Pith. sign in

REVIEW 4 major objections 5 minor 63 references

Symmetry of screening masses of mesons in two-flavor lattice QCD at high temperatures

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Above $T_c \approx 165$ MeV, two-flavor QCD restores chiral and axial $U(1)$ symmetry; the emergent spin symmetry stays broken.

desk verdict A clean chiral-fermion study showing SU(2)_L x SU(2)_R and U(1)_A restoration just above Tc while SU(2)_CS breaking persists at 2Tc, but the single-spacing result leaves the 40 MeV effect with an uncontrolled O(a^2) uncertainty. read the letter →

arxiv 2501.12675 v4 pith:BWBZFDAP submitted 2025-01-22 hep-lat hep-thnucl-th

Yasumichi Aoki , Hidenori Fukaya , Shoji Hashimoto , Issaku Kanamori , Yoshifumi Nakamura , Christian Rohrhofer , Kei Suzuki , David Ward This is my paper · ORCID
classification hep-lathep-thnucl-th
keywords latticeQCDscreeningmasseschiralsymmetryrestorationaxialU(1)anomalychiral-spindomain-wallfermionsfinite-temperatureMatsubaramass
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

The paper asks which symmetries of the strong interaction are restored when quarks are heated above the chiral crossover. It uses lattice QCD with a chirally symmetric fermion action to extract spatial screening masses for six iso-triplet meson channels at temperatures from 147 to 330 MeV, and compares channels that symmetry would make degenerate. The central finding is that the standard chiral symmetry $SU(2)_L \times SU(2)_R$ and the anomalous axial $U(1)_A$ are effectively restored at $T_c \approx 165$ MeV, while the emergent chiral-spin symmetry $SU(2)_{CS}$ is only approximate even at $T \approx 2T_c$, with an $A$--$X_t$ screening-mass splitting near 40 MeV, about 12% of the temperature. All channels move toward the free-quark Matsubara prediction $2\pi T$ as $T$ increases.

What carries the argument

The central objects are the spatial two-point correlators of six iso-triplet quark bilinears ($PS$, $S$, $V$, $A$, $T_t$, $X_t$). Screening masses are extracted by fitting the correlators with a $\cosh$ ansatz, and the symmetry content lives in the mass differences between symmetry-related channels: $V$--$A$ for $SU(2)_L\times SU(2)_R$, $X_t$--$T_t$ and $PS$--$S$ for $U(1)_A$, and $A$--$X_t$ for the emergent $SU(2)_{CS}$. The Möbius domain-wall fermion action keeps residual chiral breaking at $0.14(6)$ MeV, while the anti-periodic temporal boundary condition gives the Matsubara mass $\pi T$; at leading order the screening mass of every channel is predicted to be $2\pi T$, the reference line the data are compared with.

What would settle it

Measure the same screening-mass differences on a second, finer lattice spacing, such as $a\approx0.05$ fm, with the same Möbius domain-wall action at the same physical volumes; if the $A$--$X_t$ splitting at $T=330$ MeV shifts by more than several tens of MeV, or if the $V$--$A$ difference at $T=190$ MeV grows well above 10 MeV, the claimed symmetry pattern would not survive the continuum limit.

Watch

Extended reading notes

Core claim

At the lightest simulated quark mass (about 2.6 MeV), the vector and axial-vector screening masses agree to within 0.1% at $T=190$ MeV, and the axial-tensor/tensor pair as well as the pseudoscalar/scalar pair become degenerate within errors near $T_c\approx165$ MeV; the paper takes this as evidence that $SU(2)_L\times SU(2)_R$ and the effective $U(1)_A$ are restored at the critical temperature. In contrast, the difference between the $A$ and $X_t$ channels that the chiral-spin $SU(2)_{CS}$ would force to vanish is clearly nonzero at all simulated temperatures, remaining near $-40$ MeV at $T=330$ MeV, i.e., $|\Delta m_{A-X}|/T\approx 0.12$, and the paper concludes that $SU(2)_{CS}$ is only an approximate emergent symmetry in this range. The absolute masses approach the perturbative value $2\pi T$ from different directions depending on the channel, so the degeneracies set in before the free-quark limit is reached.

Load-bearing premise

The load-bearing premise is that the single lattice spacing $a\approx0.075$ fm, with residual mass $0.14(6)$ MeV, is close enough to the continuum and chiral limits that the measured 1--40 MeV mass splittings are physical; the paper states that discretization effects cannot be estimated at fixed lattice spacing.

