Axial U(1) symmetry at finite temperature with Mobius domain-wall fermions

Abstract

We investigate the axial U(1) symmetry restoration at finite temperature in two flavor QCD. We employ the Möbius domain-wall formalism that is designed to achieve good chiral symmetry. We show the measurements of a difference of meson susceptibilities, sensitive to the U(1) A symmetry breaking. The signal is dominated by zero and near-zero modes. By reweighting the measure to that of overlap fermions we find a suppression of the U(1) A breaking effects above the chiral transition temperature.

On the strength of the U A (1) anomaly at the chiral phase transition in N f = 2 QCD

“…the results labeled by ∆M XY . The persistent mass splitting in P and S channels implies a residual breaking of U A (1) around T C in agreement with what has been found with staggered [89], domain wall [10,11,107] and overlap [38,39] fermion formulations. To make any statement about the fate and strength of the breaking in the chiral limit, however, we still need to perform Table 5.…”

“…When looking at the domain wall fermion results [10,11] for chiral susceptibilities, one might be led to the conclusion that the breaking is significant in the chiral limit. The same is true if one looks at the eigenvalues of the associated Dirac operator [107]. However, the chiral susceptibilities include contributions from contact terms which might give an additional contribution that overwhelms the effect of chiral symmetry breaking.…”

Finite Temperature ($\mu=0$)

“…The JLQCD collaboration studied the spectrum of the Dirac operator with the Möbius domain-wall and overlap fermions [35,36]. The results seem to support their earlier findings [37] that ρ(λ ) starts with cubic powers of λ and when the chiral symmetry is restored, the χ π − χ δ difference becomes insensitive to the axial symmetry breaking, and that the axial symmetry may be effectively restored close to T c .…”

U (1) axial symmetry and Dirac spectra in QCD at high temperature

“…Recently, the Dirac spectrum in two-flavor QCD at T T c has been studied intensively in lattice QCD simulations [16,17,24,25] (see also [14,15,[35][36][37][38][39] for early works). The three possibilities R 1 (λ) ∼ m, λ, and m 2 δ(λ) were examined in detail in [17,25], whereas the Breit-Wigner form R 1 (λ) ∼ ρ 0 A/(λ 2 + A 2 ) was nicely fitted to the lattice data in [24,40] (but see [19,20,41,42] for detailed investigations of lattice artifacts stemming from partial reweighting). The δ form is motivated by the dilute instanton gas picture [12] in QCD at T → ∞, but the exact δ form is unlikely to emerge at T T c due to the overlap of neighboring instantons and anti-instantons.…”

“…Alongside these theoretical studies, the U(1) A problem at finite temperature has also been studied intensively in first-principles lattice QCD simulations [14,15], but a consensus is not reached yet: effective restoration of the U(1) A symmetry was reported in simulations with overlap fermions [16] and domain-wall fermions [17][18][19][20], whereas a violation of the U(1) A symmetry was reported in simulations using staggered fermions [21][22][23][24] and domainwall fermions [25]. 2 We warn that some of the simulations [17,[21][22][23][24][25] were performed for 2 + 1 flavors; the effect of a heavier strange quark on the possible U(1) A violation in the light-quark sector is not completely clear yet.…”