Pions: Experimental Tests of Chiral Symmetry Breaking

TL;DR

This paper reviews experimental and lattice QCD tests of chiral symmetry breaking predictions, focusing on low-energy pion interactions, properties, and the validation of chiral perturbation theory in the confinement scale regime.

Contribution

It provides a comprehensive overview of recent experimental and lattice results confirming chiral perturbation theory predictions and explores new tests of confinement scale QCD in pion interactions.

Findings

Good agreement between experiment and ChPT for scattering lengths and pion lifetime.

Lattice calculations support ChPT predictions for the $ar{ ext{N}}$ $ ext{σ}$ term and strange quark contributions.

Recent pionic atom data align with chiral calculations when isospin breaking is included.

Abstract

Based on the spontaneous breaking of chiral symmetry, chiral perturbation theory (ChPT) is believed to approximate confinement scale QCD. Dedicated and increasingly accurate experiments and improving lattice calculations are confirming this belief, and we are entering a new era in which we can test confinement scale QCD in some well chosen reactions. This is demonstrated with an overview of low energy experimental tests of ChPT predictions of $\pi\pi$ scattering, pion properties, $\pi$N scattering and electromagnetic pion production. These predictions have been shown to be consistent with QCD in the meson sector by increasingly accurate lattice calculations. At present there is good agreement between experiment and ChPT calculations, including the $\pi\pi$ and $\pi$N s wave scattering lengths and the $\pi^{0}$ lifetime. Recent, accurate pionic atom data are in agreement with chiral calculations once isospin breaking effects due to the mass difference of the up and down quarks are taken into account, as was required to extract the $\pi\pi$ scattering lengths. In addition to tests of the theory, comparisons between $\pi\pi$ and $\pi$N interactions based on general chiral principles are discussed. Lattice calculations are now providing results for the fundamental, long and inconclusively studied, $\pi$N $\sigma$ term and the contribution of the strange quark to the mass of the proton. Increasingly accurate experiments in electromagnetic pion production experiments from the proton which test ChPT calculations (and their energy region of validity) are presented. These experiments are also beginning to measure the final state $\pi$N interaction. This paper is based on the concluding remarks made at the Chiral Dynamics Workshop CD12 held at Jefferson Lab in Aug. 2012.