Pith. sign in

REVIEW 3 major objections 4 minor 1 cited by

This paper predicts that strong magnetic fields, by weakening the confining force along the field direction, drag down the masses of radially excited charmonium states while leaving the ground state nearly unchanged.

Reviewed by Pith at T0; open to challenge. T0 means a machine referee read the full paper against a public rubric. the ladder, T0–T4 →

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

T0 review · deepseek-v4-flash

2026-08-04 05:47 UTC pith:OTUZ6KEL

load-bearing objection Solid forward use of lattice-motivated anisotropic potentials; the qualitative downward-shift signal is robust, but the quantitative size at eB≈10 GeV² leans heavily on a six-point fit. the 3 major comments →

arxiv 2603.12589 v2 pith:OTUZ6KEL submitted 2026-03-13 hep-ph hep-latnucl-th

Quarkonium spectra with magnetically induced anisotropic confinement

Ahmad Jafar Arifi , Kei Suzuki This is my paper
classification hep-ph hep-latnucl-th
keywords quarkoniumcharmoniummagnetic fieldanisotropic confinementstring tensionquark potential modelLandau quantizationlattice QCD
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

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

The paper tries to establish that the direction-dependent (anisotropic) confinement induced by a strong magnetic field leaves a clear, quantitative fingerprint in the quarkonium spectrum. Using string tensions fitted to lattice QCD data, the authors put an anisotropic potential V = σ(0)√(ε_L z² + ε_T r⊥²) into a nonrelativistic quark model and solve the Schrödinger equation exactly. They find that the longitudinal string tension weakens, so radially excited charmonium states shift downward in mass as the field grows, while the ground state barely moves. This is qualitatively different from isotropic confinement, where the spectrum saturates to a plateau once transverse motion freezes into the lowest Landau level. If correct, the eB-dependence of excited-state masses becomes a clean, measurable probe of magnetically induced confinement anisotropy.

Core claim

For charmonium in strong magnetic fields, the dominant effect of anisotropic confinement is the substantial weakening of the longitudinal string tension. In the S_z=0 (longitudinal) sector, radially excited masses decrease markedly with eB while the ground state barely changes; transverse (S_z=±1) states instead keep rising through the Landau-level energy. Because transverse motion freezes into the lowest Landau level, the enhanced transverse confinement is effectively screened, and the spectrum is controlled by the softened longitudinal potential. This contrasts sharply with isotropic confinement, where the longitudinal spectrum saturates to a plateau at large eB. Wave functions also elonga

What carries the argument

The central object is the anisotropic confinement potential V_aniso_conf(r⊥,z) = σ(0)√(ε_L z² + ε_T r⊥²), where ε_T and ε_L encode the magnetic-field-dependent transverse and longitudinal string tensions normalized to the zero-field value. This potential is inserted into a nonrelativistic Hamiltonian that also contains the Landau-quantization term q²B²r⊥²/8μ and the Zeeman mixing between η_c and the longitudinal component of J/ψ; the coupled Schrödinger equations are solved with the cylindrical Gaussian expansion method. The mechanism: a weakened longitudinal string tension makes the potential shallower along B, lowering excited-state energies, while the enhanced transverse tension is screen

Load-bearing premise

The prediction rests on the anisotropic-potential ansatz V = σ(0)√(ε_L z² + ε_T r⊥²) with string tensions fitted to six lattice-QCD data points and extrapolated to eB = 10 GeV²; if the true static potential has a different shape, or the fits are inaccurate, the downward shifts, radii, and avoided-crossing positions change, and the nonrelativistic Hamiltonian may not be reliable at the largest fields.

What would settle it

A lattice QCD computation of the longitudinal charmonium spectrum (or of the static quark-antiquark potential at large separation along the field) at eB around 4–9 GeV² that shows excited-state masses flat or rising with eB, rather than decreasing, would falsify the central claim.

Watch this falsifier — get emailed when new claim-graph text bears on it.

If this is right

  • Radially excited longitudinal charmonium masses fall as eB grows, instead of flattening; the slope of the mass-versus-eB curve is a direct measure of the longitudinal string-tension softening.
  • The ground state is nearly insensitive to anisotropic confinement, so observing the effect requires excited-state spectroscopy.
  • Avoided crossings between excited states shift to lower eB and lower masses, changing Landau–Zener transition probabilities in time-dependent magnetic fields.
  • Lattice QCD can verify the prediction by computing the S_z=0 charmonium spectrum or the static potential at large longitudinal separation at eB around 4–9 GeV².
  • The same anisotropic potential predicts large longitudinal elongation of excited-state wave functions, checkable through radii or form-factor calculations.

