The composition of the scalar mesons near 1.7 GeV: are $a_0(1710)$ and $f_0(1710)$ conventional quark–antiquark states, and does $f_0(1710)$ contain the lightest glueball?

Between 2021 and 2023 the BABAR, BESIII, and LHCb Collaborations reported an isovector scalar ( $J^{PC}=0^{++}$ , isospin 1) resonance near 1.7–1.82 GeV, branded $a_0(1710)$ or $a_0(1817)$ depending on the analysis. Because the isoscalar $f_0(1710)$ has long been the leading candidate for the lightest glueball — the purely gluonic bound state that QCD predicts in this mass region — the new isovector state immediately raised the question that Afonin (2025) revisited: a 2007 Regge-trajectory analysis based on the approximate hydrogen-like degeneracy $M^2\propto L+n+\tfrac12$ of light mesons had predicted exactly this $a_0$ , which would make both $a_0(1710)$ and $f_0(1710)$ ordinary quark–antiquark ( $q\bar q$ ) mesons rather than gluonic or multiquark states. The problem is to determine, by decisive experiment and/or theory, the internal composition of these 1.7 GeV scalars — $q\bar q$ , four-quark or molecular, or carrying a sizeable glueball admixture. The same Regge-cluster scheme also yields two directly linked predictions, the still-unobserved $f_1(1700)$ and $a_0(2270)$ , and rests on a hydrogen-like degeneracy whose dynamical origin is not yet derived from QCD; these are closely related open questions that inform, but are not themselves part of, the composition problem. As of 2026 the question is actively contested and unresolved.

Background

Scalar mesons are hadrons with quantum numbers $J^{PC}=0^{++}$ ; they carry either isospin $I=0$ (isoscalar, denoted $f_0$ ) or $I=1$ (isovector, denoted $a_0$ ). In the naive quark model an ordinary light meson is a quark–antiquark ( $q\bar q$ ) pair, and isoscalar and isovector states of the same excitation form approximate multiplets. Quantum chromodynamics (QCD), however, predicts an additional spectrum of bound states made of gluons alone, called glueballs, because gluons self-interact; quenched lattice QCD (numerical simulation of QCD on a discrete space-time grid) places the lightest, scalar glueball in the 1.6–1.8 GeV region (Morningstar and Peardon 1999). The isoscalar resonance $f_0(1710)$ sits squarely in this window and is strongly produced in gluon-rich channels such as radiative $J/\psi$ decays, which has made it the long-standing leading glueball candidate, for example in the mixing analysis of Janowski, Giacosa, and Rischke (2014), which found a dominantly gluonic $f_0(1710)$ compatible with decay data.

The situation sharpened when three experiments reported an isovector partner candidate. BABAR (2021) observed a new $a_0(1700)\to\eta\pi$ in Dalitz-plot analyses of $\eta_c$ decays produced in two-photon collisions; BESIII (2022) observed an $a_0$ -like state of mass 1.817 GeV (called $a_0(1710)^+$ in the preprint) in the first amplitude analysis of $D_s^+\to K_S^0K^+\pi^0$ ; and LHCb (2023) measured $a_0(1700)$ parameters in an amplitude analysis of $\eta_c\to K_S^0K\pi$ in $B\to(K_S^0K\pi)K$ decays. Whether the ~1.7 GeV structures in $\eta_c$ decays and the 1.82 GeV structure in $D_s$ decays are one and the same resonance is itself unsettled. A genuine isovector partner of $f_0(1710)$ would be hard to accommodate with a purely gluonic $f_0(1710)$ , since a glueball carries no isospin.

