QCD S parameter from inhomogeneous Bethe-Salpeter equation

We calculate the low-energy parameters S in QCD, which is also known as L10, and the pion decay constant fπ using the inhomogeneous Bethe-Salpeter equation in the improved ladder approximation. To extract these quantities we calculate the ''V-A'' two-point function ΠVV(q2)-ΠAA(q2) in the spacelike region. We obtain S=0.43--0.48, which is about 30% larger than the experimental value. The calculated fπ is quite consistent with the result by solving the homogeneous Bethe-Salpeter equation for the pion. We also evaluate the S parameter in SU(3) gauge theory with ND doublets of fermions in connection with the walking technicolor model, and find that the value of S/ND hardly depends on ND