Schematic model for QCD. I. Low energy meson states

Abstract

A simple model for QCD is presented, which is able to reproduce the meson spectrum at low energy. The model is a Lipkin type model for quarks coupled to gluons. The basic building blocks are pairs of quark-antiquarks coupled to a definite flavor and spin. These pairs are coupled to pairs of gluons with spin zero. The multiplicity problem, which dictates that a given experimental state can be described in various manners, is removed when a particle-mixing interaction is turned on. In this first paper of a series we concentrates on the discussion of meson states at low energy, the so-called zero temperature limit of the theory. The treatment of baryonic states is indicated, also.

Mean-field description of high-spin states

“…It appears that for some cases the high-j intruder orbital contributes with a 'quantized' alignment, where however the polarization contribution from the core is not taken into account. Also, in the mass A = 80 region, cases have been reported that do not fit at all into the pseudo-oscillator scheme, where the occupation of the unique parity orbital plays a role [170].…”

The Power of Symmetries in Nuclear Structure and Some of Its Problems

“…In [31], an effective algebraic Hamiltonian of QCD, for hadrons in general, was proposed and in [31][32][33] applied to describe hadron excitations, including gluons. Moreover, thermal excitations were considered in order to describe the physics of the Quark-Gluon Plasma, with quite a good agreement to the production of hadrons during the hadronization process.…”

“…In [34], the catastrophe theory [35] was applied to a pure system of gluons in order to describe the phase transition from a non-interactive gluon system to a system of interactive gluons, which should describe the real physical state. As a Hamiltonian, the one of [31,32] was used. It was found that the transition is of first order.…”

“…The most general Hamiltonian is just a function of the generators, i.e., the Hamiltonian also has to conserve the total number of bosons in the valence shell. However, there is a special class of Hamiltonians which are glued to each of the group chains in (32). To each group appearing in (32), there belong Casimir operators and the most general Hamiltonian can also be expressed in terms of functions in these Casimir operators.…”

“…However, there is a special class of Hamiltonians which are glued to each of the group chains in (32). To each group appearing in (32), there belong Casimir operators and the most general Hamiltonian can also be expressed in terms of functions in these Casimir operators. However, when a Hamiltonian is only a function of Casimir operators within one group chain, this Hamiltonian is said to have a dynamical symmetry.…”