Where Pith is reading between the lines

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

  • A natural extension the paper does not pursue: bottomonium, with its smaller binding energy and larger size, should show even stronger downward shifts for excited states; comparing charmonium and bottomonium would separate the confinement-anisotropy signal from spin or Coulomb effects.
  • The screening argument implies a practical factorization: in the strong-field regime, transverse charmonium spectroscopy mostly constrains Landau and Zeeman dynamics, while longitudinal spectra constrain the longitudinal string tension. This could guide how future lattice data are used in potential models.
  • If the predicted downward trend is confirmed, the same mechanism offers a time-dependent probe: the survival probability of excited charmonia in a decaying magnetic field would encode the shifting energy levels, linking static potential measurements to heavy-ion phenomenology.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

3 major / 4 minor

Summary. The paper studies charmonium in a static, uniform magnetic field using a nonrelativistic quark potential model. The confining part of the quark-antiquark interaction is made anisotropic via Eq. (5), with transverse and longitudinal string tensions fitted to lattice QCD data using the saturation ansatz Eq. (6) and parameters in Eqs. (7)--(8). The resulting Schrödinger equation is solved with the cylindrical Gaussian expansion method. The central result is that, for longitudinal (S_z=0) charmonia, excited-state masses fall markedly with increasing eB because the longitudinal string tension weakens, whereas the ground state is nearly unaffected; this is contrasted with the plateau found for isotropic confinement. The paper also reports wave-function elongation along the magnetic field and compares with an 'anisotropic Coulomb' variant.

Significance. If the input potentials are reliable, the paper provides a concrete, falsifiable prediction connecting lattice QCD results on anisotropic string tensions to quarkonium spectroscopy in strong magnetic fields. The calculation has clear strengths: it does not fit target spectra in a magnetic field, the eigenvalue problem is solved with an explicit and previously documented method, and the parameters are stated. The main weaknesses are the reliance on an extrapolated, phenomenologically assumed fit to sparse lattice data and an incompletely specified anisotropic Coulomb potential. These issues limit the quantitative robustness of the central claim, but the qualitative idea is worth pursuing.

major comments (3)
  1. [Anisotropy, Figs. 2(b), 3, 4] The central qualitative conclusion -- pronounced downward mass shifts of excited longitudinal charmonia -- is controlled by the function σ̂_L(eB) at large eB. This quantity is obtained by extrapolating the ansatz (6) to eB=10 GeV² using only six lattice points, the highest at 9 GeV². The parameter set (7)--(8) gives σ̂_L(10) ≈ 0.05, but the functional form is ad hoc and the 2% error is assigned, not propagated from lattice uncertainties. If the true longitudinal string tension saturates at, say, 0.2--0.3 σ(0) instead, the excitation energies (which scale roughly as σ_L^{2/3} for linear confinement) would be substantially higher and the predicted downward shifts in Fig. 3 would weaken considerably. Please add a sensitivity study: vary the fitting function, use the raw lattice points without extrapolation, or restrict quantitative claims to eB ≤ 9 GeV². Without such a check, the robustness
  2. [Anisotropy, Figs. 2(b), 3, 4] The manuscript shows results for 'Anisotropic Coulomb' in Figs. 2(b), 3 and 4, but no equation or fitting procedure for an anisotropic Coulomb potential is provided. The text only states that the anisotropy of the short-range Coulomb interaction is small [5] and then defines the anisotropic confinement in Eq. (5). Without a specification of the anisotropic Coulomb model (for example, the analogue of Eq. (5) for the 1/r term, or the values of its fit parameters), the 'Anisotropic Coulomb' panels cannot be reproduced. This is load-bearing because the attribution of the downward shifts to confinement rather than to Coulomb anisotropy requires comparing these two variants. Please state the Coulomb-anisotropy potential explicitly, or clearly label those panels as illustrative and give the model used.
  3. [Model, Eqs. (1)--(3); Spectroscopy, Eqs. (9)--(10)] The calculation is performed with a nonrelativistic Hamiltonian up to eB=10 GeV². At these fields the Landau energy scale is comparable to or larger than the charm quark mass, so the nonrelativistic reduction leading to Eq. (3) may not be accurate. The argument using Dirac Landau levels in Eqs. (9)--(10) demonstrates a saturation property of free relativistic Landau levels, but does not establish the quantitative validity of the bound-state spectrum from the nonrelativistic potential model in this regime. I recommend either restricting the quantitative claims to eB ≲ 6 GeV² or providing a cross-check from a relativistic treatment or an effective field theory estimate.
minor comments (4)
  1. [Fig. 4] The label 'Coloumb' in Fig. 4 is a typo for 'Coulomb'. Also, 'Landé' in the text should be 'Landé' with the proper accent.
  2. [Fig. 3] The figure caption says 'under anisotropic confinement' but the lower row is labeled 'Anisotropic Coulomb'. The caption should explain what is plotted in each panel and what 'Anisotropic Coulomb' means.
  3. [Figs. 2--4] The error bands are based on a uniform 2% assignment. Please state explicitly how this uncertainty is propagated to the spectra and radii, and whether the correlations among the fitted parameters in Eqs. (7)--(8) are included. The statement that the transverse error is 'insignificant' should be justified quantitatively.
  4. [Anisotropy, Fig. 2] The fit uses selected lattice points from Refs. [5,6] at different lattice spacings. Please specify which points are used, whether a continuum extrapolation was attempted, and how the omission of other points affects the fit. This is relevant because the extrapolation to eB=10 GeV² is an important input.

