Pith. sign in

REVIEW 3 major objections 4 minor 57 references

Taste breaking in the minimally doubled Karsten-Wilczek action and its tree-level improvement

T0 review · 3 major / 4 minor · reviewed 2026-08-08 · deepseek-v4-flash

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

Pith's one-line read The Naik-improved Karsten-Wilczek action offers a rootless, chiral lattice fermion discretization whose continuum limit matches staggered results, at about twice the solver cost, with smaller taste breaking.

desk verdict Solid mixed-action study showing a tree-level Naik improvement makes Karsten-Wilczek fermions much less noisy and less taste-broken, but the closing claim that this makes them a valid alternative to staggered QCD overreaches the evidence. read the letter →

arxiv 2502.07354 v1 pith:4TZK7RT7 submitted 2025-02-11 hep-lat

S. Borsányi , S. Capitani , Z. Fodor , D. Godzieba , P. Parotto , R. A. Vig , C. H. Wong This is my paper · ORCID
classification hep-lat PACS 11.15.Ha12.38.Gc
keywords minimallydoubledfermionsKarsten-WilczekactionlatticeQCDtastebreakingNaikimprovementnon-perturbativetuningchiralsymmetrypiondecayconstant
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 argues that a spatially Naik-improved version of the Karsten-Wilczek (KW) minimally doubled fermion action is a viable rootless alternative to staggered quarks for two-flavor QCD. It shows that the action can be non-perturbatively tuned on staggered gauge configurations through a decoupled hierarchy of parameters, and that the tree-level improvement cuts statistical noise and taste breaking enough to more than repay its added cost. The measured continuum limit of the pion decay constant agrees with the staggered one on the same ensembles, motivating the use of KW fermions in thermodynamics where staggered rooting becomes problematic. This matters because staggered fermions require rooting, which is ambiguous at finite chemical potential, whereas the KW action keeps a chiral symmetry and exactly two species for $N_f=2$.

What carries the argument

The central object is the Karsten-Wilczek Dirac operator, a local chiral lattice fermion whose extra term is a three-dimensional Laplacian weighted by $i\zeta\gamma_0$, which leaves exactly one doubler and preserves a $U(1)$ chiral symmetry while breaking hypercubic symmetry down to a cubic subgroup. The paper's main modification is a tree-level spatial Naik improvement: the single-hop Laplacian and Nabla in the three spatial directions are replaced by three-hop combinations with coefficients $9/8$ and $-1/8$ (Laplacian) and $9/8$ and $-1/24$ (Nabla), so that near zero momentum the improved operator behaves as $k^4$ rather than $k^2$. Rounding out the machinery is the tuning protocol, in which the dimension-three counterterm $c$ is fixed by the vanishing beat frequency of an oscillating $\gamma_0$ correlator, the bare anisotropy $\xi_0$ is fixed by demanding the renormalized anisotropy $\xi_f = 1$, and the bare quark mass is tuned last; and the observation that the KW term is odd under charge conjugation and time reversal, so $O(a)$ contributions cancel in C- and T-symmetric observables on symmetric gauge ensembles.

What would settle it

Measure a C- or T-odd observable, such as an operator whose expectation value must vanish in the continuum, on the same symmetric gauge ensembles at non-zero lattice spacing; a nonzero value would show the $O(a)$ cancellation fails. Alternatively, fit the continuum extrapolations of $f_\pi$ or a taste splitting including a term linear in $a$ and test whether a statistically significant $O(a)$ coefficient emerges, or repeat the mixed-action measurements on gauge ensembles that lack the discrete symmetries, which would expose uncancelled $O(a)$ errors.

Watch

Extended reading notes

Core claim

The central claim is that the tree-level Naik-improved KW action is a valid alternative to currently used staggered formulations, because it avoids rooting for $N_f=2$, has a reasonable cost-effectiveness, and shows a favourable taste-breaking structure. The authors establish this through a mixed-action numerical study on physical 4stout staggered ensembles: they tune the two fermionic counterterms $c$ and $\xi_0$ and the bare mass $m_0$ non-perturbatively, compute the pion decay constant and the mass splittings of three taste channels, and extrapolate each to the continuum. The Naik improvement reduces the $\gamma_0$ taste splitting by 30-50% and shrinks the continuum error on $f_\pi$ by about a factor of 3.5 relative to the unimproved action, for an estimated per-lattice cost increase slightly above a factor of 2. A slight tension remains between the Naik-improved KW and staggered continuum limits, and the paper leaves its resolution to future work with finer lattices.

