Chiral symmetry and Heun's equation

TL;DR

This paper demonstrates that in a bag model consistent with QCD confinement, the quark mass must be zero, linking chiral symmetry to confinement through the mathematical structure of Heun's equation and quantization conditions.

Contribution

It shows that the hadron spectrum aligns with Regge trajectories only when the quark mass vanishes, establishing a connection between chiral symmetry and confinement.

Findings

Quark mass must vanish for spectrum consistency.

Heun's equation arises naturally in the confinement model.

Quantization of energy and string tension is required.

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.