0 mass difference and S parameter in the large N f QCD ∗

In the framework of the Schwinger-Dyson equation and the Bethe-Salpeter equation in the improved ladder approximation, we calculate the S parameter and an analogue of the π+ − π0 mass difference ∆mπ ≡ mπ+ −mπ0 as well as the NG boson decay constant fπ on the same footing in the large Nf QCD, through the difference between the vector current correlator ΠV V and the axialvector current correlator ΠAA. Approaching the chiral phase transition point α∗ → αcr(= π/4) from the broken phase, where α∗ is the the gauge coupling on the infrared fixed point, ∆mπ as well as f 2 π goes to zero with the essentialsingularity scaling (Miransky scaling), while the ratio indicates a blowing up enhancement reflecting the characteristic behavior of the large Nf QCD as a walking theory which is expected to scale as ∆mπ/f 2 π ∼ (α∗/αcr − 1) . On the other hand, the S parameter takes values somewhat smaller than that of the real-life QCD and indicates slightly decreasing tendency as we approach the phase transition point. A preliminary report [1] was given at the 2004 International Workshop on Dynamical Symmetry Breaking (DSB04), December 21-22, 2004, Nagoya Univeristy, Nagoya. Present address