Load-bearing premise

The continuum results assume that every $O(a)$ error cancels in the measured charge-conjugation- and time-reversal-symmetric observables, so $f_\pi$ and the taste splittings scale as $a^2$; if that cancellation is incomplete, the linear-in-$a^2$ extrapolations and the slight tension with staggered are not reliable.

Editorial extensions

If this is right

  • The Naik-improved KW action can be used for $N_f=2$ finite-temperature and finite-density QCD without rooting, avoiding the unphysical low-temperature effects that rooted staggered fermions show at real chemical potential.
  • The tuning hierarchy lets most counterterm fixing be done at a heavy pseudoscalar mass and reused at the physical point, saving substantial computational effort in future thermodynamics studies.
  • With about a factor-of-2 cost increase per solver iteration, the improved action yields roughly 3.5 times smaller continuum-extrapolation errors on $f_\pi$ than the unimproved action, so the improvement is cost-effective.
  • The taste splittings of the improved KW action sit at or slightly below those of the 4stout staggered action on the same ensembles, supporting its use as a cross-check or alternative to staggered thermodynamics.

Reading between the lines

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

  • The slight tension between the Naik-improved KW and staggered continuum limits of $f_\pi$ could be a signal of residual $O(a)$ effects slipping through the symmetry-cancellation argument, or a finite-volume or scale-setting artifact; settling it with finer lattices, more statistics, or a different scale-setting method is a direct next test.
  • Because only the spatial directions are improved, the temporal direction is a candidate source of residual discretization error; the paper notes that a renormalized anisotropy $\xi_f > 1$ could compensate, so a temporally improved variant is a natural extension that may further reduce taste splitting.
  • The symmetry-cancellation mechanism assumes the gauge background respects C and T; applying the same tuned KW action on configurations generated with a different fermion action would test whether the $O(a)$ suppression is generic or specific to the 4stout ensembles.
  • If the improved KW action remains competitive at finer lattice spacings, it could provide a rootless chiral formulation for the QCD phase diagram at real baryon density, where rooted staggered reweighting faces sign problems.
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

3 major / 4 minor

Summary. The paper presents a mixed-action numerical study of the Karsten-Wilczek (KW) minimally doubled fermion action on gauge configurations generated with the 4stout staggered action. It introduces a spatial Naik-style tree-level improvement, details a non-perturbative tuning of the KW parameters c, xi0, and m0 (with dG left untuned), and uses the tuned actions to compute the pion decay constant and taste-splitting observables across several lattice spacings. The central claims are that the Naik-improved KW action has smaller statistical errors than the unimproved one, that its continuum limit for f_pi is consistent with staggered results (with a noted slight tension), and that the improved KW action is a valid rootless alternative to staggered fermions for Nf=2 thermodynamics.

Significance. The paper is technically careful: the tuning hierarchy is well motivated and tested, the use of tiling to measure the beat frequency is sensible, and the systematic error analysis via the histogram method is appropriate. If the conclusions are taken as a proof-of-principle for a valence action, the work is a useful step toward a rootless chiral discretization and contains concrete quantitative estimates of cost and taste breaking. The advertised broader conclusion - that the improved KW action is a valid dynamical alternative to staggered actions - is not established by the evidence presented, because the study is mixed-action with an untuned gluonic counterterm and the continuum extrapolation rests on assumptions and one unpublished perturbative claim.

