Abstract
The graviton soft wall (GSW) model provides a unified description of the scalar glueball and meson spectra with a unique energy scale. This success has led us to extend the analysis to the description of the spectra of other hadrons. We use this model to calculate masses of the odd and even ground states of glueballs for various spins, and show that the GSW model is able to reproduce the Regge trajectory of these systems. In addition, the spectra of the $\ensuremath{\rho}$, ${a}_{1}$ and $\ensuremath{\eta}$ mesons will be addressed. Results are in excellent agreement with current experimental data. Furthermore such an achievement is obtained without any additional parameters. Indeed, the only two parameters appearing in these spectra are those that were previously fixed by the light scalar meson and glueball spectra. Finally, in order to describe the $\ensuremath{\pi}$ meson spectrum, a suitable modification of the dilaton profile function has been included in the analysis to properly take into account the Goldstone realization of chiral symmetry. The present investigation confirms that the GSW model provides an excellent description of the spectra of mesons and glueballs with only a small number of parameters unveiling a relevant predicting power.
Highlights
In the last few years, hadronic models, inspired by the holographic conjecture [1,2], have been widely used and developed in order to investigate nonperturbative features of glueballs and mesons, in an attempt to grasp fundamental features of QCD [3,4]
II we summarize the essence of the graviton soft wall (GSW) model [6,20,21]
A peculiarity of the GSW model, which is the reason for the name, is that the scalar glueball arises from the scalar component of the graviton and is not introduced as an independent field
Summary
In the last few years, hadronic models, inspired by the holographic conjecture [1,2], have been widely used and developed in order to investigate nonperturbative features of glueballs and mesons, in an attempt to grasp fundamental features of QCD [3,4]. The present investigation has as its starting point the holographic soft-wall (SW) model scheme, were a dilaton field is introduced to softly break conformal invariance. This procedure allows to properly reproduce the Regge trajectories of the meson spectra. To develop a unified approach where the QCD dynamics of glueballs is encoded in the modified metric, a specific dilaton, providing the correct confining mechanism for a given hadron, is constructed To this aim, a differential equation for the dilaton field is obtained, which leads to an effective phenomenological potential that produces a good description of several meson spectra. We have included three Appendixes where the determination of the dilaton equation is described in detail
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