Explain additional low-lying states in the three-gluon helicity spectrum

Explain why the three-gluon helicity-formalism calculation predicts additional low-lying glueball states that are not observed in quenched lattice calculations.

Background

The paper compares constituent-gluon descriptions with quenched lattice QCD. In the helicity-based approach, gluons are restricted to their two physical transverse polarizations, which successfully reproduces the two-gluon state counting and approximate level ordering. However, the corresponding three-gluon calculation broadly follows the lattice oddball spectrum while also predicting additional low-lying states absent from the lattice results. The origin of this discrepancy remains unresolved and bears on the reliability of constituent descriptions of the negative-charge-conjugation sector.

References

Chevalier and Mathieu extended the construction to three gluons, building totally symmetric three-particle helicity wave functions and computing the $C=-1$ spectrum; their two-gluon results agree well with the lattice, while their three-gluon spectrum broadly follows the lattice oddballs but predicts additional low-lying states not seen there, which remains to be understood.

— Glueballs: hadrons without quarks  (2609.16790 - Chevalier et al., 15 Sep 2026) in Section 2.3.3, “Semi-relativistic potential models and the gluon spin”