Fully Strange Tetraquark Studies

Updated 5 July 2026

Fully strange tetraquarks are four-quark states composed of an ss s̄ s̄ configuration, with predicted resonances between 2.0 and 3.2 GeV.
Various nonperturbative methods—including QCD sum rules, the Gaussian Expansion Method, and chiral quark models—provide complementary insights into their mass spectra and decay behaviors.
Analyses of resonances such as φ(2170), X(2300), and X(2500) reveal model-dependent assignments and underscore the need for targeted experimental searches at facilities like BESIII, Belle II, and LHCb.

Searching arXiv for recent papers on fully strange tetraquarks to ground the article in published work.
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A fully strange tetraquark is an $ss\bar s\bar s$ configuration studied as a neutral hidden-strangeness four-quark system in several nonperturbative frameworks, including QCD sum rules, nonrelativistic four-body potential models, constituent-quark calculations with the Gaussian Expansion Method (GEM) and the Complex Scaling Method (CSM), chiral quark models, and diabatic dynamical diquark models. Across these approaches, the predicted spectrum extends from about $2.0$ to $3.2\,\mathrm{GeV}$, and the sector is repeatedly connected to experimental structures such as $f_0(2100)$, $f_0(2200)$, $f_2(2340)$, $\phi(2170)$, $X(2300)$, $X(2400)$, and $X(2500)$; at the same time, the identification of particular resonances remains model-dependent [2204.13959][2008.01372][2602.01759].

1. Quark content, quantum numbers, and operator constructions

In the diquark-antidiquark picture, a fully strange tetraquark is viewed as a bound state of an $ss$ diquark and an $\bar s\bar s$ antidiquark. The two quarks and two antiquarks must obey the Pauli principle, which restricts their color-spin-orbital wave functions. QCD sum-rule studies therefore construct interpolating currents in carefully chosen color-singlet combinations, both for $S$-wave configurations and for explicit orbital excitations introduced through $\overleftrightarrow{D}\mu$ or $\overleftrightarrow{\partial}\mu$ [2204.13959][2211.14993].

A representative diquark-antidiquark $P$-wave vector current is
$$
J_{7,\alpha}^{{1^{{--}}(x)=\;[\,s^{T_a\,C\gamma_\mu\,s_b\,]\;\overset{\leftrightarrow}{D}{}_{!\alpha}\;\big[\bar}}} s_a\,\gamma^\mu\,C\,\bar s^T_b\big] \, ,
$$
while a representative local meson-meson-type current used in a systematic QCD sum-rule analysis is
$$
j_{1^{{--}^{{A,\mu}}(x)=\;i\,[\bar}} s_a\,s_a]\; [\bar s_b\,\gamma^\mu\,s_b] \, .
$$
These two examples already show that the same global $J^{PC}$ can be probed through structurally distinct operators [2204.13959][2507.11874].

Beyond diquark-antidiquark and local meson-meson currents, coupled-channel quark-model studies incorporate meson-meson, diquark-antidiquark, and K-type structures with complete color bases. In that setting, hidden-color $8\otimes8$ components and channel coupling are not peripheral corrections but central structural degrees of freedom [2602.01759].

2. Nonperturbative frameworks

QCD sum-rule analyses begin from two-point correlation functions of tetraquark currents and expand them by the operator product expansion. In the explicit-$P$-wave vector study, the correlator is written as
$$
\Pi_{\mu\nu}(p^2)=i\int d^{4x\,e^{ip\cdot} x}\langle 0|T{J_\mu(x)J_\nu^{\dagger(0)}|0\rangle} \, ,
$$
with the hadronic pole isolated as
$$
\Pi_{\mu\nu}(p^{2)=\frac{\lambda_Y^{2}{M_Y^{2-p^{2}\left(-g_{\mu\nu}+\frac{p_\mu}}}} p_\nu}{p^{2}\right)+\cdots} \, .
$$
After Borel transformation, the mass is extracted through
$$
M_Y^{2=\frac{\int_0^{{s_0}ds\,s\,\rho(s)\,e^{{-s/T^{2}}{\int_0^{{s_0}ds\,\rho(s)\,e^{{-s/T^2}}}}}}}} \, .
$$
That study kept condensates up to dimension-11; other fully strange QCD sum-rule analyses retained terms up to dimension-12 or used full light-quark propagators up to dimension-eight condensates, depending on the operator basis [2211.14993][2307.07819][2507.11874].

