Glueballs

A first installment on the non-vanilla hadron blogging project that I mentioned in a previous post notes a new review article on the topic. 

Glueballs are always bosons, which means that they can blend with other bosons with the same quantum numbers. As the article below explains:

If glueballs are easily studied in the quenched approximation, they have proved remarkably elusive in practice. This is because, in the real world, quarks are light and dynamical. Because the lowest-lying glueballs carry J^PC = 0++, 2++ and 0−+, all of which are quantum numbers that ordinary isoscalar q¯q mesons also carry, nothing forbids mixing. As a result, any physical resonance in these channels is a superposition of the possible bare resonances[.]

This is one of several reasons that it is hard to precisely predict the mass of glueball resonances even though, naively, it should be simpler than other hadron mass calculations because the only experimentally measured physical constant that enters into the calculation at leading order is the strong force coupling constant. Gluons have no electromagnetic charge, don't decay via the weak force, are themselves massless (although their energy gives rise to an emergent mass for glueballs), and don't need to take into account quark masses at leading order.

The theoretical calculations put essentially all of the potential glueball states in a narrow mass range of about 1.3-5.0 GeV, which is a mass range that is also crowded with a background of all sorts of more conventional hadron resonances, which further complicates the process of determining whether a resonance has a significant glueball component.

But despite these challenges, some experimentally observed resonances have been identified with a probable high scalar glueball or pseudoscalar glueball content, validating a key prediction of quantum chromodynamics (QCD). There are a couple of other possible glueball types that are harder to match to experimentally observed resonances.

Glueballs are colour-singlet bound states built from gluons alone. They are an unavoidable consequence of the non-Abelian structure of Quantum Chromodynamics (QCD), and, in the pure Yang--Mills limit, they are the only physical excitations of the theory. The present article reviews what is known about them. 

After establishing which spin, parity and charge-conjugation quantum numbers two- and three-gluon states can carry, the pure-gauge spectrum is surveyed. Each of the main theoretical approaches and their respective conclusions are briefly presented. They include lattice QCD, constituent-gluon and Coulomb-gauge models, functional Dyson--Schwinger and Bethe--Salpeter equations, holographic models, and QCD sum rules. Particular attention is paid to the scale-setting ambiguity that limits how precisely a quenched glueball mass can be converted into physical units. 

The discussion then turns to full QCD. After discussing the meaning of a glueball assignment in this context, unquenching effects and questions related to glueball--qq¯ mixing are addressed. The large-N(c) counting that underpins the mixing picture, as well as mass-matrix and effective-Lagrangian treatments of mixing are presented. The selection rules and dynamical mechanisms that shape glueball decays are also discussed. 

The gluon-rich production mechanisms used experimentally are finally reviewed. The candidates are assessed sector by sector: f(0)(1370)/f(0)(1500)/f(0)(1710) and the competing interpretations of the scalar sector, η(1405)/η(1475) and X(2370) in the pseudoscalar sector, the crowded tensor region, and the essentially unexplored C=−1 sector and its connection to the Odderon. 

Outlooks on the programmes that could help in validating some of these candidates or identifying others are reviewed as a conclusion.

Cyrille Chevalier, Vincent Mathieu, "Glueballs: hadrons without quarks" arXiv:2609.16790 (September 15, 2026) (Submission to Encyclopedia of Nuclear Physics (Elsevier)).