pith. sign in

arxiv: 2601.18354 · v2 · pith:X4Z5HWZQnew · submitted 2026-01-26 · ✦ hep-lat · nucl-th

Chiral Properties of (2\!+\!1)-Flavor QCD in Magnetic Fields at Zero Temperature

Heng-Tong Ding , Dan Zhang This is my paper

Pith reviewed 2026-05-21 15:15 UTC · model grok-4.3

classification ✦ hep-lat nucl-th
keywords lattice QCDmagnetic fieldschiral condensatepseudoscalar mesonsmagnetic catalysiszero temperaturecontinuum extrapolation
0
0 comments X

The pith

In (2+1)-flavor QCD at zero temperature, magnetic fields make chiral condensates grow while charged pseudoscalar masses rise then slightly fall.

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

The paper uses lattice simulations of QCD with two light quarks and one strange quark at physical masses to study how background magnetic fields change chiral symmetry breaking at zero temperature. It reports that the renormalized chiral condensates increase steadily as the field strength rises up to about 1.2 GeV squared, a pattern called magnetic catalysis. Neutral pseudoscalar mesons show steadily falling masses and strongly rising decay constants, while charged ones display masses that increase at weak fields before saturating or dipping slightly at stronger fields. The work separates sea-quark and valence-quark effects and finds that valence contributions drive most of the observed changes.

Core claim

In (2+1)-flavor QCD at zero temperature, the renormalized chiral condensates increase monotonically with the magnetic field strength up to eB ≈ 1.2 GeV², demonstrating magnetic catalysis. Neutral pseudoscalar masses decrease with increasing eB, while charged pseudoscalar masses rise at small fields before saturating and slightly decreasing at larger fields. Neutral pseudoscalar decay constants are strongly enhanced, and the magnetic-field-induced shifts in Gell-Mann--Oakes--Renner relations are small for the neutral pion but sizable for the neutral kaon. Valence-quark contributions dominate the magnetic response over sea-quark effects.

What carries the argument

Separation of sea- and valence-quark contributions to meson masses, computed with the highly improved staggered quark action on four lattice spacings for continuum extrapolation.

If this is right

  • Chiral symmetry breaking strengthens monotonically with magnetic field strength at zero temperature.
  • Charged pseudoscalar masses show nonmonotonic dependence on the field due to internal quark structure effects beyond the lowest Landau level.
  • Neutral pseudoscalar decay constants increase strongly with the magnetic field.
  • Valence quark effects account for the dominant share of the magnetic response, with sea quarks playing a smaller role at zero temperature.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Simplified models that treat only valence quarks in a magnetic background may reproduce the leading magnetic response at zero temperature.
  • The observed nonmonotonic charged-meson behavior could affect estimates of meson properties in the strong fields produced in heavy-ion collisions.
  • Repeating the analysis at small but nonzero temperature would test how the zero-temperature valence dominance changes when thermal effects are added.

Load-bearing premise

Results from simulations at four lattice spacings can be reliably extrapolated to zero spacing and the renormalization of the condensates stays accurate and independent of field strength.

What would settle it

A continuum-extrapolated calculation in which the chiral condensates stop increasing with field strength or in which charged pseudoscalar masses keep rising without saturation or decline would contradict the reported behaviors.

Figures

Figures reproduced from arXiv: 2601.18354 by Dan Zhang, Heng-Tong Ding.

Figure 1
Figure 1. Figure 1: FIG. 1. Temporal correlators [PITH_FULL_IMAGE:figures/full_fig_p006_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3. Masses of neutral pseudoscalar meson as functions [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: Here, the comparison is made at the same ex [PITH_FULL_IMAGE:figures/full_fig_p007_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4. Masses of charged pseudoscalar mesons as functions [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5. Ratio of the neutral pion mass components, [PITH_FULL_IMAGE:figures/full_fig_p008_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6. Similar as Fig. 5 for [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: FIG. 7. Ratio of the temporal correlation functions, [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗
Figure 10
Figure 10. Figure 10: FIG. 10. Continuum extrapolated results for combination of [PITH_FULL_IMAGE:figures/full_fig_p010_10.png] view at source ↗
Figure 9
Figure 9. Figure 9: FIG. 9. Same as Fig. 8 but for kaons [PITH_FULL_IMAGE:figures/full_fig_p010_9.png] view at source ↗
Figure 12
Figure 12. Figure 12: FIG. 12. Flavor decomposition of the connected neutral-pion [PITH_FULL_IMAGE:figures/full_fig_p011_12.png] view at source ↗
Figure 11
Figure 11. Figure 11: FIG. 11. Decay constants of neutral pseudoscalar mesons as [PITH_FULL_IMAGE:figures/full_fig_p011_11.png] view at source ↗
Figure 13
Figure 13. Figure 13: FIG. 13. Renormalized chiral condensates as functions of [PITH_FULL_IMAGE:figures/full_fig_p012_13.png] view at source ↗
Figure 14
Figure 14. Figure 14: FIG. 14. Magnetic-field-induced shift of the GMOR correc [PITH_FULL_IMAGE:figures/full_fig_p013_14.png] view at source ↗
Figure 15
Figure 15. Figure 15: FIG. 15. Comparison of pseudoscalar pion masses extracted [PITH_FULL_IMAGE:figures/full_fig_p015_15.png] view at source ↗
Figure 18
Figure 18. Figure 18: FIG. 18. Representative continuum extrapolation of the neu [PITH_FULL_IMAGE:figures/full_fig_p016_18.png] view at source ↗
Figure 16
Figure 16. Figure 16: FIG. 16. Same as Fig. 15 but for kaons [PITH_FULL_IMAGE:figures/full_fig_p016_16.png] view at source ↗
Figure 17
Figure 17. Figure 17: FIG. 17. Representative continuum extrapolation of the neu [PITH_FULL_IMAGE:figures/full_fig_p016_17.png] view at source ↗
read the original abstract

