0}(1950)$, $a_{1}(1260)$, $a_{1}(1640)$, $a_{2}(1700)$, $K^{*}_{0}(1430)$, $K^{*}_{0}(1950)$, $K_{1}(1270)$, $K_{1}(1440)$, $K_{1}(1650)$, and $K^{*}_{2}(1980)$. The results shed light on the spectrum of these mesons and offer guidande to search for the tetraquarks in the future.

Figures (3)

• Figure 1: Mass spectrum of S-wave $nn\bar{n}\bar{n}$ states. The data on the left corresponds to Model I, whereas the data on the right pertains to Model II. The red solid lines represent the numerical results of the $nn\bar{n}\bar{n}$ states within Model I, and the blue lines indicate the results for Model II. The gray dotted lines are the two-body thresholds, the rectangles represent the physical masses of $nn\bar{n}s\bar{n}$ quoted from PDG ParticleDataGroup:2024cfk, and the bands of the rectangles stand for the uncertainties of masses.
• Figure 2: Mass spectrum of S-wave $ns\bar{n}\bar{s}$ and $ss\bar{s}\bar{s}$ states. The data on the left corresponds to Model I, whereas the data on the right pertains to Model II. The red and green solid lines depict the numerical results of the $ns\bar{n}\bar{s}$ and $ss\bar{s}\bar{s}$ states, respectively, as calculated within Model I. Conversely, the blue and purple lines represent the numerical results of these states as determined by Model II. The gray dotted lines are the two-body thresholds, the rectangles represent $ns\bar{n}\bar{s}$ and $ss\bar{s}\bar{s}$ states' physical masses quoted from PDG ParticleDataGroup:2024cfk, and the bands of the rectangles stand for the uncertainties of masses.
• Figure 3: Mass spectrum of S-wave $nn\bar{n}\bar{s}$ and $ns\bar{s}\bar{s}$ states. The data on the left corresponds to Model I, whereas the data on the right pertains to Model II. The red and green solid lines depict the numerical results of the $nn\bar{n}\bar{s}$ and $ns\bar{s}\bar{s}$ states, respectively, as evaluated in Model I. Conversely, the blue and purple lines represent the corresponding outcomes for these states as determined by Model II. The gray dotted lines are the two-body thresholds, the rectangles represent $nn\bar{n}\bar{s}$ and $ns\bar{s}\bar{s}$ states physical masses taken from PDG ParticleDataGroup:2024cfk, and the bands of the rectangles stand for the uncertainties of masses.