Scattering of scalar and tensor glueballs

Abstract

The scalar glueball, the lightest state in the gluonic Yang-Mills (YM) sector of QCD, is stable in that framework. The scattering of two scalar glueballs is therefore a well defined process in YM, which can be studied with the tools of quantum field theory and partial wave analysis. By using a dilaton Lagrangian, which contains a single dimensionful parameter $\Lambda_G$, in the context of proper unitarization procedures, we find that a bound state is expected to form in the $S$-wave if $\Lambda_G$ is below a certain critical value. Additionally, we also evaluate the impact of a cutoff function on the obtained results and we discuss possible future comparison of our model with Lattice QCD and, eventually, with experimental searches. We show that the expansion into partial wave can also be useful (together with the covariant helicity formalism) in the study of decays of mesons. This method allows us to describe the ratio between two different waves in the same decays. We use this information to describe decay widths and other relevant quantities. Moreover, we show that the results obtained using the covariant helicity formalism do not change when rotating the reference frame centered in the decaying particle. In this way, an alternative calculation scheme is presented. Finally, we use the so-called Glueball Resonance Gas (GRG) model to describe the thermal properties of YM below the critical temperature for deconfinement. The quantities obtained from this model (such as the pressure) can be compared with those obtained from lattice works. The contribution of heavier glueballs and the interaction between scalar and tensor glueballs turns out to be rather small. Within this context, the scattering of two tensor glueballs, required to estimate its contribution in the GRG model, is investigated in detail.