We present a lattice QCD study of the chiral properties of $(2\!+\!1)$-flavor QCD in background magnetic fields at zero temperature with physical pion masses. Simulations are performed using the highly improved staggered quark action across four different lattice spacings to enable a controlled continuum extrapolation. We compute the renormalized chiral condensates together with pseudoscalar meson masses and decay constants for pions, kaons, and the fictitious $\eta^0_{s\bar{s}}$ pseudoscalar as functions of the magnetic-field strength $eB$ up to $eB\simeq1.2$ $\mathrm{GeV}^2$. The chiral condensates exhibit clear magnetic catalysis, increasing monotonically with the field strength. In the meson sector, neutral pseudoscalar masses decrease steadily with $eB$, whereas charged pseudoscalar masses display a nonmonotonic response: They rise at small fields, consistent with the lowest-Landau-level expectation, but then saturate and slightly decrease at larger fields, signaling sizable internal-structure effects. At the same time, neutral pseudoscalar decay constants are strongly enhanced by the magnetic field. To quantify deviations from chiral symmetry relations, we isolate the magnetic-field-induced shift in the Gell-Mann--Oakes--Renner corrections and find it to remain small for the neutral pion but to become sizable for the neutral kaon. To elucidate the origin of the magnetic response, we separately analyze the sea- and valence-quark contributions to both neutral and charged meson masses, finding that valence effects dominate at zero temperature. These results provide new insights into the interplay between QCD chiral symmetry breaking and strong magnetic fields.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 1 minor

Summary. The manuscript presents a (2+1)-flavor lattice QCD study at physical pion masses and zero temperature using the HISQ action on four lattice spacings. It computes renormalized chiral condensates, pseudoscalar masses, and decay constants for neutral and charged pions, kaons, and the fictitious η_s as functions of eB up to ~1.2 GeV². Key findings include monotonic magnetic catalysis in the condensates, non-monotonic response of charged-meson masses, strong enhancement of neutral decay constants, small GMOR deviations for the neutral pion but larger for the kaon, and valence-quark dominance in the magnetic response.

Significance. If the central results hold after addressing discretization concerns, the work supplies useful continuum-extrapolated lattice data on chiral symmetry breaking in strong magnetic fields, relevant to heavy-ion phenomenology. Strengths include the use of physical masses, direct separation of sea/valence contributions, and an explicit attempt at continuum extrapolation; these elements make the numerical evidence more robust than single-spacing studies.

major comments (2)
  1. [Continuum extrapolation section] Section on continuum extrapolation (likely §4 or §5): The central claims of monotonic catalysis, non-monotonic charged-meson masses, and valence dominance rest on quantities extrapolated from only four lattice spacings. When eB reaches 1.2 GeV² the magnetic length 1/√(eB) becomes comparable to a on the coarsest ensembles, potentially introducing O(a² eB) artifacts not removed by a simple a² fit performed at fixed eB. No plots or discussion of residuals versus a√(eB) are referenced, leaving the reliability of the reported field dependence uncertain.
  2. [Renormalization subsection] Renormalization subsection: The chiral condensate is stated to be renormalized in a field-independent manner, yet no explicit test (e.g., comparison of renormalization factors across eB values or check of multiplicative Z_m(eB/a²)) is provided. Any residual eB dependence in the renormalization would directly affect the magnitude of the reported magnetic catalysis and the GMOR deviation analysis.
minor comments (1)
  1. [Introduction or Methods] Notation for the fictitious η_s pseudoscalar is introduced in the abstract but should be defined more explicitly when first used in the text to avoid ambiguity for readers unfamiliar with the convention.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading of our manuscript and the constructive comments, which help clarify the presentation of our continuum-extrapolated results. We address each major comment below and outline the revisions we will implement.

read point-by-point responses

  1. Referee: [Continuum extrapolation section] Section on continuum extrapolation (likely §4 or §5): The central claims of monotonic catalysis, non-monotonic charged-meson masses, and valence dominance rest on quantities extrapolated from only four lattice spacings. When eB reaches 1.2 GeV² the magnetic length 1/√(eB) becomes comparable to a on the coarsest ensembles, potentially introducing O(a² eB) artifacts not removed by a simple a² fit performed at fixed eB. No plots or discussion of residuals versus a√(eB) are referenced, leaving the reliability of the reported field dependence uncertain.

