Quark self energy and relativistic flux tube model

Abstract

The contribution of the quark self energy to the meson masses is studied in the framework of the relativistic flux tube model. The equivalence between this phenomenological model and the more QCD based rotating string Hamiltonian is used as a guide to perform the calculations. It is shown that the addition of the quark self energy to the relativistic flux tube model preserves the linearity of the Regge trajectories. But, following the definition taken for the constituent quark masses, the Regge slope is preserved or decreased. In this last case, experimental data can only by reproduced by using a string tension around $0.245\text{ }\text{ }{\mathrm{G}\mathrm{e}\mathrm{V}}^{2}$. Two procedures are also studied to treat the pure flux tube contribution as a perturbation of a spinless Salpeter Hamiltonian.