Physics of the light quarks

TL;DR

This paper reviews recent advances in understanding low-energy QCD, highlighting experimental confirmations, discrepancies suggesting new physics, and improvements in theoretical methods for analyzing resonances.

Contribution

It introduces an exact formula for resonance parameters and discusses the limitations of resonance saturation estimates, advancing the theoretical framework of low-energy QCD.

Findings

Experimental results largely confirm Chiral Perturbation Theory

A discrepancy in Kmu3 decay suggests potential new physics

An exact formula for resonance mass and width improves analysis

Abstract

These lecture notes concern recent developments in our understanding of the low energy properties of QCD. Significant progress has been made on the lattice and the beautiful experimental results on the Ke4 and K->3pi decays, as well as those on pionic atoms also confirm the results obtained on the basis of Chiral Perturbation Theory. There is an exception: one of the precision experiments on Kmu3 decay is in flat contradiction with the Callan-Treiman relation. If confirmed, this would indicate physics beyond the Standard Model: right-handed quark couplings of the W-boson, for instance. Furthermore, I discuss two examples where the estimates of the effective coupling constants based on saturation by resonances appear to fail. In the second part, the progress made in extending the range of validity of the effective theory with dispersive methods is reviewed. In particular, I draw attention to an exact formula, which expresses the mass and width of a resonance 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 associated with broad resonances. In particular, it can now be demonstrated that the lowest resonance of QCD carries the quantum numbers of the vacuum.