Chiral lagrangian from quarks with dynamical mass

Abstract

We develop a simple model for coupling the pseudo-Goldstone bosons of QCD ( π′s, K′s, η) to quark fields. This nonlocal model incorporates a momentum dependent dynamical quark mass σ( p) in a manner consistent with global chiral symmetry. Explicit current quark masses and gauge fields are also introduced. All low energy parameters of the chiral lagrangian are expressed in terms of σ( p). In particular we obtain the ten coefficients of order p 4 terms in the energy expansion. The physical values for m π 0, m K +, ƒ π , and ƒ K are used to determine the three current quark masses, the constituent quark mass, and the quark condensate. The results are in surprisingly good agreement with the experimental values.