String-like solutions and regge trajectories in a cylindrically deformed quark bag model

Abstract

With the string picture in mind, we study quark bags of a simple fixed geometry: cylindrical. It is shown that the Dirac boundary value problem\(i\not n\psi = \psi\) of the M.I.T. bag model has no solutions, if this quark confinement condition is applied simultaneously on the radial walls as well as on the edges of the cylinder. By introducing a cruder condition,\(\bar \psi \psi = 0\), instead, but now only on the side walls, we calculate properties of non-strange baryons. A justification for the use of this cruder condition,\(\bar \psi \psi = 0\), on the side walls, instead of the proper M.I.T. condition, is then provided by showing that the M.I.T. “cylindrical” bag with smooth rounded corners gives essentially the same results, while being computationally more involved. Notwithstanding this departure from the M.I.T. confinement condition on the side walls, we find the following curious results: for high excitations, this bag attains string-like shapes. the sequence of baryonic states corresponding to pure single quark excitations fall on a linear Regge trajectory with a slope of ≈0.85 GeV−2. These trajectories hold at low-angular momenta.