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

摘要

Chiral symmetry breaking (ChSB) is reviewed to some extent within thequark-level-linear-sigma-model (QLL$\sigma$M) theory and standard chiralperturbation theory (ChPT). It is shown, on the basis of several examplesrelated to the pion, as a well-known Goldstone boson of chiral symmetrybreaking, that even the non-unitarized QLL$\sigma$M approach accounts, to agood approximation, for a rather simple, self-consistent, linear, and verypredictive description of Nature. On the other hand, ChPT -- even whenunitarized -- provides a highly distorted, nonlinear, hardly predictive pictureof Nature, which fits experiment only at the price of a lot of parameters, andrequires a great deal of unnecessary theoretical effort. As the origin of thisdistortion, we identify the fact that ChPT, reflecting only direct ChSB bynonvanishing, current-quark-mass values, does not -- contrary to QuantumChromodynamics (QCD) and the QLL$\sigma$M -- contain any mechanism for thespontaneous generation of the dynamical component of the constituent quarkmass. This leads to a very peculiar picture of Nature, since the strangecurrent quark mass has to compensate for the absence of nonstrange dynamicalquark 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 chiralperturbation theory derived from the QLL$\sigma$M, presumably being the truelow-energy limit of QCD, is expected instead to provide a distortion-freedescription of Nature, which is based on the heavy standard-model Higgs bosonas well as light scalar mesons, as the source of spontaneous generation ofcurrent and dynamical quark masses, respectively.