Potential-model calculations treat $ss\bar s\bar s$ as a genuine four-body problem rather than imposing the diquark-antidiquark approximation. One nonrelativistic study adopts a Cornell-type Hamiltonian,
$$
H=\sum_{i=1}^{4\Bigl(m_i+\frac{\mathbf} p_i^{2}{2m_i}\Bigr)-T_{\rm} cm}+\sum_{i<j}V_{ij}(r_{ij}) \, ,
$$
and solves the generalized Schrödinger eigenvalue problem in Gaussian and/or harmonic-oscillator bases. In that framework, $36$ tetraquark configurations are organized into $1S$, $1P$, and $2S$ multiplets [2008.01372].

GEM+CSM calculations pursue resonant poles directly. In the chiral quark model, one solves
$$
\bigl[H(\theta)-E(\theta)\bigr]\Psi_{JM}(\theta)=0 \, ,
$$
with complex scaling $r\to r e^{i\theta}$ and $p\to p e^{-i\theta}$. Bound states remain on the real axis, while resonances appear as $\theta$-independent complex poles $E=M-i\,\Gamma/2$. This permits a unified treatment of bound, resonant, and scattering states, together with rms radii, magnetic moments, and wave-function compositions [2602.01759].

A related but distinct coupled-channel construction is the diabatic dynamical diquark model, in which one compact diquark-antidiquark channel is coupled to explicit meson-meson thresholds through a matrix Schrödinger equation. In that formalism, threshold effects shift levels and generate resonancelike behavior without eliminating the compact $\delta\bar\delta$ core [2510.15844].

3. Spectral patterns and low-lying multiplets

The low-lying spectrum is not uniform across models. In one nonrelativistic four-body potential model, the $1S$ fully strange multiplet consists of two $0^{++}$ states at $2218$ and $2440\,\mathrm{MeV}$, one $1^{+-}$ at $2323\,\mathrm{MeV}$, and one $2^{++}$ at $2378\,\mathrm{MeV}$. The same calculation places the $1P$ $0^{-+}$ states at $2481$, $2635$, and $2761\,\mathrm{MeV}$ and the five $1^{--}$ states at $2445$, $2567$, $2627$, $2766$, and $2984\,\mathrm{MeV}$ [2008.01372].

A QCD sum-rule treatment of $S$- and $P$-wave fully strange tetraquarks yields a lower low-lying pattern for several channels. It suggests $S$-wave states near $2.0$ to $2.1\,\mathrm{GeV}$, specifically $0^{++}$ at $2.11^{{+0.19}_{-0.21}\,\mathrm{GeV}$} and $1.99^{{+0.19}_{-0.24}\,\mathrm{GeV}$,} $1^{+-}$ at $2.06^{{+0.18}_{-0.20}\,\mathrm{GeV}$,} and $2^{++}$ at $2.09^{{+0.19}_{-0.22}\,\mathrm{GeV}$.} In the same work, several $P$-wave channels populate the $2.3$ to $2.6\,\mathrm{GeV}$ interval [2204.13959].

