Inexistence of quark mass in chiral symmetry and its relation to confinement dynamics

In 1985, G"ursey showed that the spectrum of the semi-relativistic Hamiltonian for the bag model, introduced by Lichtenberg et al. for mesons, follows the Regge trajectory if the current quark mass is negligible. The model leads to the biconfluent Heun equation, which is a second-order linear ordinary differential equation (ODE) with a regular singularity at the origin and an irregular singularity at infinity. Based on rigorous mathematical computation, it is concluded that the energy spectrum is consistent with the Regge trajectory only when the quark mass vanishes. From this result, we suggest that the chiral symmetry is a consequence of confinement dynamics.