Renormalization group equations in resonance chiral theory

TL;DR

This paper simplifies resonance chiral theory using equations of motion and field redefinitions, computes the pion form-factor, and explores the renormalization group flow revealing an infrared fixed point.

Contribution

It introduces a simplified resonance chiral Lagrangian framework and analyzes its renormalization group equations, highlighting the fixed point structure and perturbative expansion viability.

Findings

Existence of an infrared fixed point in resonance theory

Simplification of the Lagrangian to O(p^2) operators

Potential for perturbative 1/Nc expansion near the fixed point

Abstract

The use of the equations of motion and meson field redefinitions allows the development of a simplified resonance chiral theory lagrangian: terms including resonance fields and a large number of derivatives can be reduced into corresponding O(p2) resonance operators, containing the lowest possible number of derivatives. This is shown by means of the explicit computation of the pion vector form-factor up to next-to-leading order in 1/Nc. The study of the renormalization group equations for the corresponding couplings demonstrates the existence of an infrared fixed point in the resonance theory. The possibility of developing a perturbative 1/Nc expansion in the slow running region around the fixed point is shown here.