Enhanced π + − π 0 mass difference and vanishing S 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 axial-vector current correlator ΠAA. Approaching the chiral phase transition point α∗ → αcr(= π/4) from the broken phase, ∆mπ as well as f2 π goes to zero with the essential-singularity scaling (Miransky scaling), while the ratio indicates a blowing up enhancement consistent with the inverse square root scaling, ∆mπ/f 2 π ∼ (α∗/αcr − 1), where α∗ is the the gauge coupling on the infrared fixed point. This enhancement is a new effect which we find is a direct consequence of the walking coupling of the large Nf QCD but has been overlooked in the discussions of the walking/conformal (scale-invariant) technicolor. On the other hand, the S parameter takes values somewhat smaller than that of the real-life QCD and indicates decreasing tendency, with ( ∆mπ/f 2 π ) · S being kept constant as we approach the phase transition point, which is consistent with a square root scaling, S ∼ (α∗/αcr − 1), implying that S parameter does vanish near the critical 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 1