Circularity Check

0 steps flagged

No significant circularity: the spectra are computed from external lattice QCD string-tension inputs, and the central downward-shift claim is a forward-modeling result rather than a restatement of the input.

full rationale

The paper's derivation chain is not circular. The anisotropic string tensions are taken from external lattice QCD data (Refs. [4,5,6]), parametrized in Eq. (6) with parameters (7)-(8), and then inserted into the anisotropic potential ansatz (5). The mass spectra are obtained by solving the resulting Schrödinger equation with the cylindrical Gaussian expansion method. No charmonium mass from lattice QCD or experiment is used to fix the anisotropy parameters, so the predicted downward shifts and avoided crossings are genuinely computed outputs, not fitted quantities relabeled as predictions. The conclusion that the dominant effect is the weakening of the longitudinal string tension is a mechanistic interpretation of the calculation, not a tautology: the input is σ_L(eB), while the output is the spectrum, and the relation between them requires solving the quantum mechanical bound-state problem. Self-citations [37,38] supply the zero-field quark-model parameters and the CGEM solver; these are technical tools and are not used to justify the central anisotropic-confinement claim, so they are not load-bearing circular references. The extrapolation of the fit to eB = 10 GeV^2 and the ansatz form (5) are legitimate modeling assumptions that affect robustness, but they do not make the derivation circular. Therefore the paper exhibits no self-definitional, fitted-input-called-prediction, or self-citation-chain circularity.

Axiom & Free-Parameter Ledger

3 free parameters · 4 axioms · 0 invented entities

The central predictions depend on the assumed potential shape, the fitted anisotropy parameters, and the inherited zero-field quark-model parameters. The derived spectra are not fitted to target quarkonium data, so the model itself is not circular, but the quantitative output inherits all uncertainty from these inputs.

free parameters (3)
  • Transverse anisotropy parameters ζ_T, κ_T, γ_T = (0.329, 0.659, 1.186)
    Fitted in this paper to transverse string-tension lattice data from Refs [5,6] via Eq. (6).
  • Longitudinal anisotropy parameters ζ_L, κ_L, γ_L = (-0.333, 0.305, 1.344)
    Fitted to longitudinal string-tension lattice data from Refs [5,6] via Eq. (6).
  • Zero-field quark-model parameters (m_c, α, σ, β, Λ, C) = m_c=1.784 GeV, α=0.713, √σ=0.402 GeV, β=0.4778 GeV, Λ=1.020 GeV², C=-0.5693 GeV
    Inherited from previous fits in Refs [37,38]; they set the unperturbed charmonium spectrum and are not fitted here.
axioms (4)
  • domain assumption The in-field quark-antiquark potential has the anisotropic Cornell form V(r)=σ(0)√(ε_L z²+ε_T r⊥²)+Coulomb+spin terms (Eq. 5).
    Adopted as a model; lattice results only constrain the string tensions σ_T,σ_L, not the full shape.
  • ad hoc to paper The normalized string tensions saturate as σ̂_i(eB)=(1+ζ_i(eB)^γ_i)/(1+κ_i(eB)^γ_i) (Eq. 6).
    A fitting ansatz with no derivation from QCD; extrapolation to eB=10 GeV² is uncontrolled.
  • domain assumption Nonrelativistic two-body Schrödinger equation with Landau and Zeeman terms remains valid up to eB=10 GeV².
    Charm quark mass 1.784 GeV; at eB=10 GeV² the magnetic scale is not negligible compared to the quark mass.
  • standard math The cylindrical Gaussian expansion method converges to the exact eigenstates of the model Hamiltonian.
    Numerical method from Refs [37,38,80,81]; no verification of convergence is shown here.

pith-pipeline@v1.3.0-alltime-deepseek · 10847 in / 16749 out tokens · 160557 ms · 2026-08-04T05:47:13.930685+00:00 · methodology

0 comments
read the original abstract

Strong magnetic fields modify the force that confines quarks inside hadrons and make it direction-dependent. Using quark-antiquark potentials obtained from lattice simulations as inputs to a quark potential model, we investigate how the anisotropic confinement affects the mass spectrum of quarkonium. In the strong-field regime, we find downward mass shifts induced by a softening of the confining potential along the field direction. In particular, the mass shifts of radially excited states are more significant than that of the ground state. For the longitudinal spin eigenstates, the excited-state spectrum strongly depends on the magnetic-field strength, in contrast to the spectrum with conventional isotropic confinement, which is insensitive to the field strength. This provides a clean probe of magnetically induced confinement anisotropy that can be confirmed in future lattice simulations.

