Abstract
We study the spectra of two-gluon glueballs and three-gluon oddballs and corresponding equation of state in $5$-dimensional deformed holographic QCD models in the graviton-dilaton system, where the metric, the dilaton field and dilaton potential are self-consistently solved from each other through the Einstein field equations and the equation of motion of the dilaton field. We compare the models by inputting the dilaton field, inputting the deformed metric and inputting the dilaton potential, and find that with only 2 parameters, the $5$-dimensional holographic QCD model predictions on glueballs/oddballs spectra in general are in good agreement with lattice results except two oddballs $0^{+-}$ and $2^{+-}$. From the results of glueballs/oddballs spectra at zero temperature and the equation of state at finite temperature, we observe that the model with quadratic dilaton field can simultaneously describe glueballs/oddballs spectra as well as equation of state of pure gluon system. The model with quadratic $A_{E}(z)$ can describe glueballs/oddballs spectra, but its corresponding equation of state behaves more like $N_{f}=2+1$ quark matter. These are consistent with dimension analysis at UV boundary.
Highlights
Glueball is one of the most crucial predictions from quantum chromodynamics (QCD), whose non-Abelian feature makes it possible to form bound states of gauge bosons, i.e., glueballs made of two/three gluons, [1]
In the framework of holography, the states JPC with the same angular momentum J and the same C-parity corresponds to different operators, the dimensions of which are the same
We would like to mention that the data predicted by the single pole (SP) and dipole (DP) Regge model [51] to fit the high energy pp scattering: using the SP Regge model, the predicted mass for 2þþ glueball is 1.747 GeV; using the DP Regge model, the predicted masses for 2þþ glueball and 3−− oddball are 1.758 GeV and 3.001 GeV, respectively
Summary
Glueball is one of the most crucial predictions from quantum chromodynamics (QCD), whose non-Abelian feature makes it possible to form bound states of gauge bosons, i.e., glueballs made of two/three gluons (gg, ggg, etc.), [1]. Evolution of the dilaton field and scalar field in 5-dimensional space-time resemble the renormalization group from ultraviolet (UV) to infrared (IR) This dynamical holographic QCD model describes the scalar glueball spectra and the light meson spectral quite well [67,102,130]. We will compare the spectra of glueballs/oddballs including scalar, vector, as well as tensor states and their excitations with those from the lattice QCD, and compare thermodynamic properties with the lattice QCD results for pure gluon system and/or 2 þ 1 flavors system in these three types of models.
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