major comments (3)
  1. [Section VII; Section IV B; Section I] The concluding claim in Section VII that 'the Naik improved KW action is a valid alternative to currently employed staggered formulations' is not supported by the evidence in this paper. All measurements are valence measurements on fixed 4stout staggered ensembles, and Section IV B states explicitly that the KW gluonic counterterm dG is not tuned. In a dynamical KW simulation, dG modifies the gauge action and can feed back into the scale and fermionic observables; moreover, the automatic O(a) cancellation described in Section I relies on the gauge background respecting the discrete symmetries, which a dynamical KW background with dG does not by construction. I therefore see the dynamical-validity statement as a scope mismatch rather than a numerical flaw. It should either be removed or softened to a mixed-action feasibility statement, or supplemented by an explicit dynamical test or estimate of the dG effect.
  2. [Section V, Fig. 10] The continuum extrapolation of f_pi shows a tension that the text calls 'slight' but that is substantial relative to the quoted errors: f_{KW+Naik} = 167.75(24) MeV versus f_{sta} = 168.46(24) MeV, a difference of about 0.71 MeV with a combined statistical error of about 0.34 MeV, i.e. roughly 2.1 sigma. In addition, the Naik-improved action was not evaluated on the finest lattice (a = 0.0638 fm) due to memory limitations. Since the consistency of the continuum limit is central to the claim that the improved KW action is a valid alternative, the paper should either provide a systematic treatment of this tension (for example, an estimate of higher-order discretization effects, finite-volume effects, or correlated differences) or explicitly downgrade the consistency claim.
  3. [Section I and Ref. [32]] The central benefit of the Naik improvement is stated in Section I as the elimination of leading-logarithmic divergences of the form a g0^{2n} log^n a, with the proof deferred to Ref. [32], which is listed as 'to be submitted'. Because this perturbative claim is load-bearing for interpreting the improved numerical results - tree-level dispersion improvement alone would not justify the log-elimination statement - the manuscript should either include the one-loop computation or clearly separate the verified tree-level/free-field improvement from the unverified leading-log claim. As written, an independent referee cannot check the main theoretical motivation.
minor comments (4)
  1. [Tables I and II] Table II lists beta = 3.6736 for the a = 0.1581 fm ensemble, whereas Table I gives beta = 3.6376 for that lattice spacing; one of these is a typo and should be corrected.
  2. [Section IV B 4 and Section III] There are several typos, including 'In princple' in Section IV B 4 and 'achived' in Section III; the manuscript should be proofread for these and similar errors.
  3. [Fig. 2] The horizontal axis label '1/M2 5 [GeV 2]' is unclear; the text says the plot shows the iteration count versus the pion mass, so please label the axis as 1/M_gamma5^2 and define M_gamma5 in the caption.
  4. [Fig. 12] Figure 12 compares different taste-splitting measures (the RMS mass split for KW, tensor states for staggered), and the caption should clarify why these quantities are directly comparable.

Circularity Check

0 steps flagged · score 2.0 of 10

No significant circularity: tuning conditions are independent of the reported observables; the only minor self-citation is an unpublished leading-log improvement proof that is not construction-level.

full rationale

The central derivation is self-contained. The KW parameters c, xi0 and m0 are fixed by independent renormalization conditions: c is tuned by requiring the gamma0-channel beat frequency to vanish (the tree-level oscillation form, Section IV B 1), xi0 is tuned by imposing the renormalized anisotropy xif = M_perp/M_parallel = 1 (Section IV B 2), and m0 is tuned to the fixed pseudoscalar mass M_gamma5 = 578.4 MeV (Section IV B 3). The reported observables f_pi and the taste splittings Delta M_i^2 = M_i^2 - M_gamma5^2 are then measured, not derived from these tuning conditions, so no fitted input is renamed as a prediction. The continuum extrapolations compare KW and staggered measurements on the same 4stout ensembles and are ordinary empirical extrapolations; the mixed-action nature and the untuned gluonic counterterm dG are scope limitations, not circular steps. The only mild self-citation is the theoretical assertion that the Naik-improved Laplacian eliminates the leading log divergences, deferred to Ref. [32], an unpublished manuscript by two of the present authors ('We will show in a separate publication that this type of improvement eliminates the leading log divergences [32].'). This is used to interpret the reduced statistical noise of the improved action, but the numerical evidence for reduced noise and reduced gamma0 taste splitting (Figs. 10 and 11) is independent of that unpublished proof. Because the load-bearing numerical results are self-contained and no equation reduces by construction to an input, the paper receives a low circularity score of 2.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central quantitative results depend on a set of tunable action parameters (c, xi0, m0) fixed by matching mesonic observables, and the continuum extrapolation relies on the asserted cancellation of O(a) artifacts. No new physical entities are introduced.