Editorial extensions

If this is right

  • Above $T_c\approx165$ MeV the screening spectrum exhibits $SU(2)_L\times SU(2)_R$ degeneracy, so chiral restoration is directly visible in meson masses; at $T=190$ MeV and the lightest quark mass, $\Delta m_{V-A}/m_A\approx 0.1\%$.
  • The axial $U(1)_A$ is effectively restored at or close to $T_c$: the $X_t$--$T_t$ and $PS$--$S$ differences are consistent with zero within errors near $T_c$ and are below about 1 MeV at $T\approx 2T_c$.
  • The emergent chiral-spin $SU(2)_{CS}$ is only approximate up to the highest temperature studied; at $T=330$ MeV the $A$--$X_t$ splitting is about $-40$ MeV and is roughly independent of quark mass.
  • All six screening masses tend toward $2\pi T$ as $T$ grows, but at $T=330$ MeV the pseudoscalar and scalar masses are still about 260 MeV below $2\pi T$, while the tensor channels sit slightly above it.
  • At the lowest simulated temperature, $T=147$ MeV, the lightest-quark screening masses are already close to zero-temperature experimental meson masses, indicating that hadron-like states form as soon as chiral symmetry is strongly broken below $T_c$.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A continuum extrapolation with the same Möbius domain-wall action at finer lattice spacings would test whether the roughly 40 MeV $SU(2)_{CS}$ breaking persists; if it does, the phase just above $T_c$ is best described as chirally restored but spin-asymmetric.
  • Measuring the Dirac eigenvalue density on these ensembles could show whether the near-degeneracy of $PS$--$S$ and $X_t$--$T_t$ at $T_c$ is accompanied by suppression of low-lying modes, connecting the screening-mass result to the microscopic mechanism of effective $U(1)_A$ restoration.
  • Extending the same analysis to the other operator combinations mentioned in the paper, such as the $(V_2, PS, S)$ triplet and the $T_k$/$X_k$ quartet, would reveal whether $SU(2)_{CS}$ restoration is channel-dependent or truly universal.
  • Simulating at higher temperatures, for example $T\approx 500$ MeV, would show whether the $-40$ MeV $A$--$X_t$ splitting shrinks as the expected $O(1/T)$ corrections decrease or remains a finite fraction of $T$.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

4 major / 5 minor

Summary. The paper studies spatial mesonic two-point correlators in N_f=2 lattice QCD with Möbius domain-wall fermions at a single lattice spacing a≈0.075 fm, for temperatures T∈[147,330] MeV with varied quark masses and several volumes. Screening masses in six iso-triplet channels (PS, S, V, A, T_t, X_t) are extracted from cosh fits, and mass differences are used as order parameters for SU(2)_L×SU(2)_R (V−A), U(1)_A (X−T and PS−S), and the emergent chiral-spin SU(2)_CS (A−X). The main claims are that chiral symmetry is restored at T_c≈165 MeV, that U(1)_A also appears effectively restored just above T_c, that at T≈2T_c the former two symmetries hold to better than about 1 MeV, while SU(2)_CS is only approximate with a breaking of order 40–60 MeV (|Δm_{A−X}|/T≈0.12), and that the screening masses approach the free-field prediction 2πT from above.

Significance. If correct, the paper provides one of the cleanest demonstrations to date of chiral and axial-U(1) restoration in a chiral-fermion formulation at high temperature, and it sharpens the quantitative question about the emergent chiral-spin symmetry: rather than being restored at T≈2T_c, SU(2)_CS shows a residual breaking comparable in size to 2πT×O(a²T²) naive discretization estimates. The work is methodologically valuable: chiral symmetry is well controlled (residual mass 0.14(6) MeV), observables are direct mass differences (no parameter is tuned to enforce the claimed degeneracies), and explicit volume and quark-mass checks are provided (Fig. 11, Tables II–III). The main novelty is the quantitative contrast between restored SU(2)_L×SU(2)_R/U(1)_A and approximate SU(2)_CS at T≈330 MeV; the strength of that conclusion is currently limited by the absence of a continuum extrapolation, a limitation the authors state explicitly in Sec. V.