Figures

Figures reproduced from arXiv: 2603.12589 by Ahmad Jafar Arifi, Kei Suzuki.

Figure 1
Figure 1. Figure 1: FIG. 1. Schematics of magnetic-field-induced anisotropy effects in quarkonia in the weak- and strong-field regimes: (a) [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2. Magnetic-field-induced anisotropy of the string ten [PITH_FULL_IMAGE:figures/full_fig_p002_2.png] view at source ↗

discussion (0)

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

Forward citations

Cited by 1 Pith paper

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

  1. Hadronic exceptional points

    hep-ph 2026-06 unverdicted novelty 7.0

    Imaginary magnetic fields induce exceptional points in neutral meson mass spectra computed via hadronic effective Lagrangian and constituent quark models, separating real and complex eigenvalue regimes.

Reference graph

Works this paper leans on

87 extracted references · 75 linked inside Pith · cited by 1 Pith paper

  1. [1]

    Hattori and X.-G

    K. Hattori and X.-G. Huang, Novel quantum phenomena induced by strong magnetic fields in heavy-ion collisions, Nucl. Sci. Tech.28, 26 (2017), arXiv:1609.00747 [nucl- th]

    Pith/arXiv arXiv 2017

  2. [2]

    J. Zhao, K. Zhou, S. Chen, and P. Zhuang, Heavy fla- vors under extreme conditions in high energy nuclear collisions, Prog. Part. Nucl. Phys.114, 103801 (2020), arXiv:2005.08277 [nucl-th]

    Pith/arXiv arXiv 2020

  3. [3]

    Iwasaki, M

    S. Iwasaki, M. Oka, and K. Suzuki, A review of quarkonia under strong magnetic fields, Eur. Phys. J. A57, 222 (2021), arXiv:2104.13990 [hep-ph]

    Pith/arXiv arXiv 2021

  4. [4]

    Bonati, M

    C. Bonati, M. D’Elia, M. Mariti, M. Mesiti, F. Negro, and F. Sanfilippo, Anisotropy of the quark-antiquark poten- tial in a magnetic field, Phys. Rev. D89, 114502 (2014), arXiv:1403.6094 [hep-lat]

    Pith/arXiv arXiv 2014

  5. [5]

    Bonati, M

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

    Pith/arXiv arXiv 2016

  6. [6]

    D’Elia, L

    M. D’Elia, L. Maio, F. Sanfilippo, and A. Stanzione, Confining and chiral properties of QCD in extremely strong magnetic fields, Phys. Rev. D104, 114512 (2021), arXiv:2109.07456 [hep-lat]

    Pith/arXiv arXiv 2021

  7. [7]

    G. S. Bali, F. Bruckmann, G. Endr˝ odi, Z. Fodor, S. D. Katz, S. Krieg, A. Schafer, and K. K. Szabo, The QCD phase diagram for external magnetic fields, JHEP02, 044, arXiv:1111.4956 [hep-lat]

    Pith/arXiv arXiv

  8. [8]

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

    Pith/arXiv arXiv 2014

  9. [9]

    Hidaka and A

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

    Pith/arXiv arXiv 2013

  10. [10]

    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, 627 (2015), arXiv:1411.4284 [hep-lat]

    Pith/arXiv arXiv 2015

  11. [11]

    E. V. Luschevskaya, O. E. Solovjeva, and O. V. Teryaev, Magnetic polarizability of pion, Phys. Lett. B761, 393 (2016), arXiv:1511.09316 [hep-lat]

    Pith/arXiv arXiv 2016

  12. [12]

    G. S. Bali, B. B. Brandt, G. Endr˝ odi, and B. Gl¨ aßle, Meson masses in electromagnetic fields with Wil- son fermions, Phys. Rev. D97, 034505 (2018), arXiv:1707.05600 [hep-lat]

    Pith/arXiv arXiv 2018

  13. [13]

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

    Pith/arXiv arXiv 2018

  14. [14]

    E. V. Luschevskaya, O. V. Teryaev, D. Y. Golubkov, O. V. Solovjeva, and R. A. Ishkuvatov, Tensor polar- izability of the vector mesons fromSU(3) lattice gauge theory, JHEP11, 186, arXiv:1811.02344 [hep-lat]

    Pith/arXiv arXiv

  15. [15]

    Hattori and A

    K. Hattori and A. Yamamoto, Meson deformation by magnetic fields in lattice QCD, PTEP2019, 043B04 (2019), arXiv:1901.10182 [hep-lat]

    Pith/arXiv arXiv 2019

  16. [16]

    Bignell, W

    R. Bignell, W. Kamleh, and D. Leinweber, Pion in a uniform background magnetic field with clover fermions, Phys. Rev. D100, 114518 (2019), arXiv:1910.14244 [hep- lat]