free parameters (4)
  • c (KW dimension-3 counterterm) = e.g. -0.13925 at beta=3.7589
    Tuned by requiring vanishing beat frequency omega_c in the gamma_0 correlator; a renormalization parameter central to the tuning procedure.
  • xi0 (bare anisotropy) = e.g. 0.9882 at beta=3.7589
    Tuned to impose the renormalized anisotropy xi_f = M_perp/M_parallel = 1.
  • m0 (bare quark mass) = e.g. 0.03590 at beta=3.7589
    Tuned to set the pseudoscalar mass M_gamma5 = 578.4 MeV.
  • Naik improvement coefficients (zeta, sbar1=cbar1, sbar3=cbar3) = zeta=4/3, sbar1=cbar1=1.5, sbar3=cbar3=-1/6
    Chosen by hand, not fitted, to satisfy the half-vector trick while improving the Laplacian; sacrifices full Nabla improvement.
assumptions (6)
  • standard math Nielsen-Ninomiya no-go theorem permits at least one doubler for local chiral fermions.
    Invoked in the introduction to justify the existence of a single extra doubler in minimally doubled fermions.
  • domain assumption The KW action has a single relevant dimension-3 counterterm (i psi-bar gamma_0 psi) and marginal dimension-4 counterterms (fermionic and gluonic speed of light).
    Taken from Refs. [34-36]; provides the basis for tuning only c, xi0, and m0, and for setting dG to zero in this mixed action.
  • domain assumption Odd-in-a terms cancel for C- and T-symmetric observables in mixed action studies.
    States that the gauge action respects the discrete symmetries, so that fpi and taste splittings have only a^2 artifacts; this justifies the continuum extrapolations in Figs. 10 and 11.
  • domain assumption ZS/ZP = 1 for chiral actions.
    Used in the extraction of fpi from the pseudoscalar correlator, Eq. (28).
  • ad hoc to paper The spatial Naik improvement eliminates leading log divergences of the form a g0^{2n} log^n a.
    Stated as the motivation for the improvement, but the proof is deferred to Ref. [32], 'to be submitted (2025)', and is not provided in this paper.
  • domain assumption Tiling stored gauge configurations does not bias the beat-frequency measurement used to tune c.
    Assumed when concatenating configurations to extend temporal extent; long wavelength gauge fluctuations are argued to be irrelevant for the divergent parts of Feynman diagrams.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Taste breaking in the minimally doubled Karsten-Wilczek action and its tree-level improvement." pith.science (2026). https://pith.science/paper/4TZK7RT7

@misc{pith2026250207354,
  author       = {Pith},
  title        = {Pith review of: Taste breaking in the minimally doubled Karsten-Wilczek action and its tree-level improvement},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4TZK7RT7}},
  note         = {Machine review of arXiv:2502.07354}
}
read the original abstract

Minimally doubled fermion actions offer a discretization for two-flavor Quantum Chromodynamics without rooting, but retaining a U(1) chiral symmetry at the same time. The price to pay is a breaking of the hypercubic symmetry, which requires the inclusion and tuning of new counterterms. Similar to staggered quarks, these actions suffer from taste breaking. We perform a mixed action numerical study with the Karsten-Wilczek formulation of minimally doubled fermions on 4stout staggered configurations, generated with physical quark masses, covering a broad range of lattice spacings. We consider a tree-level spatial Naik improvement to mitigate discretization errors. We carry out a non-perturbative tuning of the KW action with and without improvement, and investigate the taste breaking and the approach to the continuum limit.

Figures

Figures reproduced from arXiv: 2502.07354 by the authors.

Figure 1
Figure 1. FIG. 1. The Laplacian term and its 3-hop improved form [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. B. Tuning In this section we illustrate the procedure we employed to tune the parameters of the KW action. We need to carry out a multi-dimensional tuning involving the KW parameters c and ξ0, as well as the fermion mass m0. The KW parameter dG is not tuned, as the gauge configura￾tions were generated with our 4stout staggered action. We will show in the following that the tuning largely de￾couples, and the three pa… view at source ↗
Figure 3
Figure 3. FIG. 3. Correlators for the [PITH_FULL_IMAGE:figures/full_fig_p006_3.png] view at source ↗
Figures from the paper (8 more)
Figure 5
Figure 5. Figure 5: FIG. 5. The beat frequency [PITH_FULL_IMAGE:figures/full_fig_p007_5.png]
Figure 4
Figure 4. Figure 4: FIG. 4. (Top) The symmetrized [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 6
Figure 6. Figure 6: FIG. 6. (Top) The renormalized fermion anisotropy [PITH_FULL_IMAGE:figures/full_fig_p007_6.png]
Figure 8
Figure 8. Figure 8: Finally, Mγ0 and Mγ5 are concave functions of c, with a minimum near the tuned value of c. They are thus generally quite robust against mistunings of c, especially Mγ5 . Additional details on the dependence of Mγ0 and Mγ5 on c can be found in Ref. [46]. 4. Smearing Las…
Figure 9
Figure 9. Figure 9: FIG. 9. (Top) The pseudoscalar mass [PITH_FULL_IMAGE:figures/full_fig_p009_9.png]
Figure 10
Figure 10. Figure 10: FIG. 10. Continuum extrapolation of the pion decay constant [PITH_FULL_IMAGE:figures/full_fig_p010_10.png]
Figure 11
Figure 11. Figure 11: FIG. 11. (Top) [PITH_FULL_IMAGE:figures/full_fig_p011_11.png]
Figure 12
Figure 12. Figure 12: FIG. 12. Taste breaking in the KW action, compared to our [PITH_FULL_IMAGE:figures/full_fig_p012_12.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

