Spontaneous symmetry breaking in QCD

We study dynamical chiral symmetry breaking in massless QCD by the use of the generalized Hartree-Fock method. As the order parameter of chiral symmetry we choose the dynamical quark mass in the zero momentum limit which we call low energy quark mass. We calculate the low energy mass to the second order of diagrammatic expansion around shifted perturbative vacuum. We then show that the mass is finite and renormalization group invariant. After the improvement of the result by the method of effective charges we estimate the mass in the true vacuum under the gap and stationarity conditions and demonstrate that both of them produce non-zero mass proportional to a conventional scale, which breaks down the chiral symmetry.