major comments (4)
  1. [Secs. III, IV; Tables II–III; Fig. 10] The central quantitative claim—that at T=330 MeV the V−A, X−T, and PS−S splittings are all consistent with zero at the ~1 MeV level while A−X is −57(11) MeV—rests on a single lattice spacing a=0.075 fm. Since aT≈0.125, the naive O(a²T²) scale is (aT)²×2πT≈32 MeV, i.e. the same order as the measured A−X splitting. The Möbius domain-wall action is O(a)-improved for chiral symmetry, but SU(2)_CS is not a symmetry of the lattice action, so there is no reason for its discretization error to be suppressed or to vanish. The paper's own statement in Sec. V ('Due to our fixed lattice spacing at a=0.075 fm, we cannot numerically estimate the discretization effects') confirms that this is an uncontrolled systematic for the exact claim that distinguishes restored chiral/U(1)_A symmetries from approximate SU(2)_CS. I ask the authors to add a quantitative estimate of the plausible discretization scale of the A−X splitting (for example, an eigenmode-based or effective-operator estimate of the O(a²) symmetry-breaking part at this a), or to add a second lattice spacing, or to explicitly downgrade the Sec. V conclusion to a single-spacing observation whose continuum extrapolation is pending.
  2. [Secs. II–IV; Eqs. (5)–(8); Fig. 9] The emergent-symmetry argument identifies SU(2)_CS as exact in the free-quark limit at leading order, with corrections suppressed as O(1/T) in the large-T effective theory. The paper does not quantify how large the O(1/T) breaking should be at T≈2T_c, so it is unclear whether the observed |Δm_{A−X}|≈40–60 MeV at T≈220–330 MeV is consistent with the expected physical breaking or is instead dominated by discretization artifacts. A concrete test would be to compare the T-dependence of Δm_{A−X} (Figs. 9–10 and Table III, entries at T=220, 264, 330 MeV) with the 1/T scaling expected from Eq. (4) and with the known one-loop result of Ref. [23]; if the data are consistent with a physical 1/T correction of that size, the qualitative interpretation would be substantially strengthened.
  3. [Sec. IV; Tables II–III] The paper states (Sec. IV) that 'channels connected by symmetry transformations e.g. V−A, PS−S and X−T are fitted to the same range' and that 'the screening mass differences do not depend on the fitting range very much'. The key SU(2)_CS probe A−X is not among the pairs fitted to a common range, and the paper does not document the fitting-range stability of Δm_{A−X} quantitatively. Given that the leading sources at T=330 MeV have uncertainties of only 9–13 MeV, a fitting-range systematic of this size could change the quoted −57(11) MeV value, and the claim that systematics are well controlled is not directly supported for this particular difference. Please provide a fitting-range study for Δm_{A−X} (e.g., as a function of fit start z_min with a fixed end point, and vice versa).
  4. [Sec. IV; Fig. 8, Table II] The PS−S probe of U(1)_A is subject to the stated exclusion criteria (correlator negative, or no plateau in the symmetry partner PS). At lower temperatures the S channel is indeed unstable and many S entries are missing from Table II, so the near-T_c U(1)_A statement rests mainly on the X−T probe. The T=330 MeV value m_{PS−S}=−1(1) MeV (lightest mass) survives and is compatible with restoration, but the text in Sec. V should not present the PS−S probe as comparable in robustness to V−A and X−T at all temperatures. This is a presentation point that also affects the emphasis in the abstract.
minor comments (5)
  1. [Sec. IV] The sentence in Sec. IV 'this never happens since the transition from the S triplet to two PS mesons is prohibited by the exact isospin symmetry' is unclear; isospin symmetry does not obviously forbid the S correlator from converging to a two-pion-like contribution. Please clarify which symmetry (e.g., G-parity or flavor-charge conjugation) is meant.
  2. [Tables II and III] Several rows in Tables II and III are missing entries (e.g., T=147 MeV, L=48, m=0.001 for m_PS−S; T=147 MeV, L=36, m=0.001 for m_PS−S and mV−A; T=165 MeV, L=32, m=0.001 for mV−A; T=165 MeV, L=32, m=0.0025 for mX−T). If these are excluded by the stated criteria, the criteria should be listed for each missing entry explicitly; if they are typos, they should be fixed.
  3. [Abstract] The phrase 'With a lattice cut off a^{-1}~2.6 GeV' should read 'cutoff' (a^{-1} is the inverse lattice spacing, not a cut off). Minor typography.
  4. [Fig. 1] The caption of Fig. 1 says 'The data for PS, S, A, Xt channels at the lightest quark mass m=0.001 are presented', but the figure also shows the V (and implicitly T_t) channel; please update the caption to list all channels shown.
  5. [Sec. I] The reference to 'Eq. (24)' in the footnote (Ref. [57]) is not part of the published numbering of this manuscript; please check cross-referencing. Also, the text says 'we focus on the triplet' in Sec. II but the operator list in Table I includes six channels; the relation to the triplet structure (A, T_t, X_t) is defined only in the following paragraph and would benefit from an explicit statement there.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the symmetry conclusions are direct screening-mass differences compared to zero and to the external 2πT prediction, with no fitted parameter enforcing the claimed degeneracies.

full rationale

The paper's central claims are derived from screening masses extracted by independent cosh fits to spatial correlators (Sec. IV). The symmetry probes are mass differences reported in Table III and Figures 6-10, and these are compared either to zero or to the external perturbative value 2πT from Ref. [23]. No parameter is fitted to enforce the observed V-A, PS-S, or X-T degeneracies; the same fitting procedure produces large nonzero splittings below Tc, showing that the near-zero high-temperature differences are data-driven rather than imposed. The reference temperature Tc ~ 165(3) MeV is taken from a separate chiral-susceptibility measurement [39], not from the V-A mass difference, so the statement that chiral symmetry is restored at Tc is a comparison between independent observables rather than a definition. The residual mass 0.14(6) MeV and the automatic O(a) improvement are properties of the Möbius domain-wall action from previous work [31], and they are not used as evidence for the symmetry restoration itself. The acknowledged limitation of a single lattice spacing (Sec. V: 'Due to our fixed lattice spacing at a=0.075 fm, we cannot numerically estimate the discretization effects') is a systematic-uncertainty concern, not a circularity. The comparison with HotQCD and with the perturbative prediction provides external benchmarks. No self-citation chain is load-bearing, and no derived quantity reduces by construction to the inputs.

Assumptions & free parameters 0 free parameters · 4 assumptions · 0 invented entities

No free parameters are fitted to enforce the symmetry claims. The axioms are the standard assumptions of lattice QCD with chiral fermions, single-exponential dominance, an external Tc value, and the perturbative benchmark, none of which are circular with respect to the measured mass differences.

assumptions (4)
  • domain assumption Möbius domain-wall fermion with residual mass 0.14 MeV approximates continuum chiral symmetry well enough that lattice artifacts are negligible for the measured splittings.
    The interpretation of 1-40 MeV mass differences as physical relies on this; the paper does not quantify discretization effects at fixed a=0.075 fm.
  • domain assumption Spatial correlators are dominated by a single exponential in the chosen fit range.
    Screening masses are extracted from cosh fits; if excited states contribute, masses and differences would be biased.
  • domain assumption Tc=165(3) MeV from Ref. [39] applies to these ensembles.
    Used to normalize T/Tc and frame claims about below/above Tc.
  • standard math Free-quark Matsubara analysis in Sec. II identifies the relevant emergent symmetry and leading screening mass 2πT.
    Provides the perturbative benchmark M=2πT+c g^2 T from Ref. [23] to which data are compared.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Symmetry of screening masses of mesons in two-flavor lattice QCD at high temperatures." pith.science (2026). https://pith.science/paper/BWBZFDAP