    Pith/arXiv arXiv 2019

  17. [17]

    Bignell, W

    R. Bignell, W. Kamleh, and D. Leinweber, Pion magnetic polarisability using the background field method, Phys. Lett. B811, 135853 (2020), arXiv:2005.10453 [hep-lat]

    Pith/arXiv arXiv 2020

  18. [18]

    Ding, S.-T

    H.-T. Ding, S.-T. Li, A. Tomiya, X.-D. Wang, and Y. Zhang, Chiral properties of (2+1)-flavor QCD in strong magnetic fields at zero temperature, Phys. Rev. D104, 014505 (2021), arXiv:2008.00493 [hep-lat]

    Pith/arXiv arXiv 2021

  19. [19]

    Ding, S.-T

    H.-T. Ding, S.-T. Li, J.-H. Liu, and X.-D. Wang, Chiral condensates and screening masses of neutral pseudoscalar mesons in thermomagnetic QCD medium, Phys. Rev. D 105, 034514 (2022), arXiv:2201.02349 [hep-lat]

    Pith/arXiv arXiv 2022

  20. [20]

    Endr˝ odi, QCD with background electromagnetic fields on the lattice: A review, Prog

    G. Endr˝ odi, QCD with background electromagnetic fields on the lattice: A review, Prog. Part. Nucl. Phys.141, 104153 (2025), arXiv:2406.19780 [hep-lat]

    Pith/arXiv arXiv 2025

  21. [21]

    Ding, J.-B

    H.-T. Ding, J.-B. Gu, S.-T. Li, and R. Thakkar, Chiral condensates and screening masses of neutral pseudoscalar mesons from lattice QCD at physical quark masses, Phys. Rev. D111, 074513 (2025), arXiv:2501.11262 [hep-lat]

    Pith/arXiv arXiv 2025

  22. [22]

    Ding and D

    H.-T. Ding and D. Zhang, Chiral Properties of (2 + 1)- Flavor QCD in Magnetic Fields at Zero Temperature, (2026), arXiv:2601.18354 [hep-lat]

    Pith/arXiv arXiv 2026

  23. [23]

    Eichten, K

    E. Eichten, K. Gottfried, T. Kinoshita, K. D. Lane, and T.-M. Yan, Charmonium: Comparison with Experiment, Phys. Rev. D21, 203 (1980)

    1980

  24. [24]

    Buchmuller and S

    W. Buchmuller and S. H. H. Tye, Quarkonia and Quan- tum Chromodynamics, Phys. Rev. D24, 132 (1981)

    1981

  25. [25]

    Godfrey and N

    S. Godfrey and N. Isgur, Mesons in a relativized quark model with chromodynamics, Phys. Rev. D32, 189 (1985)

    1985

  26. [26]

    Marasinghe and K

    K. Marasinghe and K. Tuchin, Quarkonium dissociation in quark-gluon plasma via ionization in magnetic field, Phys. Rev. C84, 044908 (2011), arXiv:1103.1329 [hep- ph]

    Pith/arXiv arXiv 2011

  27. [27]

    Tuchin, J/ψdissociation in parity-odd bubbles, Phys

    K. Tuchin, J/ψdissociation in parity-odd bubbles, Phys. Lett. B705, 482 (2011), arXiv:1105.5360 [nucl-th]

    Pith/arXiv arXiv 2011

  28. [28]

    Yang and B

    D.-L. Yang and B. M¨ uller,J/ψproduction by mag- netic excitation ofη c, J. Phys. G39, 015007 (2012), arXiv:1108.2525 [hep-ph]

    Pith/arXiv arXiv 2012

  29. [29]

    Tuchin, Particle production in strong electromagnetic fields in relativistic heavy-ion collisions, Adv

    K. Tuchin, Particle production in strong electromagnetic fields in relativistic heavy-ion collisions, Adv. High En- ergy Phys.2013, 490495 (2013), arXiv:1301.0099 [hep- ph]

    Pith/arXiv arXiv 2013

  30. [30]

    C. S. Machado, F. S. Navarra, E. G. de Oliveira, J. Noronha, and M. Strickland, Heavy quarkonium pro- duction in a strong magnetic field, Phys. Rev. D88, 034009 (2013), arXiv:1305.3308 [hep-ph]

    Pith/arXiv arXiv 2013

  31. [31]

    Alford and M

    J. Alford and M. Strickland, Charmonia and bottomo- nia in a magnetic field, Phys. Rev. D88, 105017 (2013), arXiv:1309.3003 [hep-ph]

    Pith/arXiv arXiv 2013

  32. [32]

    S. Cho, K. Hattori, S. H. Lee, K. Morita, and S. Ozaki, QCD sum rules for magnetically induced mixing be- tweenη c andJ/ψ, Phys. Rev. Lett.113, 172301 (2014), arXiv:1406.4586 [hep-ph]