    Authors: We agree that potential O(a² eB) discretization effects merit explicit scrutiny when the magnetic length approaches the lattice spacing. Our continuum extrapolations were performed at fixed eB using linear a² fits across the four available spacings, and the resulting trends (monotonic catalysis, non-monotonic charged-meson masses, and valence dominance) remain stable. To strengthen the evidence, we will add plots of the raw data versus a√(eB) together with fit residuals in the revised manuscript. These additions will demonstrate that the observed field dependence is not driven by uncontrolled artifacts on the coarsest ensembles. revision: yes

  2. Referee: [Renormalization subsection] Renormalization subsection: The chiral condensate is stated to be renormalized in a field-independent manner, yet no explicit test (e.g., comparison of renormalization factors across eB values or check of multiplicative Z_m(eB/a²)) is provided. Any residual eB dependence in the renormalization would directly affect the magnitude of the reported magnetic catalysis and the GMOR deviation analysis.

    Authors: The renormalization constants were determined from zero-field simulations and applied uniformly, following standard practice for such studies. We acknowledge that an explicit cross-check of possible eB dependence would increase confidence in the reported catalysis and GMOR results. In the revised version we will include a direct comparison of the renormalization factors extracted at different eB values (where feasible) and discuss the consistency of the multiplicative Z_m procedure, thereby confirming the field-independent assumption. revision: yes

Circularity Check

0 steps flagged

No circularity: direct lattice computations of observables

full rationale

This is a numerical lattice QCD study that computes chiral condensates, pseudoscalar masses, and decay constants directly from the HISQ action on gauge configurations generated at physical pion masses and zero temperature. The reported trends (monotonic increase in condensates, non-monotonic charged-meson masses, valence dominance) are extracted from these simulations and subsequent continuum extrapolations at fixed eB; no step reduces a claimed prediction or first-principles result to a fitted parameter or self-citation by construction. Standard renormalization and extrapolation procedures are applied to the raw lattice data rather than presupposing the final physical signals.

Axiom & Free-Parameter Ledger

1 free parameters · 1 axioms · 0 invented entities

The study rests on the standard lattice-QCD framework with physical quark masses and a background magnetic field implemented via the staggered action; no new free parameters beyond conventional lattice spacing and quark-mass tuning are introduced in the abstract.

free parameters (1)
  • lattice spacings
    Four different lattice spacings are used to perform the continuum extrapolation; their specific values are not stated in the abstract.
axioms (1)
  • domain assumption The highly improved staggered quark action with physical pion masses faithfully reproduces (2+1)-flavor QCD at zero temperature.
    Standard assumption invoked when choosing the fermion discretization and quark-mass tuning.

pith-pipeline@v0.9.0 · 5831 in / 1397 out tokens · 49372 ms · 2026-05-21T15:15:35.231433+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/AbsoluteFloorClosure.lean reality_from_one_distinction unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We present a lattice QCD study of the chiral properties of (2+1)-flavor QCD in background magnetic fields at zero temperature with physical pion masses. Simulations are performed using the highly improved staggered quark action across four different lattice spacings to enable a controlled continuum extrapolation.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Forward citations

Cited by 5 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Mass spectra of charged mesons and the quenching of vector meson condensation via exact phase-space diagonalization

    hep-ph 2026-04 unverdicted novelty 7.0

    In the NJL model with exact phase-space diagonalization, magnetic catalysis of the chiral condensate quenches the tachyonic instability of the spin-aligned rho+ by driving the 2M threshold above the Zeeman-lowered mas...

  2. Meson Octet in a Uniform Magnetic Field

    hep-ph 2026-05 unverdicted novelty 6.0

    Next-to-leading order chiral perturbation theory yields renormalized magnetic masses and decay constants for the meson octet, with neutral pion mass decreasing, neutral kaon mass unchanged, charged meson masses modifi...

  3. QCD phase transition at finite isospin density and magnetic field

    nucl-th 2026-03 unverdicted novelty 5.0

    In the NJL model, increasing isospin chemical potential favors pion superfluidity at small magnetic fields and rho superconductivity at large magnetic fields.

  4. Delineating neutral and charged mesons in magnetic fields

    hep-ph 2026-04 unverdicted novelty 4.0

    Neutral mesons conserve continuous transverse momenta in magnetic fields while charged mesons exhibit quantized transverse dynamics, with high-spin charged mesons stabilized by cancellation of internal zero-point ener...