@misc{pith2026250112675,
  author       = {Pith},
  title        = {Pith review of: Symmetry of screening masses of mesons in two-flavor lattice QCD at high temperatures},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/BWBZFDAP}},
  note         = {Machine review of arXiv:2501.12675}
}
abstract

We investigate spatial two-point correlation functions of mesonic operators in two-flavor lattice QCD at high temperatures. The simulated temperatures over the range $T \in [147, 330]$ MeV, where the critical temperature is estimated around 165 MeV. To ensure a good control of the chiral symmetry we employ the M\"obius domain-wall fermion action for two degenerate flavors of quarks. With a lattice cut off $a^{-1}\sim 2.6$ GeV, the residual mass is reduced to 0.14 MeV. With the energy spectrum obtained from the screening mass at incremental values of the temperature range, we examine the $SU(2)_L\times SU(2)_R$ chiral symmetry, the anomalous axial $U(1)$ as well as an enhanced symmetry which exchanges the spin degrees of freedom. We also study how the data approaches the perturbative prediction given by twice the Matsubara frequency of free quarks.

Figures

Figures reproduced from arXiv: 2501.12675 by the authors.

Figure 1
Figure 1. FIG. 1: Effective screening mass plots at [PITH_FULL_IMAGE:figures/full_fig_p013_1.png] view at source ↗
Figure 2
Figure 2. FIG. 2: The same plots as Fig. 1 but at [PITH_FULL_IMAGE:figures/full_fig_p014_2.png] view at source ↗
Figure 3
Figure 3. FIG. 3: The same plots as Fig. 1 but at [PITH_FULL_IMAGE:figures/full_fig_p014_3.png] view at source ↗
Figures from the paper (11 more)
Figure 4
Figure 4. Figure 4: FIG. 4 [PITH_FULL_IMAGE:figures/full_fig_p015_4.png]
Figure 5
Figure 5. Figure 5: FIG. 5: The same figure as Fig. 4 but the temperature is normalized by [PITH_FULL_IMAGE:figures/full_fig_p016_5.png]
Figure 6
Figure 6. Figure 6: FIG. 6: Temperature [PITH_FULL_IMAGE:figures/full_fig_p017_6.png]
Figure 7
Figure 7. Figure 7: FIG. 7: Temperature [PITH_FULL_IMAGE:figures/full_fig_p017_7.png]
Figure 8
Figure 8. Figure 8: FIG. 8: Temperature [PITH_FULL_IMAGE:figures/full_fig_p018_8.png]
Figure 9
Figure 9. Figure 9: FIG. 9: Temperature [PITH_FULL_IMAGE:figures/full_fig_p018_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10: Quark mass dependence of ∆ [PITH_FULL_IMAGE:figures/full_fig_p019_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11: The lattice size [PITH_FULL_IMAGE:figures/full_fig_p020_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12: Plots of the raw correlators for [PITH_FULL_IMAGE:figures/full_fig_p021_12.png]
Figure 13
Figure 13. Figure 13: FIG. 13: The three higher temperature raw correlator plots like Fig.12. These plots are also [PITH_FULL_IMAGE:figures/full_fig_p022_13.png]
Figure 14
Figure 14. Figure 14: FIG. 14: These plots correspond to the three other quark mass ensembles above the physical point [PITH_FULL_IMAGE:figures/full_fig_p023_14.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

63 extracted references · 18 canonical work pages

  1. [23]

    Mesonic correlation lengths in high temperature QCD,

    M. Laine and M. Vepsalainen, “Mesonic correlation lengths in high temperature QCD,” JHEP02(2004), 004 doi:10.1088/1126-6708/2004/02/004 [arXiv:hep-ph/0311268 [hep-ph]]

    arXiv 2004

  2. [1]

    Remarks on the Chiral Phase Transition in Chromodynamics,

    R. D. Pisarski and F. Wilczek, “Remarks on the Chiral Phase Transition in Chromodynamics,” Phys. Rev. D29, 338 (1984). doi:10.1103/PhysRevD.29.338

    doi:10.1103/physrevd.29.338 1984

  3. [2]

    QCD and Instantons at Finite Temperature,

    D. J. Gross, R. D. Pisarski and L. G. Yaffe, “QCD and Instantons at Finite Temperature,” Rev. Mod. Phys.53, 43 (1981) doi:10.1103/RevModPhys.53.43

    doi:10.1103/revmodphys.53.43 1981

  4. [3]

    CHIRAL CONDENSATE IN THE INSTANTON V ACUUM,

    D. Diakonov and V. Y. Petrov, “CHIRAL CONDENSATE IN THE INSTANTON V ACUUM,” Phys. Lett. B147, 351-356 (1984) doi:10.1016/0370-2693(84)90132-1

    work page doi:10.1016/0370-2693(84)90132-1 1984

  5. [4]

    Higher Order Quantum Corrections in the Presence of an Instanton Background Field,

    T. R. Morris, D. A. Ross and C. T. Sachrajda, “Higher Order Quantum Corrections in the Presence of an Instanton Background Field,” Nucl. Phys. B255, 115-148 (1985) doi:10.1016/0550-3213(85)90131-2 20 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 0 5 10 15 20 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 0 5 10 15 20 483 × 18 T=147 MeV C(z) z/a 2.6 MeV Quark Mass P S ...

    work page doi:10.1016/0550-3213(85)90131-2 1985

  6. [5]

    Instantons in QCD,

    T. Sch¨ afer and E. V. Shuryak, “Instantons in QCD,” Rev. Mod. Phys.70, 323-426 (1998) doi:10.1103/RevModPhys.70.323 [arXiv:hep-ph/9610451 [hep-ph]]

    arXiv 1998

  7. [6]