The chiral quark model with GEM+CSM produces a different low-lying positive-parity pattern: $J^{P=0^+$} poles at $1645$, $2067-i\,0.1$, and $2506-i\,0.4\,\mathrm{MeV}$; $J^{P=1^+$} poles at $2262-i\,0.6$ and $2638-i\,11.3\,\mathrm{MeV}$; and $J^{P=2^+$} poles at $2012$, $2693-i\,4.9$, and $3087-i\,2.3\,\mathrm{MeV}$. The $1^+$ pole at $2262-i\,0.6\,\mathrm{MeV}$ is singled out as a compact fully strange tetraquark near $2.3\,\mathrm{GeV}$ [2602.01759].

A systematic decay analysis based on the $36$-state spectrum reports that most fully strange tetraquark states have a relatively narrow fall-apart decay width of $\mathcal{O}(10)\,\mathrm{MeV}$. For the $1S$ multiplet, it quotes total widths of $37\,\mathrm{MeV}$ for $T_{(4s)0^{{++}(2218)}$,} $37\,\mathrm{MeV}$ for $T_{(4s)0^{{++}(2440)}$,} $17\,\mathrm{MeV}$ for $T_{(4s)1^{{+-}(2323)}$,} and $2\,\mathrm{MeV}$ for $T_{(4s)2^{++}(2378)}$ [2601.03614].

These differences are not merely numerical. They indicate that the placement of the lowest fully strange multiplets depends strongly on operator choice, treatment of orbital excitation, and whether channel coupling and hidden-color configurations are included explicitly.

4. Vector and axial-vector sectors

The vector sector has been the most contested part of the fully strange tetraquark literature because it is directly tied to $\phi(2170)$ and nearby structures.

An explicit-$P$-wave QCD sum-rule study finds that the current of type $C\gamma_\alpha\otimes\stackrel{\leftrightarrow}{\partial}\mu\otimes\gamma^\alpha C$ with fully strange quarks couples potentially to a tetraquark state with mass $2.16\pm0.14\,\mathrm{GeV}$. That result supports assigning the $Y/\phi(2175)$ as a diquark-antidiquark type tetraquark state with $J^{{PC}=1^{--}$.} The same work gives higher fully strange vector masses at $2.35\pm0.17\,\mathrm{GeV}$, $2.98\pm0.10\,\mathrm{GeV}$, and $3.13\pm0.11\,\mathrm{GeV}$, and notes that replacing $\overleftrightarrow{\partial}\mu$ by $\overleftrightarrow{D}_\mu$ shifts them by $\lesssim30\,\mathrm{MeV}$ [2211.14993].

Another QCD sum-rule study of fully strange $1^{--}$ currents gives $M=2.46\pm0.15\,\mathrm{GeV}$ for a representative current $A$, while an earlier diquark-antidiquark QCD sum-rule analysis reports $1^{--}$ masses at $2.34^{{+0.23}_{-0.30}$,} $2.43^{{+0.20}_{-0.24}$,} and $2.44^{{+0.20}_{-0.25}\,\mathrm{GeV}$} and suggests that both the $\phi(2170)$ and $X(2400)$ may be explained as $P$-wave $ss\bar s\bar s$ tetraquarks [2507.11874][2204.13959].

By contrast, the nonrelativistic four-body potential model places the five $1^{--}$ fully strange states in the range $2.445$ to $2.984\,\mathrm{GeV}$ and concludes that since $\phi(2170)$ has $M\approx2175\,\mathrm{MeV}$ well below $2445\,\mathrm{MeV}$, it is unlikely to be a pure $ss\bar s\bar s$ tetraquark in that model. A constituent quark model study of compact $S$-wave fully strange systems goes further: because its lowest compact resonance appears near $2.7\,\mathrm{GeV}$ and compact $P$-wave states are expected to be heavier, it argues that $\phi(2170)$ and $X(2370)$ are unlikely to be compact tetraquark states [2008.01372][2408.00503].

