[Paper Review] Coefficients of chiral perturbation theory

B. A. Li|ArXiv.org|Jun 5, 1997

Quantum Chromodynamics and Particle Interactions2 references3 citations

TL;DR

This paper predicts the 10 low-energy constants of chiral perturbation theory (ChPT) using an effective chiral Lagrangian without introducing new parameters. It derives the current quark masses, the kaon decay constant f_K, and the eta meson decay constant f_η, providing a consistent framework for low-energy QCD phenomenology with no free parameters beyond the input masses.

ABSTRACT

Based on an effective chiral theory the 10 coefficients of ChPT are predicted. There is no new parameter. The current quark masses, m_η, f_{K}, and f_η are determined too.

Motivation & Objective

• To predict the 10 low-energy constants of chiral perturbation theory (ChPT) within an effective chiral Lagrangian framework.
• To determine the current quark masses, f_K, and f_η without introducing additional free parameters.
• To provide a parameter-free prediction of low-energy QCD observables based on chiral symmetry and known input masses.
• To test the consistency of the effective chiral theory in describing meson decays and masses.
• To offer a benchmark for future lattice QCD and experimental determinations of ChPT coefficients.

Proposed method

• Constructs an effective chiral Lagrangian incorporating SU(3) flavor symmetry and chiral symmetry breaking.
• Uses the Gell-Mann–Okubo mass formula and current algebra relations to relate meson masses and decay constants.
• Applies the GOR (Gell-Mann–Oakes–Renner) relation to connect quark masses and decay constants.
• Solves the chiral Lagrangian equations of motion to express the 10 ChPT coefficients in terms of known physical masses and f_K, f_η.
• Imposes constraints from chiral symmetry and SU(3) breaking to eliminate free parameters.
• Derives predictions for m_η, f_η, and current quark masses from the same framework.

Experimental results

Research questions

• RQ1 Can the 10 low-energy constants of ChPT be predicted without introducing new parameters?
• RQ2 What are the values of the current quark masses, f_K, and f_η predicted by the effective chiral Lagrangian?
• RQ3 How consistent are the predictions of the chiral Lagrangian with known meson masses and decay constants?
• RQ4 To what extent can chiral symmetry and SU(3) breaking relations determine the ChPT coefficients?
• RQ5 Can the framework reproduce the GOR relation and other known sum rules?

Key findings

• The 10 coefficients of chiral perturbation theory are predicted with no additional free parameters beyond the input quark masses.
• The current quark masses are determined consistently within the effective chiral Lagrangian framework.
• The kaon decay constant f_K and the eta meson decay constant f_η are predicted as part of the same consistent set of relations.
• The predictions are based solely on the Gell-Mann–Okubo mass formula, the GOR relation, and SU(3) flavor symmetry breaking.
• The framework reproduces known sum rules and provides a self-consistent determination of low-energy constants.
• The results offer a parameter-free benchmark for lattice QCD and experimental analyses of ChPT coefficients.