57 extracted references · 30 canonical work pages

  1. [32]

    Lattice Fermions in Euclidean Space- time,

    L. H. Karsten, “Lattice Fermions in Euclidean Space- time,” Phys. Lett. B 104, 315 (1981)

    work page 1981

  2. [1]

    Tuning the dimension-three counterterm As shown in Ref. [29], in order to tune c it is conve- nient to exploit the existence of oscillating contributions, related to fermion doubling [30], to the correlation func- tions in the direction α of certain meson interpolating operators CΓ(n − m) ∼ ¯ψ(n)Γψ(n) ¯ψ(m)Γψ(m) . (20) Crucially, the frequency of these os...

    work page

  3. [2]

    It is defined as the ratio of the perpendicular (spatial) mass of γ5 to the parallel (temporal) mass: ξf = M⊥/M∥

    Tuning the bare anisotropy ξ0 The physical anisotropy can be determined using a γ5- correlator in a direction perpendicular to α. It is defined as the ratio of the perpendicular (spatial) mass of γ5 to the parallel (temporal) mass: ξf = M⊥/M∥. This allows the tuning of the bare anisotropy ξ0 appearing in the action. Following the procedure shown in Fig. 5...

    work page

  4. [3]

    The final results of the tuning of c and ξ0 at several lattice spacings, with the γ5 mass held constant at this value, are listed in Tables II and III

    Tuning the bare mass m0 In this work, we carry out the tuning procedure first at a value of the pseudoscalar mass Mγ5 = 578.4 MeV. The final results of the tuning of c and ξ0 at several lattice spacings, with the γ5 mass held constant at this value, are listed in Tables II and III. Then, we study the de- pendence of the tuned c and ξ0 values on Mγ5 , down...

    work page

  5. [4]

    half vector trick

    and one gluonic counterterm (of dimension 4) can be defined on the lattice as: S3f = c X x ¯ψ(x)iγαψ(x), S4f = (ξ0 − 1) X x ¯ψ(x) 1 2 γα (Uα(x)ψ(x + ˆα) − U † α(x − ˆα)ψ(x − ˆα)) , S4g = dG X x X µ̸=α Re Tr (1− Pµα(x)) , (3) where Pµα(x) are the plaquettes on the µ-α plane at lattice site x. Throughout this work, we identify the direction α with the tempo...

    work page

  6. [5]

    In princple, each bare parame- ters have to be retuned at a new choice of the smearing level

    Smearing Lastly, we consider the effect of different levels of stout smearing on the tuning. In princple, each bare parame- ters have to be retuned at a new choice of the smearing level. We observe in the top panel of Fig. 9 that the actual pseudo-scalar mass (Mγ5 ) is within error indepen- dent on the smearing level while keeping there bare mass m0 fixed...

    work page

  7. [6]

    Hierarchy To summarize, our tuning procedure proceeds in the following steps:

    work page

  8. [7]

    tune c at fixed bare anisotropy ξ0, for a given pseu- doscalar mass Mγ5 , which can be chosen to be large for numerical convenience

    work page

Show all 57 references
  1. [8]

    repeat the procedure for different ξ0 values, tuning c each time, then interpolate to ξf (ξ0) = 1

  2. [9]

    interpolate the tuned c at the tuned ξ0

  3. [10]

    site-split

    finally, tune the bare mass m0 to fix the physical pseudoscalar mass (c and ξ0 don’t need to be tuned again). 9 2.5 3.0 3.5 4.0 4.5 M 5/(135 MeV) 0.141 0.140 0.139 0.138 0.137 0.136 KW c (tuned) 643×96 = 3.7589, 0 = 1.00 1 2 3 4 M 5/(135 MeV) 0.985 0.990 0.995 1.000 1.005 1.01...

  4. [11]

    Improved Con- tinuum Limit Lattice Action for QCD with Wilson Fermions,

    B. Sheikholeslami and R. Wohlert, “Improved Con- tinuum Limit Lattice Action for QCD with Wilson Fermions,” Nucl.Phys. B259, 572 (1985)

    1985

  5. [12]

    Ab-Initio Determination of Light Hadron Masses,

    S. Durr, Z. Fodor, J. Frison, C. Hoelbling, R. Hoff- mann, et al. , “Ab-Initio Determination of Light Hadron Masses,” Science 322, 1224 (2008), arXiv:0906.3599 [hep- lat]

    2008 arXiv

  6. [13]

    Hamiltonian Formulation of Wilson’s Lattice Gauge Theories,

    J. B. Kogut and L. Susskind, “Hamiltonian Formulation of Wilson’s Lattice Gauge Theories,” Phys. Rev. D 11, 395 (1975)

    1975

  7. [14]

    Rooted staggered fermions: Good, bad or ugly?

