Evidence of effective axialU(1)symmetry restoration at high temperature QCD

Abstract

We study the axial U (1) symmetry at finite temperature in two-flavor lattice QCD. Employing the Möbius domain-wall fermions, we generate gauge configurations slightly above the critical temperature T c with different lattice sizes L = 2-4 fm. Our action allows frequent topology tunneling while keeping good chiral symmetry close enough to that of overlap fermions. This allows us to recover full chiral symmetry by an overlap/domain-wall reweighting. Above the phase transition, a strong suppression of the low-lying modes is observed in both of overlap and domainwall Dirac spectra. We, however, find a sizable violation of the Ginsparg-Wilson relation in the Möbius domain-wall Dirac eigenmodes, which dominates the signals of the axial U (1) symmetry breaking near the chiral limit. We also find that the use of overlap fermion only in the valence sector is dangerous since it suffers from the artifacts due to partial quenching. Reweighting the Möbius domain-wall fermion determinant to that of the overlap fermion, we observe the axial U (1) breaking to vanish in the chiral limit, which is stable against the changes of the lattice volume and lattice spacing.2

Patterns and partners for chiral symmetry restoration

“…Namely, in that work, π − a 0 and other Uð1Þ A symmetry partners degenerate asymptotically, but their difference is still sizable near the point where π − σ degeneracy occurs. On the other hand, a Oð4Þ × Uð1Þ A pattern for N f ¼ 2 has been suggested in [24][25][26] near the chiral limit and in [27] for the massive case, the latter through the analysis of screening masses. Parity degeneracy in the baryon sector has also been studied in [28].…”

Mesonic and nucleon fluctuation effects at finite baryon density

“…Had we considered a general background where both M, ψ = 0 (one should think of appropriate sources that imply them), the meson and nucleon propagators would have mixed due to the Yukawa coupling. Concerning our ansatz (14), this mixing would solely be responsible for the flow of V k,N (a diagrammatical evaluation is also possible [11]), but here we do not calculate it and thus, set V k,N ≡ V Λ,N . This also means that m N,k ≡ m N and g k ≡ g (and also m 2 p/n,k ≡ m 2 p/n , accordingly).…”

“…see (14). Following the procedure of [15], and projecting the mesonic part of the flow equation (18) onto each operator, one derives evolution equations for U k (ρ 2 ), C k (ρ 2 ), A k (ρ 2 ), and H k ,…”

“…Lattice QCD results are controversial at the moment having different predictions in * fejos@rcnp.osaka-u.ac.jp † hosaka@rcnp.osaka-u.ac.jp the restoration of the U A (1) subgroup at finite temperature [12][13][14]. Concerning effective model calculations for 2 + 1 flavors, due to the melting of the chiral condensate at finite temperature, they predict a drop in the η mass around the critical temperature [9][10][11], but a common feature of these calculations is to treat the anomaly parameter without being affected by fluctuations.…”

SU(2NF) symmetry of confinement in QCD and its observation at high temperature.

“…a density of the quasi-zero modes is zero. Even more, there are clear indications from the simulations with the chirally invariant Dirac operator that above T c also U(1) A is restored and a gap opens in the Dirac spectrum [15,16]. Then, one can expect that at high temperatures not only the S U(2) L × S U(2) R × U(1) A symmetry of the QCD Lagrangian is manifest but also the S U(2) CS and S U(4) symmetries emerge with far reaching consequences [17].…”