    Confronting instanton perturbation theory with QCD lattice results,

    A. Ringwald and F. Schrempp, “Confronting instanton perturbation theory with QCD lattice results,” Phys. Lett. B459, 249-258 (1999) doi:10.1016/S0370-2693(99)00682-6 [arXiv:hep-lat/9903039 [hep-lat]]

    arXiv 1999

  8. [7]

    The High temperature phase of QCD and U(1)-A symmetry,

    T. D. Cohen, “The High temperature phase of QCD and U(1)-A symmetry,” Phys. Rev. D 54, R1867 (1996) doi:10.1103/PhysRevD.54.R1867 [hep-ph/9601216]

    arXiv 1996

Show all 63 references
  1. [8]

    The Spectral density of the Dirac operator above T(c) rep,

    T. D. Cohen, “The Spectral density of the Dirac operator above T(c) rep,” nucl-th/9801061

    arXiv

  2. [9]

    Chiral symmetry restoration, eigenvalue density of Dirac operator and axial U(1) anomaly at finite temperature,

    S. Aoki, H. Fukaya and Y. Taniguchi, “Chiral symmetry restoration, eigenvalue density of Dirac operator and axial U(1) anomaly at finite temperature,” Phys. Rev. D86, 114512 (2012) doi:10.1103/PhysRevD.86.114512 [arXiv:1209.2061 [hep-lat]]

    2012 arXiv

  3. [10]

    Relevance of the axial anomaly at the finite-temperature chiral 21 transition in QCD,

    A. Pelissetto and E. Vicari, “Relevance of the axial anomaly at the finite-temperature chiral 21 transition in QCD,” Phys. Rev. D88, no. 10, 105018 (2013) doi:10.1103/PhysRevD.88.105018 [arXiv:1309.5446 [hep-lat]]

    2013 arXiv

  4. [11]

    Quasi-instantons in QCD with chiral symmetry restoration,

    T. Kanazawa and N. Yamamoto, “Quasi-instantons in QCD with chiral symmetry restoration,” Phys. Rev. D91, 105015 (2015) doi:10.1103/PhysRevD.91.105015 [arXiv:1410.3614 [hep-th]]

    2015 arXiv

  5. [12]

    LinkingU(2)×U(2) toO(4) model via decoupling,

    T. Sato and N. Yamada, “LinkingU(2)×U(2) toO(4) model via decoupling,” Phys. Rev. D 91, no. 3, 034025 (2015) doi:10.1103/PhysRevD.91.034025 [arXiv:1412.8026 [hep-lat]]

    2015 arXiv

  6. [13]

    Conformal Bootstrap Dashing Hopes of Emergent Symmetry,

    Y. Nakayama and T. Ohtsuki, “Conformal Bootstrap Dashing Hopes of Emergent Symmetry,” Phys. Rev. Lett.117, no. 13, 131601 (2016) doi:10.1103/PhysRevLett.117.131601 [arXiv:1602.07295 [cond-mat.str-el]]

    2016 arXiv

  7. [14]

    Cossu, S

    G. Cossu, S. Aoki, H. Fukaya, S. Hashimoto, T. Kaneko, H. Matsufuru and J. I. Noaki, “Finite temperature study of the axial U(1) symmetry on the lattice with overlap fermion 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 0 2 4 6 8 10 12 14 16 10−8 10−7 10−6 10−5 10−4 10−3 10−2 10−1 0...

    2013 arXiv

  8. [15]

    QCD chiral transition, U(1)A symmetry and the dirac spectrum using domain wall fermions,

    M. I. Buchoffet al., “QCD chiral transition, U(1)A symmetry and the dirac spectrum using domain wall fermions,” Phys. Rev. D89, no. 5, 054514 (2014) doi:10.1103/PhysRevD.89.054514 [arXiv:1309.4149 [hep-lat]]

    2014 arXiv

  9. [16]

    Microscopic origin ofU A(1) symmetry violation in the high temperature phase of QCD,

    V. Dick, F. Karsch, E. Laermann, S. Mukherjee and S. Sharma, “Microscopic origin ofU A(1) symmetry violation in the high temperature phase of QCD,” Phys. Rev. D91, no. 9, 094504 (2015) doi:10.1103/PhysRevD.91.094504 [arXiv:1502.06190 [hep-lat]]

    2015 arXiv

  10. [17]

    On the strength of theU A(1) anomaly at the chiral phase transition inN f = 2 QCD,

    B. B. Brandt, A. Francis, H. B. Meyer, O. Philipsen, D. Robaina and H. Wittig, “On the strength of theU A(1) anomaly at the chiral phase transition inN f = 2 QCD,” JHEP1612, 158 (2016) doi:10.1007/JHEP12(2016)158 [arXiv:1608.06882 [hep-lat]]

    2016 arXiv

  11. [18]

    Nature of chiral phase transition in 23 two-flavor QCD,

    K.-I. Ishikawa, Y. Iwasaki, Y. Nakayama and T. Yoshie, “Nature of chiral phase transition in 23 two-flavor QCD,” arXiv:1706.08872 [hep-lat]

    arXiv

  12. [19]

    Bazavovet al., Phys

    A. Bazavovet al., Phys. Rev. D100, no. 9, 094510 (2019) doi:10.1103/PhysRevD.100.094510 [arXiv:1908.09552 [hep-lat]]

    2019 arXiv

  13. [20]