  5. Lattice QCD at finite temperature and density

    hep-lat 2026-03 unverdicted novelty 2.0

    A review of lattice QCD findings on the finite-temperature QCD transition at zero baryon chemical potential, its chiral limit behavior, constraints on the phase boundary and critical endpoint at finite density, plus a...

Reference graph

Works this paper leans on

105 extracted references · 105 canonical work pages · cited by 5 Pith papers · 58 internal anchors

  1. [1]

    The effects of topological charge change in heavy ion collisions: "Event by event P and CP violation"

    D.E. Kharzeev, L.D. McLerran and H.J. Warringa, The Effects of topological charge change in heavy ion collisions: ’Event by event P and CP violation’,Nucl. Phys.A803(2008) 227 [0711.0950]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  2. [2]

    Estimate of the magnetic field strength in heavy-ion collisions

    V. Skokov, A.Y. Illarionov and V. Toneev,Estimate of the magnetic field strength in heavy-ion collisions,Int. J. Mod. Phys.A24(2009) 5925 [0907.1396]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  3. [3]

    Event-by-event generation of electromagnetic fields in heavy-ion collisions

    W.-T. Deng and X.-G. Huang,Event-by-event generation of electromagnetic fields in heavy-ion collisions,Phys. Rev.C85(2012) 044907 [1201.5108]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  4. [4]

    Vachaspati,Magnetic fields from cosmological phase transitions,Phys

    T. Vachaspati,Magnetic fields from cosmological phase transitions,Phys. Lett.B265(1991) 258

    work page 1991

  5. [5]

    Duncan and C

    R.C. Duncan and C. Thompson,Formation of very strongly magnetized neutron stars - implications for gamma-ray bursts,Astrophys. J. Lett.392(1992) L9

    work page 1992

  6. [6]

    Hattori, K

    K. Hattori, K. Itakura and S. Ozaki,Strong-field physics in QED and QCD: From fundamentals to applications,Prog. Part. Nucl. Phys.133(2023) 104068 [2305.03865]

    work page arXiv 2023

  7. [7]

    Endrodi,QCD with background electromagnetic fields on the lattice: A review,Prog

    G. Endrodi,QCD with background electromagnetic fields on the lattice: A review,Prog. Part. Nucl. Phys. 141(2025) 104153 [2406.19780]

    work page arXiv 2025

  8. [8]

    Yamamoto,Overview of external electromagnetism and rotation in lattice QCD,Eur

    A. Yamamoto,Overview of external electromagnetism and rotation in lattice QCD,Eur. Phys. J. A57 (2021) 211 [2103.00237]

    work page arXiv 2021

  9. [9]

    QCD Phase Transition in a Strong Magnetic Background

    M. D’Elia, S. Mukherjee and F. Sanfilippo,QCD Phase Transition in a Strong Magnetic Background, Phys. Rev.D82(2010) 051501 [1005.5365]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  10. [10]

    Magnetic Catalysis: A Review

    I.A. Shovkovy,Magnetic Catalysis: A Review,Lect. Notes Phys.871(2013) 13 [1207.5081]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  11. [11]

    H.-T. Ding, C. Schmidt, A. Tomiya and X.-D. Wang, Chiral phase structure of three flavor QCD in a background magnetic field,Phys. Rev. D102(2020) 054505 [2006.13422]

    work page arXiv 2020

  12. [12]

    G.S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S.D. Katz, S. Krieg et al.,The QCD phase diagram for external magnetic fields,JHEP02(2012) 044 [1111.4956]. 18

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  13. [13]

    G.S. Bali, F. Bruckmann, G. Endrodi, Z. Fodor, S.D. Katz and A. Schafer,QCD quark condensate in external magnetic fields,Phys. Rev.D86(2012) 071502 [1206.4205]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  14. [14]

    Magnetic catalysis (and inverse catalysis) at finite temperature in two-color lattice QCD

    E.M. Ilgenfritz, M. Muller-Preussker, B. Petersson and A. Schreiber,Magnetic catalysis (and inverse catalysis) at finite temperature in two-color lattice QCD,Phys. Rev.D89(2014) 054512 [1310.7876]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  15. [15]

    Deconfinement transition in two-flavour lattice QCD with dynamical overlap fermions in an external magnetic field

    V.G. Bornyakov, P.V. Buividovich, N. Cundy, O.A. Kochetkov and A. Sch¨ afer,Deconfinement transition in two-flavor lattice QCD with dynamical overlap fermions in an external magnetic field,Phys. Rev.D90(2014) 034501 [1312.5628]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  16. [16]

    G.S. Bali, F. Bruckmann, G. Endr¨ odi, S.D. Katz and A. Sch¨ afer,The QCD equation of state in background magnetic fields,JHEP08(2014) 177 [1406.0269]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  17. [17]

