The scalar glueball G is the lightest particle of the Yang–Mills sector of QCD, with a lattice predicted mass of about $$m_{G}\simeq 1.7\,{\mathrm{GeV}}$$
m
G
≃
1.7
GeV
. It is natural to investigate glueball-glueball scattering and the possible emergence of a bound state, that we call glueballonium. We perform this study in the context of a widely used dilaton potential, that depends on a single dimensionful parameter $$\Lambda _G$$
Λ
G
. We consider a unitarization prescription that allows us to predict the lowest partial waves in the elastic window. These quantities can be in principle calculated on the lattice, thus offering possibility for testing the validity of the dilaton potential and an independent determination of its parameter. Moreover, we also show that a stable glueballonium exists if $$\Lambda _{G}$$
Λ
G
is small enough. In particular, for $$\Lambda _{G}$$
Λ
G
compatible with the expectations from the gluon condensate, the glueballonium has a mass of about $$3.4\,{\mathrm{GeV}}$$
3.4
GeV
.
According to lattice simulations and other theoretical approaches, the scalar glueball is the lightest state in the Yang-Mills sector of QCD. Since within this sector the scalar glueball is stable, the scattering between two glueballs is a well-defined process. Moreover, a glueball-glueball bound state, called glueballonium, might exist if the attraction turns out to be large enough. In this work, we concentrate on the formation of the glueballonium in the context of the dilaton potential. In particular, we investigate the parameter values for which such a glueballonium emerges.
We study the thermodynamic properties – pressure, entropy and trace anomaly – of a gas of glueballs that includes the glueball states obtained by various lattice simulations. We show that this model, called glueball resonance gas (GRG) approach, describes well the thermal properties of the Yang–Mills sector of QCD below the critical temperature $$T_c$$
T
c
, provided that $$T_c$$
T
c
is properly matched to the corresponding determination of the glueball masses, obtaining $$T_c \sim 320 \pm 20$$
T
c
∼
320
±
20
MeV. The inclusion into the GRG of heavier glueballs not yet seen on the lattice, assuming that glueballs follow Regge trajectories as quark-antiquark states do, leads only to a small correction. We consider the contribution to the pressure of the interactions between scalar-scalar and tensor-tensor glueballs, which turn out to be also negligible.
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