The axial sector is presently centered on $X(2300)$. A systematic QCD sum-rule study favors a $J^{{PC}=1^{+-}$} assignment with $M_{1^{{+-},A}=2.29\pm0.14\,\mathrm{GeV}$,} in excellent agreement with $X(2300)$. The chiral quark model finds a compact fully strange tetraquark with $J^{P=1^+$} at $2262-i\,0.6\,\mathrm{MeV}$, also presented as a natural interpretation of $X(2300)$. The diabatic dynamical diquark model likewise gives a fully strange $1^{+-}$ state at $2.271\,\mathrm{GeV}$ with $\delta\bar\delta=82.7\%$ [2507.11874][2602.01759][2510.15844].

Resonance	Assignments reported	Representative values
$\phi(2170)/Y(2175)$	explicit-$P$-wave $ss\bar s\bar s$ $1^{--}$ in some QCD sum rules; unlikely to be a pure $ss\bar s\bar s$ or compact tetraquark in other models	$2.16\pm0.14\,\mathrm{GeV}$; $2.445$–$2.984\,\mathrm{GeV}$; lowest compact state around $2.7\,\mathrm{GeV}$
$X(2300)$	fully strange axial state	$2.29\pm0.14\,\mathrm{GeV}$; $2262-i\,0.6\,\mathrm{MeV}$; $2.271\,\mathrm{GeV}$
$X(2500)$	low-lying $1P$ $0^{-+}$ fully strange tetraquark	$2481\,\mathrm{MeV}$; $2.55^{{+0.21}_{-0.23}\,\mathrm{GeV}$}

Strong-decay analyses sharpen this picture. Treating $\phi(2170)$ and $X(2436)$ as two fully strange $1^{--}$ tetraquarks, one study finds
$$
M_{Y_1}=2.41\pm0.25\,\mathrm{GeV},\qquad M_{Y_2}=2.34\pm0.17\,\mathrm{GeV},
$$
with $Y_1\leftrightarrow X(2436)$ and $Y_2\leftrightarrow\phi(2170)$. Its relative branching ratios are
$$
B(\phi(2170)\to\phi\eta:\phi\eta':\phi f_0:h_1(1415)\eta)\simeq 1.00:0.63:19.52:0.69 \, ,
$$
and
$$
R_{\eta/\eta'}^{{\phi(2170)}\simeq1.59} \, .
$$
Those ratios are proposed as diagnostic observables rather than as settled evidence [2310.16612].

5. Exotic quantum numbers and decay signatures

Fully strange tetraquarks are also studied in channels forbidden to pure $q\bar q$. A QCD sum-rule analysis of exotic $J^{{PC}=0^{+-}$} and $2^{+-}$ currents constructs diagonal and off-diagonal correlators, forms nearly non-correlated mixing currents, and extracts
$$
M_{0^{{+-}}=2.47^{{+0.33}_{-0.44}\,\mathrm{GeV},\qquad}}
M_{2^{{+-}}=3.07^{{+0.25}_{-0.33}\,\mathrm{GeV}}} \, .
$$
Fierz rearrangement indicates that these states may be searched for in the $P$-wave $\phi(1020)f_0(1710)$ and $\phi(1020)f_2'(1525)$ channels, with final states $\phi K\bar K$ and $\phi\pi\pi$ [2307.07819].

The same broad theme appears in other approaches, but at different masses. The systematic QCD sum-rule study of local meson-meson currents predicts an exotic $0^{--}$ state at $2.46\pm0.13\,\mathrm{GeV}$ and notes that such a state would be unambiguous evidence of four-quark dynamics. The earlier diquark-antidiquark sum-rule study extracts two non-correlated $1^{-+}$ masses, $2.45^{{+0.20}_{-0.25}\,\mathrm{GeV}$} and $2.49^{{+0.21}_{-0.25}\,\mathrm{GeV}$,} explicitly identifying them as $ss\bar s\bar s$ states with quantum numbers forbidden to pure $q\bar q$ [2507.11874][2204.13959].