    Kaczmarek, R

    O. Kaczmarek, R. Shanker and S. Sharma, Phys. Rev. D108(2023) no.9, 094501 doi:10.1103/PhysRevD.108.094501 [arXiv:2301.11610 [hep-lat]]

    2023 arXiv

  14. [21]

    Heavy quark symmetry,

    M. Neubert, “Heavy quark symmetry,” Phys. Rept.245, 259-396 (1994) doi:10.1016/0370-1573(94)90091-4 [arXiv:hep-ph/9306320 [hep-ph]]

    1994 arXiv

  15. [22]

    Effective Field Theories for Heavy Quarkonium,

    N. Brambilla, A. Pineda, J. Soto and A. Vairo, “Effective Field Theories for Heavy Quarkonium,” Rev. Mod. Phys.77, 1423 (2005) doi:10.1103/RevModPhys.77.1423 [arXiv:hep-ph/0410047 [hep-ph]]

    2005 arXiv

  16. [24]

    SU(4) symmetry of the dynamical QCD string and genesis of hadron spectra,

    L. Y. Glozman, “SU(4) symmetry of the dynamical QCD string and genesis of hadron spectra,” Eur. Phys. J. A51, no.3, 27 (2015) doi:10.1140/epja/i2015-15027-x [arXiv:1407.2798 [hep-ph]]

    2015 arXiv

  17. [25]

    SU(2N F ) symmetry of QCD at high temperature and its implications,

    L. Y. Glozman, “SU(2N F ) symmetry of QCD at high temperature and its implications,” Acta Phys. Polon. Supp.10, 583 (2017) doi:10.5506/APhysPolBSupp.10.583 [arXiv:1610.00275 [hep-lat]]

    2017 arXiv

  18. [26]

    Chiralspin symmetry and QCD at high temperature,

    L. Y. Glozman, “Chiralspin symmetry and QCD at high temperature,” Eur. Phys. J. A54, no. 7, 117 (2018) doi:10.1140/epja/i2018-12560-0 [arXiv:1712.05168 [hep-ph]]

    2018 arXiv

  19. [27]

    Low lying eigenmodes and meson propagator symmetries,

    C. B. Lang, “Low lying eigenmodes and meson propagator symmetries,” Phys. Rev. D97, no. 11, 114510 (2018) doi:10.1103/PhysRevD.97.114510, 10.1103/PHYSREVD.97.114510 [arXiv:1803.08693 [hep-ph]]

    2018 arXiv

  20. [28]

    On SU(2)CS-like groups and invariance of the fermionic action in QCD,

    M. Catillo, “On SU(2)CS-like groups and invariance of the fermionic action in QCD,” Int. J. Mod. Phys. A37, no.16, 2250102 (2022) doi:10.1142/S0217751X22501020 [arXiv:2109.03532 [hep-lat]]

    2022 arXiv

  21. [29]

    Chiral spin symmetry and the QCD phase diagram,

    L. Y. Glozman, O. Philipsen and R. D. Pisarski, “Chiral spin symmetry and the QCD phase diagram,” Eur. Phys. J. A58, no.12, 247 (2022) doi:10.1140/epja/s10050-022-00895-4 [arXiv:2204.05083 [hep-ph]]

    2022 arXiv

  22. [30]

    Violation of chirality of the M¨ obius domain-wall Dirac operator from the eigenmodes,

    G. Cossuet al.[JLQCD], “Violation of chirality of the M¨ obius domain-wall Dirac operator from the eigenmodes,” Phys. Rev. D93(2016) no.3, 034507 24 doi:10.1103/PhysRevD.93.034507 [arXiv:1510.07395 [hep-lat]]

    2016 arXiv

  23. [31]

    Evidence of effective axial U(1) symmetry restoration at high temperature QCD,

    A. Tomiya, G. Cossu, S. Aoki, H. Fukaya, S. Hashimoto, T. Kaneko and J. Noaki, “Evidence of effective axial U(1) symmetry restoration at high temperature QCD,” Phys. Rev. D96 (2017) no.3, 034509 doi:10.1103/PhysRevD.96.034509 [arXiv:1612.01908 [hep-lat]]

    2017 arXiv

  24. [32]

    Study of the axialU(1) anomaly at high temperature with lattice chiral fermions,

    S. Aokiet al.[JLQCD], “Study of the axialU(1) anomaly at high temperature with lattice chiral fermions,” Phys. Rev. D103, no.7, 074506 (2021) doi:10.1103/PhysRevD.103.074506 [arXiv:2011.01499 [hep-lat]]

    2021 arXiv

  25. [33]

    A Method for simulating chiral fermions on the lattice,

    D. B. Kaplan, “A Method for simulating chiral fermions on the lattice,” Phys. Lett. B288, 342 (1992) doi:10.1016/0370-2693(92)91112-M [hep-lat/9206013]

    1992 arXiv

  26. [34]

    Shamir, Nucl

    Y. Shamir, Nucl. Phys. B406, 90 (1993) doi:10.1016/0550-3213(93)90162-I. [hep-lat/9303005]

    1993 arXiv

  27. [35]

    Axial symmetries in lattice QCD with Kaplan fermions,

    V. Furman and Y. Shamir, “Axial symmetries in lattice QCD with Kaplan fermions,” Nucl. Phys. B439, 54 (1995) doi:10.1016/0550-3213(95)00031-M. [hep-lat/9405004]

    1995 arXiv

  28. [36]