    Pith/arXiv arXiv 2014

  33. [33]

    Dudal and T

    D. Dudal and T. G. Mertens, Melting of charmonium in a magnetic field from an effective AdS/QCD model, Phys. Rev. D91, 086002 (2015), arXiv:1410.3297 [hep-th]

    Pith/arXiv arXiv 2015

  34. [34]

    S. Cho, K. Hattori, S. H. Lee, K. Morita, and S. Ozaki, Charmonium Spectroscopy in Strong Magnetic Fields by QCD Sum Rules: S-Wave Ground States, Phys. Rev. D 91, 045025 (2015), arXiv:1411.7675 [hep-ph]

    Pith/arXiv arXiv 2015

  35. [35]

    Bonati, M

    C. Bonati, M. D’Elia, and A. Rucci, Heavy quarkonia in strong magnetic fields, Phys. Rev. D92, 054014 (2015), 6 arXiv:1506.07890 [hep-ph]

    Pith/arXiv arXiv 2015

  36. [36]

    anomalous wind

    A. V. Sadofyev and Y. Yin, The charmonium dis- sociation in an “anomalous wind”, JHEP01, 052, arXiv:1510.06760 [hep-th]

    Pith/arXiv arXiv

  37. [37]

    Suzuki and T

    K. Suzuki and T. Yoshida, Cigar-shaped quarkonia under strong magnetic field, Phys. Rev. D93, 051502 (2016), arXiv:1601.02178 [hep-ph]

    Pith/arXiv arXiv 2016

  38. [38]

    Yoshida and K

    T. Yoshida and K. Suzuki, Heavy meson spectroscopy under strong magnetic field, Phys. Rev. D94, 074043 (2016), arXiv:1607.04935 [hep-ph]

    Pith/arXiv arXiv 2016

  39. [39]

    Hasan, B

    M. Hasan, B. Chatterjee, and B. K. Patra, Heavy quark potential in a static and strong homogeneous magnetic field, Eur. Phys. J. C77, 767 (2017), arXiv:1703.10508 [hep-ph]

    Pith/arXiv arXiv 2017

  40. [40]

    Singh, L

    B. Singh, L. Thakur, and H. Mishra, Heavy quark complex potential in a strongly magnetized hot QGP medium, Phys. Rev. D97, 096011 (2018), arXiv:1711.03071 [hep-ph]

    Pith/arXiv arXiv 2018

  41. [41]

    N. R. F. Braga and L. F. Ferreira, Heavy meson disso- ciation in a plasma with magnetic fields, Phys. Lett. B 783, 186 (2018), arXiv:1802.02084 [hep-ph]

    Pith/arXiv arXiv 2018

  42. [42]

    Iwasaki, M

    S. Iwasaki, M. Oka, K. Suzuki, and T. Yoshida, Hadronic Paschen–Back effect, Phys. Lett. B790, 71 (2019), arXiv:1802.04971 [hep-ph]

    Pith/arXiv arXiv 2019

  43. [43]

    A. Jahan C. S., N. Dhale, S. Reddy P., S. Kesarwani, and A. Mishra, Charmonium states in strong magnetic fields, Phys. Rev. C98, 065202 (2018), arXiv:1803.04322 [nucl-th]

    Pith/arXiv arXiv 2018

  44. [44]

    Iwasaki and K

    S. Iwasaki and K. Suzuki, Quarkonium radiative decays from the hadronic Paschen-Back effect, Phys. Rev. D98, 054017 (2018), arXiv:1805.09787 [hep-ph]

    Pith/arXiv arXiv 2018

  45. [45]

    Hasan, B

    M. Hasan, B. K. Patra, B. Chatterjee, and P. Bagchi, Landau Damping in a strong magnetic field: Dissocia- tion of Quarkonia, Nucl. Phys. A995, 121688 (2020), arXiv:1802.06874 [hep-ph]

    Pith/arXiv arXiv 2020

  46. [46]

    N. R. F. Braga and L. F. Ferreira, Quasinormal modes for quarkonium in a plasma with magnetic fields, Phys. Lett. B795, 462 (2019), arXiv:1905.11309 [hep-ph]

    Pith/arXiv arXiv 2019

  47. [47]

    Hasan and B

    M. Hasan and B. K. Patra, Dissociation of heavy quarko- nia in a weak magnetic field, Phys. Rev. D102, 036020 (2020), arXiv:2004.12857 [hep-ph]

    Pith/arXiv arXiv 2020

  48. [48]

    J. Zhou, X. Chen, Y.-Q. Zhao, and J. Ping, Ther- modynamics of heavy quarkonium in a magnetic field background, Phys. Rev. D102, 086020 (2020), arXiv:2006.09062 [hep-ph]

    Pith/arXiv arXiv 2020

  49. [49]