    Phase structure of three flavor QCD in external magnetic fields using HISQ fermions

    A. Tomiya, H.-T. Ding, X.-D. Wang, Y. Zhang, S. Mukherjee and C. Schmidt,Phase structure of three flavor QCD in external magnetic fields using HISQ fermions,PoSLA TTICE2018(2019) 163 [1904.01276]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  18. [18]

    Chiral Properties of Strong Interactions in a Magnetic Background

    M. D’Elia and F. Negro,Chiral Properties of Strong Interactions in a Magnetic Background,Phys. Rev. D 83(2011) 114028 [1103.2080]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  19. [19]

    Phase diagram of QCD in a magnetic field: A review

    J.O. Andersen, W.R. Naylor and A. Tranberg,Phase diagram of QCD in a magnetic field: A review,Rev. Mod. Phys.88(2016) 025001 [1411.7176]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  20. [20]

    The quark mass gap in a magnetic field

    T. Kojo and N. Su,The quark mass gap in a magnetic field,Phys. Lett.B720(2013) 192 [1211.7318]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  21. [21]

    Inverse magnetic catalysis and the Polyakov loop

    F. Bruckmann, G. Endrodi and T.G. Kovacs,Inverse magnetic catalysis and the Polyakov loop,JHEP04 (2013) 112 [1303.3972]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  22. [22]

    Magnetic Catalysis vs Magnetic Inhibition

    K. Fukushima and Y. Hidaka,Magnetic Catalysis Versus Magnetic Inhibition,Phys. Rev. Lett.110 (2013) 031601 [1209.1319]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  23. [23]

    Inverse magnetic catalysis in the (2+1)-flavor Nambu--Jona-Lasinio and Polyakov--Nambu--Jona-Lasinio models

    M. Ferreira, P. Costa, O. Louren¸ co, T. Frederico and C. Providˆ encia,Inverse magnetic catalysis in the (2+1)-flavor Nambu-Jona-Lasinio and Polyakov-Nambu-Jona-Lasinio models,Phys. Rev. D89(2014) 116011 [1404.5577]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  24. [24]

    L. Yu, H. Liu and M. Huang,Spontaneous generation of local CP violation and inverse magnetic catalysis, Phys. Rev. D90(2014) 074009 [1404.6969]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  25. [25]

    B. Feng, D. Hou, H.-c. Ren and P.-p. Wu, Bose-Einstein Condensation of Bound Pairs of Relativistic Fermions in a Magnetic Field,Phys. Rev. D93(2016) 085019 [1512.08894]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  26. [26]

    Thermodynamics of 2+1 Flavor Polyakov-Loop Quark-Meson Model under External Magnetic Field

    X. Li, W.-J. Fu and Y.-X. Liu,Thermodynamics of 2+1 Flavor Polyakov-Loop Quark-Meson Model under External Magnetic Field,Phys. Rev.D99(2019) 074029 [1902.03866]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  27. [27]

    From Inverse to Delayed Magnetic Catalysis in Strong Magnetic Field

    S. Mao,From inverse to delayed magnetic catalysis in a strong magnetic field,Phys. Rev.D94(2016) 036007 [1605.04526]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  28. [28]

    Inverse Magnetic Catalysis from improved Holographic QCD in the Veneziano limit

    U. G¨ ursoy, I. Iatrakis, M. J¨ arvinen and G. Nijs, Inverse Magnetic Catalysis from improved Holographic QCD in the Veneziano limit,JHEP03(2017) 053 [1611.06339]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  29. [29]

    K. Xu, J. Chao and M. Huang,Effect of the anomalous magnetic moment of quarks on magnetized QCD matter and meson spectra,Phys. Rev. D103 (2021) 076015 [2007.13122]

    work page arXiv 2021

  30. [30]

    Abreu, E.B.S

    L.M. Abreu, E.B.S. Corrˆ ea and E.S. Nery,Inverse magnetic catalysis and size-dependent effects on the chiral symmetry restoration,Eur. Phys. J. A59(2023) 157 [2211.11083]

    work page arXiv 2023

  31. [31]

    Li and S

    L. Li and S. Mao,Mass spectra and Mott transitions of neutral mesons at finite temperature and magnetic field in frame of three-flavor Polyakov-extended Nambu-Jona-Lasino model,2511.14150

    work page arXiv

  32. [32]

    Mao,Reduction of pseudocritical temperatures of chiral restoration and deconfinement phase transitions in a magnetized PNJL model,Phys

    S. Mao,Reduction of pseudocritical temperatures of chiral restoration and deconfinement phase transitions in a magnetized PNJL model,Phys. Rev. D110 (2024) 054002 [2404.05294]

    work page arXiv 2024

  33. [33]

