The Peskin-Takeuchi $S$ parameter and vector meson decay constants in $N_f=8$ QCD

Abstract

We use lattice gauge theory to investigate the Peskin-Takeuchi S parameter in SU(3) gauge theory with eight light fundamental fermions (eight-flavor QCD), a candidate for walking technicolor. We develop a new approach to computing S using the first time moment of current correlators, in addition to the conventional vacuum-polarization method, and obtain consistent results. Finite-volume (FV) corrections are estimated using data at multiple lattice volumes and a formula motivated by chiral perturbation theory. At the smallest fermion mass, the one-doublet contribution is S = 0.281(5)(17), smaller than the value $\sim 0.35$ in scaled-up 2+1-flavor QCD (without subtracting the SM contribution). However, contrary to naive expectations, S toward smaller fermion masses is not necessarily suppressed once FV corrections are included. The resulting Gasser-Leutwyler parameter $L_{10}^r(M_ρ)$ is similar to that in real-world QCD. We also determine the vector and axial-vector meson decay constants, $F_ρ$ and $F_{a_1}$. The ratio $F_ρ/F_π$ is stable against the fermion mass and consistent with the KSRF estimate, implying a $ρππ$ coupling similar to that in real-world QCD. We predict the techni-rho decay width into weak bosons to be $Γ_ρ/M_ρ\lesssim 0.24/N$, where N is the number of weak doublets. We further find that the rho- and $a_1$-dominated Weinberg spectral-function and Das-Mathur-Okubo sum rules are satisfied, yielding S and $L_{10}^r(M_ρ)$ consistent with our main results. We discuss implications for BSM model building.