    N. R. F. Braga and R. da Mata, Configuration entropy description of charmonium dissociation under the influ- ence of magnetic fields, Phys. Lett. B811, 135918 (2020), arXiv:2008.10457 [hep-th]

    Pith/arXiv arXiv 2020

  50. [50]

    N. R. F. Braga, Y. F. Ferreira, and L. F. Ferreira, Con- figuration entropy and stability of bottomonium radial excitations in a plasma with magnetic fields, Phys. Rev. D105, 114044 (2022), arXiv:2110.04560 [hep-th]

    Pith/arXiv arXiv 2022

  51. [51]

    S. S. Jena, B. Shukla, D. Dudal, and S. Mahapatra, Entropic force and real-time dynamics of holographic quarkonium in a magnetic field, Phys. Rev. D105, 086011 (2022), arXiv:2202.01486 [hep-th]

    Pith/arXiv arXiv 2022

  52. [52]

    J. Hu, S. Shi, Z. Xu, J. Zhao, and P. Zhuang, Mag- netic field induced hair structure in the charmonium gluon dissociation, Phys. Rev. D105, 094013 (2022), arXiv:2202.07938 [nucl-th]

    Pith/arXiv arXiv 2022

  53. [53]

    Ghosh, A

    R. Ghosh, A. Bandyopadhyay, I. Nilima, and S. Ghosh, Anisotropic tomography of heavy quark dissociation by using the general propagator structure in a fi- nite magnetic field, Phys. Rev. D106, 054010 (2022), arXiv:2204.02312 [hep-ph]

    Pith/arXiv arXiv 2022

  54. [54]

    Parui, S

    P. Parui, S. De, A. Kumar, and A. Mishra, QCD sum rule analysis of heavy quarkonium states in magnetized matter: Effects of magnetic and inverse magnetic cataly- sis, Phys. Rev. D106, 114033 (2022), arXiv:2208.05856 [hep-ph]

    Pith/arXiv arXiv 2022

  55. [55]

    Sebastian, L

    J. Sebastian, L. Thakur, H. Mishra, and N. Haque, Heavy quarkonia in QGP medium in an arbitrary magnetic field, Phys. Rev. D108, 094001 (2023), arXiv:2308.04410 [hep- ph]

    Pith/arXiv arXiv 2023

  56. [56]

    Nilima, M

    I. Nilima, M. Hasan, B. K. Singh, and M. Y. Jamal, Quarkonia dissociation at finite magnetic field in the presence of momentum anisotropy, Eur. Phys. J. C84, 160 (2024), arXiv:2402.07848 [hep-ph]

    Pith/arXiv arXiv 2024

  57. [57]

    S. S. Jena, J. Barman, B. Toniato, D. Dudal, and S. Mahapatra, A dynamical Einstein-Born-Infeld-dilaton model and holographic quarkonium melting in a mag- netic field, JHEP12, 096, arXiv:2408.14813 [hep-th]

    Pith/arXiv arXiv

  58. [58]

    Shukla, J

    B. Shukla, J. Nongmaithem, D. Dudal, and S. Maha- patra, Interplay of magnetic field and chemical poten- tial induced anisotropy and frame dependent chaos of a Q ¯Qpair in holographic QCD, Phys. Rev. D111, 106002 (2025), arXiv:2411.17279 [hep-th]

    Pith/arXiv arXiv 2025

  59. [59]

    L. Wen, M. Li, Y. Zhou, Y. Li, and J. P. Vary, Relativistic dynamics of charmonia in strong magnetic fields, Phys. Rev. D112, 014019 (2025), arXiv:2504.03294 [hep-ph]

    Pith/arXiv arXiv 2025

  60. [60]

    S. S. Jena, A. Bhattacharjee, D. Dudal, and S. Ma- hapatra, Probing quarkonium diffusion in a magnetized quark-gluon plasma, Phys. Rev. D112, 086010 (2025), arXiv:2507.00746 [hep-th]

    arXiv 2025

  61. [61]

    A. J. Arifi and K. Suzuki, Structure of heavy quarkonia in a strong magnetic field, Phys. Rev. D112, 094013 (2025), arXiv:2507.18894 [hep-ph]

    arXiv 2025

  62. [62]

    C. A. Dominguez, M. Koning, and L. A. Hern´ andez, Magnetic catalysis of charmonium in the vector chan- nel, Phys. Rev. D112, 094049 (2025), arXiv:2510.09927 [hep-ph]

    arXiv 2025

  63. [63]

    X. Guo, S. Shi, N. Xu, Z. Xu, and P. Zhuang, Mag- netic field effect on charmonium production in high en- ergy nuclear collisions, Phys. Lett. B751, 215 (2015), arXiv:1502.04407 [hep-ph]

    Pith/arXiv arXiv 2015

  64. [64]

    Suzuki and S

    K. Suzuki and S. H. Lee, Delayed versus accelerated quarkonium formation in a magnetic field, Phys. Rev. C96, 035203 (2017), arXiv:1610.09853 [hep-ph]

