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

Abstract : 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 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 γm≃1 and a light flavor-singlet scalar meson as a technidilaton, which can be identified with the 125 GeV composite Higgs in the Nf=8 one-family model.
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Physical Review D, American Physical Society, 2017, 96 (1), pp.014508. 〈10.1103/PhysRevD.96.014508〉
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Yasumichi Aoki, Tatsumi Aoyama, Ed Bennett, Masafumi Kurachi, Toshihide Maskawa, et al.. Light flavor-singlet scalars and walking signals in $N_f=8$ QCD on the lattice. Physical Review D, American Physical Society, 2017, 96 (1), pp.014508. 〈10.1103/PhysRevD.96.014508〉. 〈hal-01582744〉

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