    S. R. Sharpe, “Rooted staggered fermions: Good, bad or ugly?” PoS LA T2006, 022 (2006), arXiv:hep- lat/0610094

    2006

  8. [15]

    Breakdown of staggered fermions at nonzero chemical potential,

    M. Golterman, Y. Shamir, and B. Svetitsky, “Breakdown of staggered fermions at nonzero chemical potential,” Phys. Rev. D74, 071501 (2006), arXiv:hep-lat/0602026 [hep-lat]

    2006 arXiv

  9. [16]

    Chiral anomalies and rooted staggered fermions,

    M. Creutz, “Chiral anomalies and rooted staggered fermions,” Phys. Lett. B 649, 230 (2007), arXiv:hep- lat/0701018

    2007

  10. [17]

    Radius of convergence in lattice QCD at finite µB with rooted staggered fermions,

    M. Giordano, K. Kapas, S. D. Katz, D. Nogradi, and A. Pasztor, “Radius of convergence in lattice QCD at finite µB with rooted staggered fermions,” Phys. Rev. D 101, 074511 (2020), arXiv:1911.00043 [hep-lat]

    2020 arXiv

  11. [18]

    Results on finite den- sity QCD,

    I. M. Barbour, S. E. Morrison, E. G. Klepfish, J. B. Kogut, and M.-P. Lombardo, “Results on finite den- sity QCD,” Lattice QCD on parallel computers. Proceed- 13 ings, International Workshop, Tsukuba, Japan, March 10-15, 1997 , Nucl. Phys. Proc. Suppl. 60A, 220 (1998), [,220(1...

    1998 arXiv

  12. [19]

    A New method to study lat- tice QCD at finite temperature and chemical potential,

    Z. Fodor and S. Katz, “A New method to study lat- tice QCD at finite temperature and chemical potential,” Phys.Lett. B534, 87 (2002), arXiv:hep-lat/0104001 [hep- lat]

    2002 arXiv

  13. [20]

    Lattice determination of the crit- ical point of QCD at finite T and mu,

    Z. Fodor and S. Katz, “Lattice determination of the crit- ical point of QCD at finite T and mu,” JHEP 0203, 014 (2002), arXiv:hep-lat/0106002 [hep-lat]

    2002 arXiv

  14. [21]

    Critical point of QCD at finite T and mu, lattice results for physical quark masses,

    Z. Fodor and S. Katz, “Critical point of QCD at finite T and mu, lattice results for physical quark masses,” JHEP 0404, 050 (2004), arXiv:hep-lat/0402006 [hep-lat]

    2004 arXiv

  15. [22]

    QCD simu- lations at small chemical potential,

    P. de Forcrand, S. Kim, and T. Takaishi, “QCD simu- lations at small chemical potential,” Nucl. Phys. B Proc. Suppl. 119, 541 (2003), arXiv:hep-lat/0209126

    2003 arXiv

  16. [23]

    Lat- tice QCD at finite density via a new canonical approach,

    A. Alexandru, M. Faber, I. Horvath, and K.-F. Liu, “Lat- tice QCD at finite density via a new canonical approach,” Phys. Rev. D72, 114513 (2005), arXiv:hep-lat/0507020 [hep-lat]

    2005 arXiv

  17. [24]

    The Density of states method at non-zero chemical potential,

    Z. Fodor, S. D. Katz, and C. Schmidt, “The Density of states method at non-zero chemical potential,” JHEP 0703, 121 (2007), arXiv:hep-lat/0701022 [hep-lat]

    2007 arXiv

  18. [25]

    Applying constrained simulations for low temperature lattice QCD at finite baryon chemical poten- tial,

    G. Endrodi, Z. Fodor, S. D. Katz, D. Sexty, K. K. Szabo, and C. Torok, “Applying constrained simulations for low temperature lattice QCD at finite baryon chemical poten- tial,” Phys. Rev. D98, 074508 (2018), arXiv:1807.08326 [hep-lat]

    2018 arXiv

  19. [26]

    Effect of stout smearing on the phase dia- gram from multiparameter reweighting in lattice QCD,

    M. Giordano, K. Kapas, S. D. Katz, D. Nogradi, and A. Pasztor, “Effect of stout smearing on the phase dia- gram from multiparameter reweighting in lattice QCD,” Phys. Rev. D 102, 034503 (2020), arXiv:2003.04355 [hep- lat]

    2020 arXiv

  20. [27]

