Light flavor-singlet scalars and walking signals in $N_f=8$ QCD on the lattice

Based on the highly improved staggered quark action, we perform lattice simulations of $N_f=8$ QCD and confirm our previous observation of a flavor-singlet scalar meson (denoted as $\sigma$) as light as the pion and various "walking signals" through low-lying spectra, with higher statistics, smaller fermion masses $m_f$, and larger volumes. We measure $M_\pi$, $F_\pi$, $M_\rho$, $M_{a_0}$, $M_{a_1}$, $M_{b_1}$, $M_N$, $M_\sigma$, $F_\sigma$, $\langle \bar{\psi} \psi\rangle$ (both directly and through the GMOR relation), and the string tension. The data are consistent with the spontaneously broken phase of the chiral symmetry, in agreement with the previous results: ratios of the quantities to $M_\pi$ monotonically increase in the smaller $m_f$ region towards the chiral limit similarly to $N_f=4$ QCD, in sharp contrast to $N_f=12$ QCD where the ratios become flattened. The hyperscaling relation holds with roughly a universal value of the anomalous dimension, $\gamma_m \simeq 1$, with a notable exception of $M_\pi$ with $\gamma_m \simeq 0.6$ as in the previous results. This is a salient feature ("walking signal") of $N_f=8$, unlike either $N_f=4$ which has no hyperscaling relation at all, or $N_f=12$ QCD which exhibits universal hyperscaling. We further confirm the previous observation of the light $\sigma$ with mass comparable to the pion in the studied $m_f$ region. In a chiral limit extrapolation of the $\sigma$ mass using the dilaton chiral perturbation theory and also using the simple linear fit, we find the value consistent with the 125 GeV Higgs boson within errors. Our results suggest that the theory could be a good candidate for walking technicolor model, having anomalous dimension $\gamma_m \simeq 1$ and a light flavor-singlet scalar meson as a technidilaton, which can be identified with the 125 GeV composite Higgs in $N_f=8$ one-family model.