    Hofmann,Chiral Perturbation Theory Analysis of the Quark Condensate in a Magnetic Field,Phys

    C.P. Hofmann,Chiral Perturbation Theory Analysis of the Quark Condensate in a Magnetic Field,Phys. Rev. D102(2020) 094010 [2006.07717]

    work page arXiv 2020

  34. [34]

    QCD phase diagram in a magnetic background for different values of the pion mass

    M. D’Elia, F. Manigrasso, F. Negro and F. Sanfilippo, QCD phase diagram in a magnetic background for different values of the pion mass,Phys. Rev.D98 (2018) 054509 [1808.07008]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  35. [35]

    Endrodi, M

    G. Endrodi, M. Giordano, S.D. Katz, T.G. Kov´ acs and F. Pittler,Magnetic catalysis and inverse catalysis for heavy pions,JHEP07(2019) 007 [1904.10296]

    work page arXiv 2019

  36. [36]

    Magnetic field effects on the static quark potential at zero and finite temperature

    C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro, A. Rucci et al.,Magnetic field effects on the static quark potential at zero and finite temperature,Phys. Rev.D94(2016) 094007 [1607.08160]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  37. [37]

    Gell-Mann, R.J

    M. Gell-Mann, R.J. Oakes and B. Renner,Behavior of current divergences under SU(3) x SU(3),Phys. Rev. 175(1968) 2195

    work page 1968

  38. [38]

    Flavour-symmetry breaking of the quark condensate and chiral corrections to the Gell-Mann-Oakes-Renner relation

    M. Jamin,Flavor symmetry breaking of the quark condensate and chiral corrections to the Gell-Mann-Oakes-Renner relation,Phys. Lett. B538 (2002) 71 [hep-ph/0201174]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  39. [39]

    Chiral corrections to the $SU(2)\times SU(2)$ Gell-Mann-Oakes-Renner relation

    J. Bordes, C. Dominguez, P. Moodley, J. Penarrocha and K. Schilcher,Chiral corrections to the SU(2)×SU(2)Gell-Mann-Oakes-Renner relation, JHEP05(2010) 064 [1003.3358]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  40. [40]

    Corrections to the ${\bf SU(3)\times SU(3)}$ Gell-Mann-Oakes-Renner relation and chiral couplings $L^r_8$ and $H^r_2$

    J. Bordes, C. Dominguez, P. Moodley, J. Penarrocha and K. Schilcher,Corrections to theSU(3)×SU(3) Gell-Mann-Oakes-Renner relation and chiral couplings Lr 8 andH r 2,JHEP10(2012) 102 [1208.1159]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  41. [41]

    Dynamical Twisted Mass Fermions with Light Quarks

    J. Gasser and H. Leutwyler,Chiral Perturbation Theory: Expansions in the Mass of the Strange Quark, Nucl. Phys. B250(1985) 465. [42]ETMcollaboration,Dynamical twisted mass fermions with light quarks,Phys. Lett.B650(2007) 304 [hep-lat/0701012]

    work page internal anchor Pith review Pith/arXiv arXiv 1985

  42. [42]

    Chiral symmetry breaking in QCD Lite

    G.P. Engel, L. Giusti, S. Lottini and R. Sommer, Chiral Symmetry Breaking in QCD with Two Light Flavors,Phys. Rev. Lett.114(2015) 112001 [1406.4987]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  43. [43]

    Gasser and H

    J. Gasser and H. Leutwyler,Light Quarks at Low Temperatures,Phys. Lett.B184(1987) 83

    work page 1987

  44. [44]

    Quark condensate in a magnetic field

    I.A. Shushpanov and A.V. Smilga,Quark condensate in a magnetic field,Phys. Lett.B402(1997) 351 [hep-ph/9703201]

    work page internal anchor Pith review Pith/arXiv arXiv 1997

  45. [45]

    Gell-Mann - Oakes - Renner relation in a magnetic field at finite temperature

    N.O. Agasian and I.A. Shushpanov, Gell-Mann-Oakes-Renner relation in a magnetic field at finite temperature,JHEP10(2001) 006 [hep-ph/0107128]

    work page internal anchor Pith review Pith/arXiv arXiv 2001

  46. [46]

    Adhikari and B.C

    P. Adhikari and B.C. Tiburzi,Chiral Symmetry Breaking and Pion Decay in a Magnetic Field, 2406.00818

    work page arXiv

  47. [47]

    Ding et al.,Chiral Phase Transition Temperature in ( 2+1 )-Flavor QCD,Phys

    H.T. Ding et al.,Chiral Phase Transition Temperature in ( 2+1 )-Flavor QCD,Phys. Rev. Lett.123(2019) 062002 [1903.04801]. 19

    work page arXiv 2019

  48. [48]

    Ding,New developments in lattice QCD on equilibrium physics and phase diagram,Nucl

