Pion Chiral Symmetry Breaking in the Quark-Level Linear Sigma Model and Chiral Perturbation Theory

Abstract

Chiral symmetry breaking (ChSB) is reviewed to some extent within the quark-level-linear-sigma-model (QLL$σ$M) theory and standard chiral perturbation theory (ChPT). It is shown, on the basis of several examples related to the pion, as a well-known Goldstone boson of chiral symmetry breaking, that even the non-unitarized QLL$σ$M approach accounts, to a good approximation, for a rather simple, self-consistent, linear, and very predictive description of Nature. On the other hand, ChPT -- even when unitarized -- provides a highly distorted, nonlinear, hardly predictive picture of Nature, which fits experiment only at the price of a lot of parameters, and requires a great deal of unnecessary theoretical effort. As the origin of this distortion, we identify the fact that ChPT, reflecting only direct ChSB by nonvanishing, current-quark-mass values, does not -- contrary to Quantum Chromodynamics (QCD) and the QLL$σ$M -- contain any mechanism for the spontaneous generation of the dynamical component of the constituent quark mass. This leads to a very peculiar picture of Nature, since the strange current quark mass has to compensate for the absence of nonstrange dynamical quark masses. We thus conclude that standard ChPT -- contrary to common wisdom -- is unlikely to be the low-energy limit of QCD. On the contrary, a chiral perturbation theory derived from the QLL$σ$M, presumably being the true low-energy limit of QCD, is expected instead to provide a distortion-free description of Nature, which is based on the heavy standard-model Higgs boson as well as light scalar mesons, as the source of spontaneous generation of current and dynamical quark masses, respectively.