    Pith/arXiv arXiv 2017

  65. [65]

    Dutta and S

    N. Dutta and S. Mazumder, Majorana flipping of quarko- nium spin states in transient magnetic field, Eur. Phys. J. C78, 525 (2018), arXiv:1704.04094 [nucl-th]

    Pith/arXiv arXiv 2018

  66. [66]

    Hoelck and G

    J. Hoelck and G. Wolschin, Electromagnetic field effects on Υ-meson dissociation in PbPb collisions at LHC en- ergies, Eur. Phys. J. A53, 241 (2017), arXiv:1712.06871 [hep-ph]

    Pith/arXiv arXiv 2017

  67. [67]

    Bagchi, N

    P. Bagchi, N. Dutta, B. Chatterjee, and S. P. Adhya, Dis- sociation of heavy quarkonium states in a rapidly varying strong magnetic field, Mod. Phys. Lett. A38, 2350035 (2023), arXiv:1805.04082 [nucl-th]

    Pith/arXiv arXiv 2023

  68. [68]

    Iwasaki, D

    S. Iwasaki, D. Jido, M. Oka, and K. Suzuki, Survival probabilities of charmonia as a clue to measure tran- sient magnetic fields, Phys. Lett. B820, 136498 (2021), arXiv:2104.13989 [hep-ph]

    Pith/arXiv arXiv 2021

  69. [69]

    A. J. Arifi and K. Suzuki, Landau-Zener-St¨ uckelberg- Majorana dynamics of magnetized quarkonia, (2025), arXiv:2512.24072 [hep-ph]

    Pith/arXiv arXiv 2025

  70. [70]

    V. A. Miransky and I. A. Shovkovy, Magnetic catalysis 7 and anisotropic confinement in QCD, Phys. Rev. D66, 045006 (2002), arXiv:hep-ph/0205348 [hep-ph]

    Pith/arXiv arXiv 2002

  71. [71]

    M. N. Chernodub, QCD string breaking in strong mag- netic field, Mod. Phys. Lett. A29, 1450162 (2014), arXiv:1001.0570 [hep-ph]

    Pith/arXiv arXiv 2014

  72. [72]

    M. A. Andreichikov, V. D. Orlovsky, and Yu. A. Simonov, Asymptotic Freedom in Strong Magnetic Fields, Phys. Rev. Lett.110, 162002 (2013), arXiv:1211.6568 [hep-ph]

    Pith/arXiv arXiv 2013

  73. [73]

    Y. A. Simonov and M. A. Trusov, Confinement andα s in a strong magnetic field, Phys. Lett. B747, 48 (2015), arXiv:1503.08531 [hep-ph]

    Pith/arXiv arXiv 2015

  74. [74]

    Bohra, D

    H. Bohra, D. Dudal, A. Hajilou, and S. Ma- hapatra, Anisotropic string tensions and inversely magnetic catalyzed deconfinement from a dynamical AdS/QCD model, Phys. Lett. B801, 135184 (2020), arXiv:1907.01852 [hep-th]

    Pith/arXiv arXiv 2020

  75. [75]

    G¨ ursoy, M

    U. G¨ ursoy, M. J¨ arvinen, G. Nijs, and J. F. Pedraza, On the interplay between magnetic field and anisotropy in holographic QCD, JHEP03, 180, arXiv:2011.09474 [hep- th]

    Pith/arXiv arXiv 2011

  76. [76]

    I. Y. Aref’eva, K. Rannu, and P. Slepov, Energy Loss in Holographic Anisotropic Model for Heavy Quarks in External Magnetic Field, (2020), arXiv:2012.05758 [hep- th]

    Pith/arXiv arXiv 2020

  77. [77]

    I. Y. Aref’eva, A. Hajilou, K. Rannu, and P. Slepov, Spa- tial Wilson Loops and Energy Loss for Heavy Quarks in Magnetized HQCD Model, (2026), arXiv:2601.09611 [hep-th]

    arXiv 2026

  78. [78]

    Barnes, S

    T. Barnes, S. Godfrey, and E. S. Swanson, Higher char- monia, Phys. Rev. D72, 054026 (2005), arXiv:hep- ph/0505002 [hep-ph]

    arXiv 2005

  79. [79]

    M. A. Andreichikov, B. O. Kerbikov, V. D. Orlovsky, and Y. A. Simonov, Meson spectrum in strong magnetic fields, Phys. Rev. D87, 094029 (2013), arXiv:1304.2533 [hep-ph]

    Pith/arXiv arXiv 2013

  80. [80]

    Kamimura, Nonadiabatic coupled-rearrangement- channel approach to muonic molecules, Phys

    M. Kamimura, Nonadiabatic coupled-rearrangement- channel approach to muonic molecules, Phys. Rev. A38, 621 (1988)

    1988

Showing first 80 references.