2026/02/16 by Ting-Wai Chiu, Tung-Han Hsieh · 2 citations
#hep-lat #hep-ph
We introduce a renormalization-group-invariant (RGI), scheme-independent symmetry ratio κAB, for the quantitative characterization of symmetry breaking in QCD. As a first application, we employ κAB to investigate the relative strength of SU(2)L × SU(2)R chiral symmetry and U(1)A axial symmetry breaking in Nf=2+1+1 lattice QCD using optimal domain-wall fermions at the physical point. Our study covers three lattice spacings and twelve temperatures in the range 164--385~MeV. We examine three independent symmetry-breaking channels in the nonsinglet sector with quark-connected correlators: the U(1)A-sensitive scalar--pseudoscalar channel (κPS), probing the π--δ system; the SU(2)L × SU(2)R-sensitive vector--axial-vector channel (κVA), probing the ρ--a1 system; and an additional U(1)A-sensitive tensor vector--axial-tensor vector channel (κTX), probing the ρT--b1 system. At finite lattice spacing, we observe a clear hierarchy κPS > κVA > κTX. A controlled continuum extrapolation reveals that this hierarchy collapses, with all three symmetry-breaking strengths becoming statistically indistinguishable within our precision. This result provides a new, model-independent benchmark from a chirally symmetric lattice action. Our findings indicate that in the continuum limit the SU(2)L × SU(2)R and U(1)A channels in the nonsinglet sector reach degeneracy at the same temperature, already at the lowest simulated point of 164~MeV, so that the two symmetries restore concurrently near the chiral crossover rather than at parametrically separated scales.