    H.-T. Ding,New developments in lattice QCD on equilibrium physics and phase diagram,Nucl. Phys. A 1005(2021) 121940 [2002.11957]

    work page arXiv 2021

  49. [49]

    Chiral phase structure of three flavor QCD at vanishing baryon number density

    A. Bazavov, H.T. Ding, P. Hegde, F. Karsch, E. Laermann, S. Mukherjee et al.,Chiral phase structure of three flavor QCD at vanishing baryon number density,Phys. Rev.D95(2017) 074505 [1701.03548]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  50. [50]

    Kotov, M.P

    A.Y. Kotov, M.P. Lombardo and A. Trunin,QCD transition at the physical point, and its scaling window from twisted mass Wilson fermions,Phys. Lett. B823 (2021) 136749 [2105.09842]

    work page arXiv 2021

  51. [51]

    Aarts et al.,Properties of the QCD thermal transition with Nf=2+1 flavors of Wilson quark,Phys

    G. Aarts et al.,Properties of the QCD thermal transition with Nf=2+1 flavors of Wilson quark,Phys. Rev. D105(2022) 034504 [2007.04188]

    work page arXiv 2022

  52. [52]

    The QCD phase transition with physical-mass, chiral quarks

    T. Bhattacharya et al.,QCD Phase Transition with Chiral Quarks and Physical Quark Masses,Phys. Rev. Lett.113(2014) 082001 [1402.5175]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  53. [53]

    O(4) scaling analysis in two-flavor QCD at finite temperature and density with improved Wilson quarks

    T. Umeda, S. Ejiri, R. Iwami, K. Kanaya, H. Ohno, A. Uji et al.,O(4) scaling analysis in two-flavor QCD at finite temperature and density with improved Wilson quarks,PoSLA TTICE2016(2017) 376 [1612.09449]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  54. [54]

    Li and H

    S. Li and H. Ding,Chiral Crossover and Chiral Phase Transition Temperatures from Lattice QCD,Nucl. Phys. Rev.37(2020) 674

    work page 2020

  55. [55]

    Mesons in strong magnetic fields: (I) General analyses

    K. Hattori, T. Kojo and N. Su,Mesons in strong magnetic fields: (I) General analyses,Nucl. Phys. A951(2016) 1 [1512.07361]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  56. [56]

    $\pi_0$ pole mass calculation in a strong magnetic field and lattice constraints

    S.S. Avancini, R.L.S. Farias, M. Benghi Pinto, W.R. Tavares and V.S. Tim´ oteo,π0 pole mass calculation in a strong magnetic field and lattice constraints,Phys. Lett. B767(2017) 247 [1606.05754]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  57. [57]

    Meson properties in magnetized quark matter

    Z. Wang and P. Zhuang,Meson properties in magnetized quark matter,Phys. Rev.D97(2018) 034026 [1712.00554]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  58. [58]

    Pions in magnetic field at finite temperature

    S. Mao,Pions in magnetic field at finite temperature, Phys. Rev.D99(2019) 056005 [1808.10242]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  59. [59]

    Neutral meson properties in hot and magnetized quark matter: a new magnetic field independent regularization scheme applied to NJL-type model

    S.S. Avancini, R.L.S. Farias and W.R. Tavares,Neutral meson properties in hot and magnetized quark matter: a new magnetic field independent regularization scheme applied to NJL-type model,Phys. Rev.D99 (2019) 056009 [1812.00945]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  60. [60]

    Coppola, D

    M. Coppola, D. Gomez Dumm, S. Noguera and N.N. Scoccola,Neutral and charged pion properties under strong magnetic fields in the NJL model,Phys. Rev.D100(2019) 054014 [1907.05840]

    work page arXiv 2019

  61. [61]

    Cao,Magnetic catalysis effect prevents vacuum superconductivity in strong magnetic fields,Phys

    G. Cao,Magnetic catalysis effect prevents vacuum superconductivity in strong magnetic fields,Phys. Rev. D100(2019) 074024 [1906.01398]

    work page arXiv 2019

  62. [62]

    K. Xu, S. Shi, H. Zhang, D. Hou, J. Liao and M. Huang,Extracting the magnitude of magnetic field at freeze-out in heavy-ion collisions,Phys. Lett. B809 (2020) 135706 [2004.05362]

    work page arXiv 2020

  63. [63]

    Kojo,Neutral and charged mesons in magnetic fields: A resonance gas in a non-relativistic quark model,Eur

    T. Kojo,Neutral and charged mesons in magnetic fields: A resonance gas in a non-relativistic quark model,Eur. Phys. J. A57(2021) 317 [2104.00376]

    work page arXiv 2021

  64. [64]

    Z. Xing, J. Chao, L. Chang and Y.-x. Liu,Exposing the effect of the p-wave component in the pion triplet under a strong magnetic field,Phys. Rev. D105 (2022) 114003 [2110.01245]

    work page arXiv 2022

  65. [65]

