Low-energy meson action from QCD: Extended Skyrme model

Abstract

In the limit of extremely low energies QCD describes essentially the interactions between the approximately massless pseudoscalars. They are the bound states of the ‘‘chiral’’ quarks. Equivalently they are collective Goldstone modes of dynamically broken chiral symmetry, and interact in a nonlinear way with the ‘‘constituent’’ quarks. These two pictures are related by going into the ‘‘constituent gauge,’’ which we define in this paper as a QCD analog of the unitary gauge in theories with Higgs scalars. We develop a framework for extracting the low-energy dynamics of pions directly from QCD in the limit of a large number of colors, and under some additional assumptions we calculate the pure pion theory truncated to four derivatives. The model obtained is a somewhat extended Skyrme model, and contains the anomaly term (Wess-Zumino term) as well as the nontopological terms, the coefficients of which depend on a classical scalar-meson-field background. Stability of the soliton is discussed. We show that in the limit in which symmetry breaking is turned off, the coefficients in front of the pseudoscalar interactions vanish. Under a plausible assumption about the behavior of a scalar-meson background, we interpret this as a natural realization of the space cutoff entering the topological soliton bag model.