Afonin (2025) recalled that this isovector state was in fact predicted in 2007 within the Regge approach. A Regge trajectory is the approximately linear dependence of a meson's squared mass on its orbital angular momentum $L$ ; radial excitations (denoted by radial quantum number $n$ ) fill parallel 'daughter' trajectories. Light non-strange mesons cluster near certain masses, and the averaged cluster positions obey $M^2(N)\simeq a\,(N+0.54)$ GeV $^2$ with $N=L+n$ , i.e. the mass depends only on the sum $L+n$ — the same pattern of dynamical degeneracy that the enlarged $O(4)$ symmetry of the Coulomb potential produces in the hydrogen atom, hence 'hydrogen-like degeneracy'. The cluster at $N=2$ predicted an $a_0$ at $1700\pm60$ MeV. Afonin re-fit the cluster data (Shapiro–Wilk tests — a standard statistical test checking that the cluster mass-squared values scatter around the fitted linear law like Gaussian noise, $\bar M^2(N)=(1.12\pm0.03)(N+0.54\pm0.09)$ GeV $^2$ ), argued the prediction was reliable, and concluded that states lying on such trajectories are ordinary $q\bar q$ mesons, so that $a_0(1710)$ and $f_0(1710)$ 'should be conventional mesons'. Partial-wave analysis (PWA), the model-dependent decomposition of final-state invariant-mass and angular distributions into resonant waves, is the standard experimental tool for such channels.

Competing interpretations are live: Guo, Chen, Chen, Liu, and Zhu (2022) place the BESIII state (as $a_0(1817)$ ) on a $q\bar q$ Regge trajectory with $a_0(980)$ and $a_0(1450)$ while stressing that $f_0(1710)$ as glueball cannot be excluded; Achasov and Shestakov (2023) treat $a_0(1700/1800)$ as a four-quark $q^2\bar q^2$ state strongly coupled to two vector mesons; and the Oset school (2008 prediction and works of 2023–2026) generate both $f_0(1710)$ and $a_0(1710)$ dynamically as $K^*\bar K^*$ -dominated molecular states from coupled-channel final-state interactions, explicitly noting that an isospin partner would rule out $f_0(1710)$ as the glueball.

Problem Statement

Determine the internal composition of the scalar mesons near 1.7 GeV — the isovector $a_0(1710)$ / $a_0(1817)$ structures and the isoscalar $f_0(1710)$ — and thereby decide between the competing assignments now in the literature: ordinary $q\bar q$ states of the same nonet (the Regge-cluster interpretation of Afonin), four-quark states (Achasov–Shestakov), dynamically generated $K^*\bar K^*$ molecular states (Oset school), or, for $f_0(1710)$ , a state with a leading lightest-glueball component (a lightest-glueball mixing fraction comparable to or exceeding the largest $q\bar q$ component). Concretely, the problem comprises: (i) establish whether the enhancements seen near 1.7 GeV in $\eta_c$ decays ( $\eta\pi$ , $K\bar K$ channels) and near 1.82 GeV in $D_s$ decays are a single isovector resonance, and determine its mass, width, and $J^{PC}$ ; and (ii) establish whether $a_0(1710)$ and $f_0(1710)$ are isospin partners in a conventional $q\bar q$ scalar nonet, by measuring the discriminating observables — decay branching fractions, production rates in gluon-rich channels (radiative $J/\psi$ decays) versus quark-rich channels (two-photon fusion, $D$ / $B$ decays), and coupled-channel partial-wave amplitudes including the vector channels $K^*\bar K^*$ , $\rho\phi$ , $\rho\omega$ — at a level that quantitatively excludes, or establishes, a leading lightest-glueball component in $f_0(1710)$ . Two closely related questions provide context for this decision but are not themselves required parts of it: within the same Regge-cluster scheme, its remaining concrete predictions, the still-unobserved $f_1(1700)$ and $a_0(2270)$ states, await confirmation or exclusion; and the dynamical basis of the scheme itself — deriving (or refuting) the hydrogen-like law $M^2\approx a\,(L+n+\tfrac12)$ , with its flavor-dependent corrections from $s\bar s$ admixture, from QCD-based dynamics rather than semiclassical string arguments — remains an open problem of nonperturbative QCD in its own right. The objective is to decide whether the 1.7 GeV scalar sector is conventional quark–antiquark spectroscopy, an exotic (four-quark or molecular) configuration, or contains the long-sought lightest glueball, and the problem is complete when that decision rests on generally accepted experimental or theoretical evidence rather than on competing model assumptions.

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