Abstract
We present our lattice studies of SU(3) gauge theory with $N_f$ = 8 degenerate fermions in the fundamental representation. Using nHYP-smeared staggered fermions we study finite-temperature transitions on lattice volumes as large as $L^3 \times N_t = 48^3 \times 24$, and the zero-temperature composite spectrum on lattice volumes up to $64^3 \times 128$. The spectrum indirectly indicates spontaneous chiral symmetry breaking, but finite-temperature transitions with fixed $N_t \leq 24$ enter a strongly coupled lattice phase as the fermion mass decreases, which prevents a direct confirmation of spontaneous chiral symmetry breaking in the chiral limit. In addition to the connected spectrum we focus on the lightest flavor-singlet scalar particle. We find it to be degenerate with the pseudo-Goldstone states down to the lightest masses reached so far by non-perturbative lattice calculations. Using the same lattice approach, we study the behavior of the composite spectrum when the number of light fermions is changed from eight to four. A heavy flavor-singlet scalar in the 4-flavor theory affirms the contrast between QCD-like dynamics and the low-energy behavior of the 8-flavor theory.
Highlights
The discovery of a Higgs particle at the Large Hadron Collider (LHC) [1,2] was a major step towards the longstanding goal of determining the mechanism of electroweak symmetry breaking
On most ensembles it is degenerate with the pion within our uncertainty; in all cases, in the range of fermion masses we study both σ and π are much lighter than the heaviest hadron, which is the ρ meson
The presence of a light, unflavored stable scalar meson σ in the spectrum of the SU(3) Nf 1⁄4 8 theory which is approximately degenerate with the pseudo-Nambu–Goldstone bosons (PNGBs) π when Mπ=Mρ < 0.5 is perhaps the most dramatic difference between this theory and QCD where Mπ=Mρ ≈ 0.2 and the lightest f0 meson is a broad, unstable resonance well above decay threshold [24]
Summary
The discovery of a Higgs particle at the Large Hadron Collider (LHC) [1,2] was a major step towards the longstanding goal of determining the mechanism of electroweak symmetry breaking. 8-flavor theory in order to learn more about its lowenergy dynamics and relate it to phenomenological model building These investigations employ a wide variety of methods, including the computation of the running coupling and its discrete β function [26,27,33,34], exploration of the phase diagram through calculations at finite temperature [35,36,37,38,39,40,41], analysis of hadron masses and decay constants [11,14, 19,20,21,28,30,31,32,42,43,44,45], study of the eigenmodes of the Dirac operator [29,42,43,44,46], and more [47,48,49,50,51,52,53,54,55]. In the Appendices we provide additional information about autocorrelations and topological charge evolution, more technical details about fitting correlation functions for the flavor-singlet scalar, and studies of finite-volume and discretization effects
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