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Two- and three-gluon glueballs within the helicity formalism

Cyrille Chevalier*

Vincent Mathieu†

  • Service de Physique Nucléaire et Subnucléaire, Université de Mons, UMONS Research Institute for Complex Systems, Place du Parc 20, 7000 Mons, Belgium

  • *Contact author: cyrille.chevalier@umons.ac.be
  • †Contact author: vmathieu@ub.edu
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Phys. Rev. D 112, 014015 – Published 8 July, 2025

DOI: https://doi.org/10.1103/cvld-kwkd

Abstract

Both positive and negative charge conjugation glueball spectra are computed with a constituent gluon approach. We first compute the spectrum of the Hamiltionian describing two-gluon bound states having C=+, before tackling the three-gluon bound states having C=−. We review the construction of two and three particle helicity states in order to build totally symmetric wave functions for our glueball states. In the literature, two different couplings schemes are used to build three particle states. We derive for the first time the relation between these two three-body state definitions. The glueball spectra are compared with those obtained from quantum chromodynamics simulations on a lattice. The two-gluon glueball spectra show a good agreement with the constituent approach and the numerical lattice simulations. The three-gluon spectrum is in overall agreement with the masses observed on the lattice but also predicts additional low-lying states.

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Phys. Rev. D 112, 014015– Published 8 July, 2025
  • Received 25 March 2025
  • Accepted 14 May 2025
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