On how to complete the Dynamical Generation of Quark-Level Linear Sigma Model like Theories beyond one Loop

TL;DR

This paper proposes a self-consistent, renormalization scheme independent method to extend the dynamical generation of Quark-Level Linear Sigma Model-like theories beyond one loop, focusing on scalar and pseudoscalar fields.

Contribution

It introduces a novel approach to complete the dynamical generation of these models beyond one loop, addressing regularization and renormalization issues.

Findings

Provides a scheme for renormalization scheme independence.

Addresses scalar and pseudoscalar degrees of freedom.

Discusses regularization methods like dimensional and implicit regularization.

Abstract

A self-consistent strategy is proposed to complete in a renormalization scheme independent way the dynamical generation of Quark-Level Linear Sigma Model like Lagrangean theories beyond one loop like the theories of strong and electroweak interactions. The present discussion refers for simplicity to scalar and pseudoscalar degrees of freedom only while disregarding yet - without loss of generality - vector and axial vector degrees of freedom. Moreover points the discussion to approximations underlying dimensional and implicit regularization as presently used.