QCD-based effective Lagrangian including quark mass effects: Calculation offK

Abstract

Quark mass effects are included in the construction of an effective Lagrangian with bilocal pion and kaon fields. We discuss the appropriate Schwinger-Dyson equations and the choice of pseudo- scalar particle wave functions in the presence of explicit chiral-symmetry breaking. Identifying the pseudoscalar-mass terms in the effective Lagrangian, we reproduce the standard current-algebra mass formulas for charged pions and kaons. Approximate solutions to the u-, d-, and s-quark Schwinger-Dyson equations are constructed. The low-$q^2$ region is realistically modeled and the intermediate- and large-$q^2$ regions are represented by a superposition of the well-known ‘‘spontaneous’’ and ‘‘explicit’’ breaking asymptotic QCD solutions. We couple the W-boson gauge invariantly to the dynamical quarks and derive formulas for the pion and kaon decay constants $f_{\pi }$ and $f_K$ in the one-quark-loop approximation. With $f_{\pi }$=93 MeV as input, we calculate the value $f_K$/$f_{\pi }$=1.13, compared to 1.16 experimentally, for a representative value ${\Lambda }_{\mathrm{QCD}=200\mathrm{}}$ MeV. In addition, we comment on the calculation of the pion electromagnetic form factor.