    Mobius fermions,

    R. C. Brower, H. Neff and K. Orginos, “Mobius fermions,” Nucl. Phys. Proc. Suppl.153, 191 (2006) doi:10.1016/j.nuclphysbps.2006.01.047 [hep-lat/0511031]

    2006 arXiv

  29. [37]

    The M¨ obius domain wall fermion algorithm,

    R. C. Brower, H. Neff and K. Orginos, “The M¨ obius domain wall fermion algorithm,” Comput. Phys. Commun.220, 1 (2017) doi:10.1016/j.cpc.2017.01.024 [arXiv:1206.5214 [hep-lat]]

    2017 arXiv

  30. [38]

    Exactly massless quarks on the lattice,

    H. Neuberger, “Exactly massless quarks on the lattice,” Phys. Lett. B417, 141 (1998) doi:10.1016/S0370-2693(97)01368-3 [hep-lat/9707022]

    1998 arXiv

  31. [39]

    Chiral susceptibility and axial U(1) anomaly near the (pseudo-)critical temperature,

    S. Aokiet al.[JLQCD:], “Chiral susceptibility and axial U(1) anomaly near the (pseudo-)critical temperature,” PoSLA TTICE2023(2024), 184 doi:10.22323/1.453.0184 [arXiv:2401.06459 [hep-lat]]

    2024 arXiv

  32. [40]

    Mathur, A

    N. Mathur, A. Alexandru, Y. Chen, S. J. Dong, T. Draper, I. Horvath, F. X. Lee, K. F. Liu, S. Tamhankar and J. B. Zhang, Phys. Rev. D76(2007), 114505 doi:10.1103/PhysRevD.76.114505 [arXiv:hep-ph/0607110 [hep-ph]]

    2007 arXiv

  33. [41]

    Approximate degeneracy ofJ= 1 spatial correlators in high temperature QCD,

    C. Rohrhofer, Y. Aoki, G. Cossu, H. Fukaya, L. Y. Glozman, S. Hashimoto, C. B. Lang and S. Prelovsek, “Approximate degeneracy ofJ= 1 spatial correlators in high temperature QCD,” Phys. Rev. D96, no. 9, 094501 (2017) Erratum: [Phys. Rev. D99, no. 3, 039901 (2019)] doi:10.1103/P...

    2017 arXiv

  34. [42]

    Symmetries of spatial meson correlators in high temperature QCD,

    C. Rohrhoferet al., “Symmetries of spatial meson correlators in high temperature QCD,” Phys. Rev. D100, no. 1, 014502 (2019) doi:10.1103/PhysRevD.100.014502 [arXiv:1902.03191 [hep-lat]]

    2019 arXiv

  35. [43]

    Chiral-spin symmetry of the meson spectral function aboveT c,

    C. Rohrhofer, Y. Aoki, L. Y. Glozman and S. Hashimoto, “Chiral-spin symmetry of the meson spectral function aboveT c,” Phys. Lett. B802, 135245 (2020) doi:10.1016/j.physletb.2020.135245 [arXiv:1909.00927 [hep-lat]]

    2020

  36. [44]

    Symmetries of meson correlators in high-temperature QCD with physical (u/d,s,c) domain-wall quarks,

    T. W. Chiu, “Symmetries of meson correlators in high-temperature QCD with physical (u/d,s,c) domain-wall quarks,” Phys. Rev. D107, no.11, 114501 (2023) doi:10.1103/PhysRevD.107.114501 [arXiv:2302.06073 [hep-lat]]

    2023 arXiv

  37. [45]

    Symmetries of spatial correlators of light and heavy mesons in high temperature lattice QCD,

    T. W. Chiu, “Symmetries of spatial correlators of light and heavy mesons in high temperature lattice QCD,” Phys. Rev. D110, no.1, 014502 (2024) doi:10.1103/PhysRevD.110.014502 [arXiv:2404.15932 [hep-lat]]

    2024 arXiv

  38. [46]

    Symmetries in high-temperature lattice QCD with (u, d, s, c, b) optimal domain-wall quarks,

    T. W. Chiu, “Symmetries in high-temperature lattice QCD with (u, d, s, c, b) optimal domain-wall quarks,” [arXiv:2411.16705 [hep-lat]]

    arXiv

  39. [47]

    Study of symmetries in finite temperatureN f = 2 QCD with M¨ obius Domain Wall Fermions,

    D. Ward, S. Aoki, Y. Aoki, H. Fukaya, S. Hashimoto, I. Kanamori, T. Kaneko, J. Goswami and Y. Zhang, “Study of symmetries in finite temperatureN f = 2 QCD with M¨ obius Domain Wall Fermions,” [arXiv:2412.06574 [hep-lat]]

    arXiv

  40. [48]

    Study of Chiral Symmetry andU(1) A using Spatial Correlators forN f = 2 + 1 QCD at finite temperature with Domain Wall Fermions,

    D. Ward, S. Aoki, Y. Aoki, H. Fukaya, S. Hashimoto, I. Kanamori, T. Kaneko, J. Goswami and Y. Zhang, “Study of Chiral Symmetry andU(1) A using Spatial Correlators forN f = 2 + 1 QCD at finite temperature with Domain Wall Fermions,” PoSLA TTICE2023(2024), 182 doi:10.22323/1.453...

