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

International audience ; Based on the highly improved staggered quark action, we perform lattice simulations of Nf=8 QCD and confirm our previous observations, both of a flavor-singlet scalar meson (denoted as σ) as light as the pion and of various “walking signals” through the low-lying spectra, with higher statistics, smaller fermion masses mf, and larger volumes. We measure Mπ, Fπ, Mρ, Ma0, Ma1, Mb1, MN, Mσ, Fσ, ⟨ψ¯ψ⟩ (both directly and through the Gell-Mann-Oakes-Renner 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 Mπ monotonically increase in the smaller mf region towards the chiral limit similarly to Nf=4 QCD, in sharp contrast to Nf=12 QCD where the ratios become flattened. We perform fits to chiral perturbation theory, with the value of Fπ found in the chiral limit extrapolation reduced dramatically to roughly 2/3 of the previous result, suggesting the theory is much closer to the conformal window. In fact, each quantity obeys the respective hyperscaling relation throughout a more extensive mf region compared with earlier works. The hyperscaling relation holds with roughly a universal value of the anomalous dimension, γm≃1, with the notable exception of Mπ with γm≃0.6 as in the previous results, which reflects the above growing up of the ratios towards the chiral limit. This is a salient feature (walking signal) of Nf=8, unlike either Nf=4, which has no hyperscaling relation at all, or Nf=12 QCD, which exhibits universal hyperscaling. The effective γm≡γm(mf) of Mπ defined for each mf region has a tendency to grow towards unity near the chiral limit, in conformity with the Nambu-Goldstone boson nature, as opposed to the case of Nf=12 QCD where it is almost constant. We further confirm the previous observation of the light σ with mass comparable to the pion in the studied mf region. In a chiral limit extrapolation of the σ mass using the dilaton chiral perturbation ...