Spontaneous symmetry breaking and Goldstone theorem for composite states revisited

TL;DR

This paper revisits spontaneous symmetry breaking and Goldstone theorem in a meson composite model, providing new proofs and insights into meson wave functions and mass eigenstates.

Contribution

It offers a novel proof of the Goldstone theorem within a meson composite framework and explores meson wave functions and mass eigenstates.

Findings

Validated the Goldstone theorem in the composite meson context

Derived mass eigenstates consistent with symmetry breaking

Proposed meson wave function models

Abstract

We discuss the well-known phenomenon of spontaneous symmetry breaking for a linear sigma model for scalar and pseudoscalar mesons based on the meson composite structure and the normalization of the quantum states. To test our formulation and validate our approach we give another proof of the Goldstone theorem and derive the corresponding mass eigenstates of the theory. We briefly describe the possible wave function of a meson that leads to the adequate mass eigenstates.