    2024 arXiv

  41. [49]

    Role of the axial U(1) anomaly in the chiral susceptibility of QCD at high temperature,

    S. Aokiet al.[JLQCD], “Role of the axial U(1) anomaly in the chiral susceptibility of QCD at high temperature,” PTEP2022, no.2, 023B05 (2022) doi:10.1093/ptep/ptac001 [arXiv:2103.05954 [hep-lat]]

    2022 arXiv

  42. [50]

    Axial U(1) symmetry near the pseudocritical temperature in Nf = 2 + 1 lattice QCD with chiral fermions,

    S. Aokiet al.[JLQCD], “Axial U(1) symmetry near the pseudocritical temperature in Nf = 2 + 1 lattice QCD with chiral fermions,” PoSLA TTICE2023(2024), 185 doi:10.22323/1.453.0185 [arXiv:2401.14022 [hep-lat]]

    2024 arXiv

  43. [51]

    Characterizing Strongly Interacting Matter at Finite Temperature: (2+1)-Flavor QCD with M¨ obius Domain Wall fermions,

    J. Goswamiet al.[JLQCD], “Characterizing Strongly Interacting Matter at Finite Temperature: (2+1)-Flavor QCD with M¨ obius Domain Wall fermions,” PoS LA TTICE2023(2024), 187 doi:10.22323/1.453.0187

    2024 doi

  44. [52]

    JLQCD 26 IroIro++ lattice code on BG/Q,

    G. Cossu, J. Noaki, S. Hashimoto, T. Kaneko, H. Fukaya, P. A. Boyle and J. Doi, “JLQCD 26 IroIro++ lattice code on BG/Q,” [arXiv:1311.0084 [hep-lat]]

    arXiv

  45. [53]

    Grid: A next generation data parallel C++ QCD library,

    P. Boyle, A. Yamaguchi, G. Cossu and A. Portelli, “Grid: A next generation data parallel C++ QCD library,” [arXiv:1512.03487 [hep-lat]]

    arXiv

  46. [54]

    Development of an object oriented lattice QCD code ’Bridge++’,

    S. Ueda, S. Aoki, T. Aoyama, K. Kanaya, H. Matsufuru, S. Motoki, Y. Namekawa, H. Nemura, Y. Taniguchi and N. Ukita, “Development of an object oriented lattice QCD code ’Bridge++’,” J. Phys. Conf. Ser.523, 012046 (2014) doi:10.1088/1742-6596/523/1/012046

    2014 doi

  47. [55]

    Sharing lattice QCD data over a widely distributed file system,

    T. Amagasa, S. Aoki, Y. Aoki, T. Aoyama, T. Doi, K. Fukumura, N. Ishii, K. I. Ishikawa, H. Jitsumoto and H. Kamano,et al.“Sharing lattice QCD data over a widely distributed file system,” J. Phys. Conf. Ser.664, no.4, 042058 (2015) doi:10.1088/1742-6596/664/4/042058

    2015 doi

  48. [56]

    Krasniqi, M

    A. Krasniqi, M. C` e, R. J. Hudspith and H. B. Meyer, Phys. Rev. D110(2024) no.11, 114506 doi:10.1103/PhysRevD.110.114506 [arXiv:2407.01657 [hep-lat]]

    2024 arXiv

  49. [57]

    Non-perturbative thermal QCD at all temperatures: the case of mesonic screening masses,

    M. Dalla Brida, L. Giusti, T. Harris, D. Laudicina and M. Pepe, “Non-perturbative thermal QCD at all temperatures: the case of mesonic screening masses,” JHEP04, 034 (2022) doi:10.1007/JHEP04(2022)034 [arXiv:2112.05427 [hep-lat]]

    2022 arXiv

  50. [58]

    Laudicina, M

    D. Laudicina, M. Dalla Brida, L. Giusti, T. Harris and M. Pepe, PoSLA TTICE2022 (2023), 182 doi:10.22323/1.430.0182 [arXiv:2212.02167 [hep-lat]]

    2023 arXiv

  51. [59]

    Giusti, T

    L. Giusti, T. Harris, D. Laudicina, M. Pepe and P. Rescigno, Phys. Lett. B855(2024), 138799 doi:10.1016/j.physletb.2024.138799 [arXiv:2405.04182 [hep-lat]]

    2024

  52. [60]

    Aspects of the chiral crossover transition in (2+1)-flavor QCD with M¨ obius domain-wall fermions,

    R. V. Gavai, M. E. Jaensch, O. Kaczmarek, F. Karsch, M. Sarkar, R. Shanker, S. Sharma, S. Sharma and T. Ueding, “Aspects of the chiral crossover transition in (2+1)-flavor QCD with M¨ obius domain-wall fermions,” [arXiv:2411.10217 [hep-lat]]

    arXiv

  53. [61]

    Luscher and P

    M. Luscher and P. Weisz, Phys. Lett.158B, 250 (1985). doi:10.1016/0370-2693(85)90966-9

    1985 doi

  54. [62]

    Morningstar and M

    C. Morningstar and M. J. Peardon, Phys. Rev. D69, 054501 (2004) doi:10.1103/PhysRevD.69.054501 [arXiv:hep-lat/0311018 [hep-lat]]

    2004 arXiv

  55. [63]

    Scale setting in lattice QCD,

    R. Sommer, “Scale setting in lattice QCD,” PoSLA TTICE2013, 015 (2014) doi:10.22323/1.187.0015 [arXiv:1401.3270 [hep-lat]]. 27 L3 ×L t L(fm)T[MeV]T Lamm[MeV] No. samples mS mP S mV mA mX mT 483 ×18 3.6 147 2.7 0.00100 2.6 146 113(34) 951(111) 1106(182) 1120(201) 1068(154) 0.00...

    2014 arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.