The + - 0 Mass Difference and the S Parameter in Large Nf QCD

In the framework of the Schwinger-Dyson equation and the Bethe-Salpeterequation in the improved ladder approximation, we calculate the S parameter andan analogue of the \pi^+ - \pi^0 mass difference \Delta m_\pi^2 \equivm_{\pi^+}^2 -m_{\pi^0}^2 as well as the NG boson decay constant f_\pi on thesame footing in the large N_f QCD, through the difference between the vectorcurrent correlator \Pi_{VV} and the axial-vector current correlator \Pi_{AA}.Approaching the chiral phase transition point \alpha_*\to \alpha_{\rm cr}(=\pi/4) from the broken phase, where \alpha_* is the the gauge coupling on theinfrared fixed point, \Delta m_\pi^2 as well as f_\pi^2 goes to zero with theessential-singularity scaling (Miransky scaling), while the ratio indicates ablowing up enhancement reflecting the characteristic behavior of the large N_fQCD as a walking theory which is expected to scale as \Delta m_\pi^2/f_\pi^2\sim (\alpha_*/\alpha_{\rm cr}-1)^{-1/2}. On the other hand, the S parametertakes values somewhat smaller than that of the real-life QCD and indicatesslightly decreasing tendency as we approach the phase transition point.Comment: Change of title & abstract, new reference, new discussions on ultraviolet contributions from outside of those explicitly calculated. 32 pages, 12 figure