Effective-potential study of dynamical chiral symmetry breaking in quantum chromodynamics

Starting from the QCD lagrangian with massless fermions and using the bilinear external sources, the effective potential as a functional of composite operators, i.e., functional of fermion propagator and gluon propagator, and the Dyson-Schwinger equation for the propagators are derived. There exist two sets of solution, the chiral-symmetry solution and chiral-breaking solution. By studying on the asympotic solution of equation, it is found that for the coupling constant beyond a critical value (α = 1/4), a chiral-breaking solution is found, while for α < 1/4 the chiral-symmetry conserves. Using the asympotic behavior of the quark self-energy and the experimantal value for π ion decay constant fπ, the dynamical generated quark mass value is estimated, which is in agreement with the values obtained from other theoretical and experimental methods. Significance of the results are discussed