Schematic $SO$(4) model for the description of hadrons

An algebraic model is proposed which simulates the strong interaction between quarks, for the description of hadron states. The model is based on the SO(4)-group. The effects of the long-range quark–quark interactions, like zero-color confined states, symmetries and energy dependence, required for a correct description of hadrons at low energy, are considered through the assignment of SO(4)-quantum numbers to the hadron states. A simpler version of this model was used earlier to illustrate the relevance of many-body methods implemented for pseudo-scalar and vector meson-like states, particularly the low energy portion of the pion spectrum. In this work an algebraic Hamiltonian is proposed, its spectrum is calculated for several meson quantum numbers J P = 0±, 1±, 2±, as well as baryon quantum numbers , and compared to data. Our purpose is to investigate how adequate is this model when applied to the description of several characteristics of the hadron spectrum, like the observed masses, density of states and sequences of spin and parity.