On the low energy end of the QCD spectrum

TL;DR

This paper reviews the current understanding of the QCD energy spectrum, emphasizing the low-energy structure, the limitations of chiral perturbation theory, and recent advances in dispersive methods for analyzing resonances.

Contribution

It discusses the status of chiral expansions in the strange quark mass and introduces dispersive techniques for more reliable resonance analysis in QCD.

Findings

Lattice results on quark condensate violations are inconsistent.

Dispersive methods can extend the validity of chiral perturbation theory.

An exact formula for resonance parameters improves previous determinations.

Abstract

The energy gap of QCD is now understood very well. There is no doubt that the expansion in powers of the two lightest quark masses does represent a very useful tool for the analysis of the low energy structure. Concerning the expansion in powers of m_s, however, the current situation leaves much to be desired. While some of the lattice results indicate, for instance, that the violations of the Okubo-Iizuka-Zweig rule in the quark condensate and in the decay constants are rather modest, others point in the opposite direction. I am confident that the dust will settle soon, so that the effective coupling constants that govern the dependence of the various quantities of physical interest on m_s can be determined, to next-to-next-to-leading order of the chiral expansion. The range of validity of ChPT can be extended by means of dispersive methods. The properties of the physical states occurring in the spectrum of QCD below KKbar threshold can reliably be investigated on this basis. In particular, as shown only rather recently, general principles of quantum field theory lead to an exact formula that expresses the mass and width of resonances in terms of observable quantities. The formula removes the ambiguities inherent in the analytic continuation from the real axis into the complex plane, which plagued previous determinations of the pole positions of broad resonances.