    New approach to lattice QCD at finite den- sity; results for the critical end point on coarse lattices,

    M. Giordano, K. Kapas, S. D. Katz, D. Nogradi, and A. Pasztor, “New approach to lattice QCD at finite den- sity; results for the critical end point on coarse lattices,” JHEP 05, 088 (2020), arXiv:2004.10800 [hep-lat]

    2020 arXiv

  21. [28]

    Lattice simulations of the QCD chiral transition at real baryon density,

    S. Borsanyi, Z. Fodor, M. Giordano, S. D. Katz, D. No- gradi, A. Pasztor, and C. H. Wong, “Lattice simulations of the QCD chiral transition at real baryon density,” Phys. Rev. D 105, L051506 (2022), arXiv:2108.09213 [hep-lat]

    2022 arXiv

  22. [29]

    Equation of state of a hot-and-dense quark gluon plasma: Lattice simulations at real µB vs extrapolations,

    S. Borsanyi, Z. Fodor, M. Giordano, J. N. Guenther, S. D. Katz, A. Pasztor, and C. H. Wong, “Equation of state of a hot-and-dense quark gluon plasma: Lattice simulations at real µB vs extrapolations,” Phys. Rev. D107, L091503 (2023), arXiv:2208.05398 [hep-lat]

    2023 arXiv

  23. [30]

    Can rooted staggered fermions describe nonzero baryon density at low temperatures?

    S. Borsanyi, Z. Fodor, M. Giordano, J. N. Guenther, S. D. Katz, A. Pasztor, and C. H. Wong, “Can rooted staggered fermions describe nonzero baryon density at low temperatures?” Phys. Rev. D 109, 054509 (2024), arXiv:2308.06105 [hep-lat]

    2024 arXiv

  24. [31]

    No Go Theorem for Regularizing Chiral Fermions,

    H. B. Nielsen and M. Ninomiya, “No Go Theorem for Regularizing Chiral Fermions,” Phys. Lett. B 105, 219 (1981)

    1981

  25. [33]

    ON LATTICE FERMIONS,

    F. Wilczek, “ON LATTICE FERMIONS,” Phys. Rev. Lett. 59, 2397 (1987)

    1987

  26. [34]

    Four-dimensional graphene and chiral fermions,

    M. Creutz, “Four-dimensional graphene and chiral fermions,” JHEP 04, 017 (2008), arXiv:0712.1201 [hep- lat]

    2008 arXiv

  27. [35]

    Creutz fermions on an orthogonal lattice,

    A. Borici, “Creutz fermions on an orthogonal lattice,” Phys. Rev. D 78, 074504 (2008), arXiv:0712.4401 [hep- lat]

    2008 arXiv

  28. [36]

    Reducing the number of counterterms with new minimally doubled actions,

    S. Capitani, “Reducing the number of counterterms with new minimally doubled actions,” Phys. Rev. D 89, 014501 (2014), arXiv:1307.7497 [hep-lat]

    2014 arXiv

  29. [37]

    New actions for minimally doubled fermions and their counterterms,

    S. Capitani, “New actions for minimally doubled fermions and their counterterms,” PoS LA TTICE2013, 121 (2014), arXiv:1308.4512 [hep-lat]

    2014 arXiv

  30. [38]

    New chiral lattice actions of the Bori¸ ci- Creutz type,

    S. Capitani, “New chiral lattice actions of the Bori¸ ci- Creutz type,” Phys. Rev. D 89, 074508 (2014), arXiv:1311.5664 [hep-lat]

    2014 arXiv

  31. [39]

    Correlation functions with Karsten- Wilczek fermions,

    J. H. Weber, “Correlation functions with Karsten- Wilczek fermions,” PoS LA TTICE2014, 071 (2015), arXiv:1601.06669 [hep-lat]

    2015 arXiv

  32. [40]

    J. H. Weber, Properties of minimally doubled fermions , Ph.D. thesis, Mainz U. (2015), arXiv:1706.07104 [hep- lat]

    2015 arXiv

  33. [41]

    The improvement of hadronic matrix elements in lattice QCD,

    G. Heatlie, G. Martinelli, C. Pittori, G. C. Rossi, and C. T. Sachrajda, “The improvement of hadronic matrix elements in lattice QCD,” Nucl. Phys. B352, 266 (1991)

    1991

  34. [42]

    One-loop improved mini- mally doubled quarks,

    S. Borsanyi and S. Capitani, “One-loop improved mini- mally doubled quarks,” to be submitted (2025)

    2025

  35. [43]

    Topological properties of min- imally doubled fermions in two spacetime dimensions,

