Glueballs are particles whose valence degrees of freedom are gluons and therefore in their description the gauge field plays a dominant role. We review recent results in the physics of glueballs with the aim set on phenomenology and discuss the possibility of finding them in conventional hadronic experiments and in the Quark Gluon Plasma. In order to describe their properties we resort to a variety of theoretical treatments which include, lattice QCD, constituent models, AdS/QCD methods, and QCD sum rules. The review is supposed to be an informed guide to the literature. Therefore, we do not discuss in detail technical developments but refer the reader to the appropriate references.
The gauge invariant generation of an effective gluon mass proceeds through the well-known Schwinger mechanism, whose key dynamical ingredient is the nonperturbative formation of longitudinally coupled massless bound-state excitations. These excitations introduce poles in the vertices of the theory, in such a way as to maintain the Slavnov-Taylor identities intact in the presence of massive gluon propagators. In the present work we first focus on the modifications induced to the nonperturbative three-gluon vertex by the inclusion of massless two-gluon bound-states into the kernels appearing in its skeleton-expansion. Certain general relations between the basic build-
Further progress in hadron spectroscopy necessitates the phenomenological description of three particle reactions. We consider the isobar approximation, where the connected part of the 3 → 3 amplitude is first expressed as a sum over initial and final pairs, and then expanded into a truncated partial wave series. The resulting unitarity equation is automatically fulfilled by the B-matrix solution, which is an integral equation for the partial wave amplitudes, analogous to the K-matrix parameterization used to describe 2 → 2 amplitudes. We study the one particle exchange and how its analytic structure impacts rescattering solutions such as the triangle diagram. The analytic structure is compared to other parameterizations discussed in the literature. We briefly discuss the analogies with recent formalisms for extracting 3 → 3 scattering amplitudes in lattice QCD.
In the last decade, lattice QCD has been able to compute the low-lying glueball spectrum with accuracy. Like other effective approaches of QCD, potential models still have difficulties to cope with gluonic hadrons. Assuming that glueballs are bound states of valence gluons with zero current mass, it is readily understood that the use of a potential model, intrinsically non covariant, could be problematic in this case. The main challenge for this kind of model is actually to find a way to introduce properly the more relevant degree of freedom of the gluon: spin or helicity. In this work, we use the so-called helicity formalism of Jacob and Wick to describe two-gluon glueballs. We show in particular that this helicity formalism exactly reproduces the J P C numbers which are observed in lattice QCD when the constituent gluons have a helicity-1, without introducing extra states as it is the case in most of the potential models. These extra states appear when gluons are seen as spin-1 particles. Using a simple spinless Salpeter model with Cornell potential within the helicity formalism, we obtain a glueball mass spectrum which is in good agreement with lattice QCD predictions for helicity-1 gluons provided instanton-induced interactions are taken into account.
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