A compact-resonance analysis of the strange analogues of $X(6900)$ instead finds a family of exotic $S$-wave states in the higher interval $2.7$ to $3.3\,\mathrm{GeV}$, including $0^{+-}$ zero-width states at $2725$, $2873$, $3148$, and $3285\,\mathrm{MeV}$, a $1^{++}$ sequence at $2723$, $2863$, and $3151\,\mathrm{MeV}$, and a $2^{+-}$ zero-width state at $2896\,\mathrm{MeV}$. In that study, all states are compact, with rms radii of about $1.0$ to $1.5\,\mathrm{fm}$ [2408.00503].

Decay channels proposed across the literature are strongly patterned by $J^{PC}$. Recurrent fully strange modes include $\phi\phi$, $\eta\eta$, $\eta'\eta'$, $\eta\eta'$, $\phi\eta$, $\phi\eta'$, $\phi f_0(980)$, $\phi f_0(1370)$, $\phi f_1(1420)$, $\phi f_2'(1525)$, and $\phi h_1(1415)$. A systematic fall-apart study identifies several especially diagnostic channels: $\phi\phi$, $\phi\phi(1680)$, $\eta^{{(\prime)}\phi$,} $\eta^{{(\prime)}h_1(1415)$,} and $\phi f_2'(1525)$ [2601.03614].

6. Structural interpretation, controversies, and experimental program

A central structural issue is whether fully strange tetraquarks are predominantly compact or threshold-driven. The diabatic dynamical diquark model finds that in every channel the $\delta\bar\delta$ fraction exceeds about $80\%$, with no molecular-like, threshold-driven state appearing in the $ss\bar s\bar s$ sector. The chiral quark model reaches a compatible conclusion for several low-lying poles, but with a more explicit emphasis on hidden-color and K-type components; for the $J^{P=1^+$} pole at $2262-i\,0.6\,\mathrm{MeV}$ it quotes
$$
{S,H,Di,K}={18.2\%,81.5\%,0.1\%,0.2\%},
$$
together with $r_{\rm rms}\approx0.8\,\mathrm{fm}$ and $\mu=0$. This suggests a compact state whose dominant internal structure is hidden-color rather than a simple meson-meson configuration [2510.15844][2602.01759].

The principal controversy is spectroscopic assignment. For $\phi(2170)$, the literature contains both direct support for an explicit-$P$-wave fully strange $1^{--}$ tetraquark and arguments that it lies too low to be a pure or compact $ss\bar s\bar s$ state. For $X(2300)$, several recent studies converge on an axial fully strange interpretation, but the detailed labeling varies between $J^{{PC}=1^{+-}$} and $J^{P=1^+$.} For $X(2500)$, there is comparatively broader agreement that a low-lying $1P$ $0^{-+}$ fully strange tetraquark is a plausible assignment [2211.14993][2008.01372][2507.11874][2602.01759][2601.03614].

The experimental program repeatedly emphasized in these works centers on BESIII, Belle II, and LHCb, with additional mentions of GlueX, COMPASS, J-PARC, PANDA, and future $e^{+e^-$} machines. The recommended search modes are highly specific: $\phi\phi$ for scalar and tensor states, $\phi\eta$ and $\phi\eta'$ for axial and vector states, $\phi h_1(1415)$ and $\phi f_2'(1525)$ for several $1P$ exotics, and $P$-wave $\phi f_0(1710)$ or $\phi f_2'(1525)$ for the exotic $0^{+-}$ and $2^{+-}$ channels [2307.07819][2601.03614].

Taken together, the literature does not yet provide a single canonical fully strange tetraquark spectrum. It does, however, provide a dense set of testable benchmarks: masses between about $2.0$ and $3.2\,\mathrm{GeV}$, multiple candidate assignments for $\phi(2170)$, $X(2300)$, and $X(2500)$, explicit predictions for exotic $J^{PC}$ channels, and decay patterns narrow enough in many cases to be accessible to dedicated invariant-mass scans and partial-wave analyses.