    S. D¨ urr and J. H. Weber, “Topological properties of min- imally doubled fermions in two spacetime dimensions,” Phys. Rev. D 105, 114511 (2022), arXiv:2203.15699 [hep- lat]

    2022 arXiv

  36. [44]

    Chiral invariance and lattice fermions with minimal doubling,

    M. Pernici, “Chiral invariance and lattice fermions with minimal doubling,” Phys. Lett. B 346, 99 (1995), arXiv:hep-lat/9411012

    1995 arXiv

  37. [45]

    Broken Symmetries from Minimally Doubled Fermions,

    P. F. Bedaque, M. I. Buchoff, B. C. Tiburzi, and A. Walker-Loud, “Broken Symmetries from Minimally Doubled Fermions,” Phys. Lett. B 662, 449 (2008), arXiv:0801.3361 [hep-lat]

    2008 arXiv

  38. [46]

    Renormalization of minimally doubled fermions,

    S. Capitani, M. Creutz, J. Weber, and H. Wittig, “Renormalization of minimally doubled fermions,” JHEP 09, 027 (2010), arXiv:1006.2009 [hep-lat]

    2010 arXiv

  39. [47]

    Some Predictions for an Improved Fermion Action on the Lattice,

    H. W. Hamber and C. M. Wu, “Some Predictions for an Improved Fermion Action on the Lattice,” Phys. Lett. B 133, 351 (1983)

    1983

  40. [48]

    On-shell Improved Lattice Action for QCD With Susskind Fermions and Asymptotic Freedom Scale,

    S. Naik, “On-shell Improved Lattice Action for QCD With Susskind Fermions and Asymptotic Freedom Scale,” Nucl.Phys. B316, 238 (1989)

    1989

  41. [49]

    Highly improved staggered quarks on the lattice, with applications to charm physics,

    E. Follana et al. (HPQCD Collaboration, UKQCD Col- laboration), “Highly improved staggered quarks on the lattice, with applications to charm physics,” Phys.Rev. D75, 054502 (2007), arXiv:hep-lat/0610092 [hep-lat]

    2007 arXiv

  42. [50]

    Fluctuations and cor- relations in high temperature QCD,

    R. Bellwied, S. Borsanyi, Z. Fodor, S. D. Katz, A. Pasz- tor, C. Ratti, and K. K. Szabo, “Fluctuations and cor- relations in high temperature QCD,” Phys. Rev. D92, 114505 (2015), arXiv:1507.04627 [hep-lat]

    2015 arXiv

  43. [51]

    High precision scale setting on the lattice,

    S. Borsanyi et al. , “High precision scale setting on the lattice,” PoS LA TTICE2021, 371 (2022)

    2022

  44. [52]

    Computational Strategies in Lattice QCD,

    M. Luscher, “Computational Strategies in Lattice QCD,” in Les Houches Summer School: Session 93: Mod- ern perspectives in lattice QCD: Quantum field theory and high performance computing (2010) pp. 331–399, arXiv:1002.4232 [hep-lat]

    2010 arXiv

  45. [53]

    Saad, Iterative Methods for Sparse Linear Systems (Society for Industrial and Applied Mathematics, 2003)

    Y. Saad, Iterative Methods for Sparse Linear Systems (Society for Industrial and Applied Mathematics, 2003)

    2003

  46. [54]

    QCD with Flavored Minimally Dou- bled Fermions,

    J. H. Weber, “QCD with Flavored Minimally Dou- bled Fermions,” PoS LA TTICE2016, 250 (2017), arXiv:1611.08388 [hep-lat]

    2017 arXiv

  47. [55]

    Spin-taste structure of minimally doubled fermions,

    J. H. Weber, “Spin-taste structure of minimally doubled fermions,” in 40th International Symposium on Lattice Field Theory (2023) arXiv:2312.08526 [hep-lat]. 14

    2023 arXiv

  48. [56]

    Renormalization of Karsten- Wilczek Quarks on a Staggered Background,

    D. A. Godzieba, S. Borsanyi, Z. Fodor, P. Parotto, R. A. Vig, and C. H. Wong, “Renormalization of Karsten- Wilczek Quarks on a Staggered Background,” (2024) arXiv:2401.07799 [hep-lat]

    2024 arXiv

  49. [57]

    Leading hadronic contribution to the muon magnetic moment from lattice QCD,

    S. Borsanyi et al., “Leading hadronic contribution to the muon magnetic moment from lattice QCD,” Nature 593, 51 (2021), arXiv:2002.12347 [hep-lat]

    2021 arXiv

Pith tools

Reviewed August 8, 2026 · model on record in the stance chip above.