Chiral symmetry and Heun's equation

Abstract

We show that the current quark mass should vanish to be consistent with the QCD color confinement: a bag model leads us to Heun's equation, which requests that not only the energy but also the string tension should be quantized. This is due to the presence of higher order singularity which requests higher regularity condition demanding that parameters of the theory should be related to one another. As a result, the Hadron spectrum is consistent with the Regge trajectory only when quark mass vanishes. Therefore, in this model, the chiral symmetry is a consequence of the confinement.