    J. Mei, T. Xia and S. Mao,Mass spectra of neutral mesons K0,π0,η,η’ at finite magnetic field, temperature and quark chemical potential,Phys. Rev. D107(2023) 074018 [2212.04778]

    work page arXiv 2023

  66. [66]

    Coppola, D

    M. Coppola, D. Gomez Dumm, S. Noguera and N.N. Scoccola,Masses of magnetized pseudoscalar and vector mesons in an extended NJL model: The role of axial vector mesons,Phys. Rev. D109(2024) 054014 [2312.16675]

    work page arXiv 2024

  67. [67]

    R. Wen, S. Yin, W.-j. Fu and M. Huang,Functional renormalization group study of neutral and charged pions in magnetic fields in the quark-meson model, Phys. Rev. D108(2023) 076020 [2306.04045]

    work page arXiv 2023

  68. [68]

    QCD determination of the magnetic field dependence of QCD and hadronic parameters

    C. Dominguez, M. Loewe and C. Villavicencio,QCD determination of the magnetic field dependence of QCD and hadronic parameters,Phys. Rev. D98 (2018) 034015 [1806.10088]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  69. [69]

    Magnetic field-dependence of the neutral pion mass in the linear sigma model coupled to quarks: The weak field case

    A. Ayala, R.L.S. Farias, S. Hern´ andez-Ortiz, L.A. Hern´ andez, D.M. Paret and R. Zamora,Magnetic field-dependence of the neutral pion mass in the linear sigma model coupled to quarks: The weak field case, Phys. Rev. D98(2018) 114008 [1809.08312]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  70. [70]

    Chiral pions in a magnetic background

    G. Colucci, E.S. Fraga and A. Sedrakian,Chiral pions in a magnetic background,Phys. Lett. B728(2014) 19 [1310.3742]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  71. [71]

    Charged vector mesons in a strong magnetic field

    Y. Hidaka and A. Yamamoto,Charged vector mesons in a strong magnetic field,Phys. Rev.D87(2013) 094502 [1209.0007]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  72. [72]

    Superconductivity of QCD vacuum in strong magnetic field

    M.N. Chernodub,Superconductivity of QCD vacuum in strong magnetic field,Phys. Rev.D82(2010) 085011 [1008.1055]

    work page internal anchor Pith review Pith/arXiv arXiv 2010

  73. [73]

    Spontaneous electromagnetic superconductivity of vacuum in strong magnetic field: evidence from the Nambu--Jona-Lasinio model

    M.N. Chernodub,Spontaneous electromagnetic superconductivity of vacuum in strong magnetic field: evidence from the Nambu–Jona-Lasinio model,Phys. Rev. Lett.106(2011) 142003 [1101.0117]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  74. [74]

    The $\rho$ and $A$ mesons in strong abelian magnetic field in SU(2) lattice gauge theory

    E.V. Luschevskaya and O.V. Larina,TheρandA mesons in a strong abelian magnetic field inSU(2) lattice gauge theory,Nucl. Phys.B884(2014) 1 [1203.5699]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  75. [75]

    Magnetic polarizabilities of light mesons in $SU(3)$ lattice gauge theory

    E.V. Luschevskaya, O.E. Solovjeva, O.A. Kochetkov and O.V. Teryaev,Magnetic polarizabilities of light mesons inSU(3)lattice gauge theory,Nucl. Phys. B898(2015) 627 [1411.4284]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  76. [76]

    Magnetic polarizability of pion

    E. Luschevskaya, O. Solovjeva and O. Teryaev, Magnetic polarizability of pion,Phys. Lett. B761 (2016) 393 [1511.09316]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  77. [77]

    Meson masses in electromagnetic fields with Wilson fermions

    G.S. Bali, B.B. Brandt, G. Endr˝ odi and B. Gl¨ aßle, Meson masses in electromagnetic fields with Wilson fermions,Phys. Rev.D97(2018) 034505 [1707.05600]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  78. [78]

    Weak decay of magnetized pions

    G.S. Bali, B.B. Brandt, G. Endr˝ odi and B. Gl¨ aßle, Weak decay of magnetized pions,Phys. Rev. Lett.121 (2018) 072001 [1805.10971]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  79. [79]

    Coppola, D

    M. Coppola, D. Gomez Dumm, S. Noguera and N.N. Scoccola,Pion-to-vacuum vector and axial vector amplitudes and weak decays of pions in a magnetic field,Phys. Rev.D99(2019) 054031 [1810.08110]

    work page arXiv 2019

  80. [80]

    Coppola, D

    M. Coppola, D. Gomez Dumm, S. Noguera and N.N. Scoccola,Magnetic field driven enhancement of the weak decay width of charged pions,JHEP09 (2020) 058 [1908.10765]

    work page arXiv 2020

Showing first 80 references.