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arxiv: 2606.08329 · v2 · pith:BGFSNCLEnew · submitted 2026-06-06 · ✦ hep-ph · hep-th· nucl-th

Lepton g-2 non-universality of hadronic contributions and a sub-GeV window to New Physics

Siyuan Li , Vladimir Pascalutsa , Maxim Pospelov This is my paper

Pith reviewed 2026-06-27 19:11 UTC · model grok-4.3

classification ✦ hep-ph hep-thnucl-th
keywords lepton g-2hadronic vacuum polarizationnew physicsflavor non-universalitysub-GeV particlesanomalous magnetic momentmuon-electron difference
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The pith

A mass-rescaled difference of muon and electron anomalous magnetic moments cancels short-range hadronic effects and reduces their uncertainty by about 85 percent.

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

The paper introduces the quantity a_{μ-e} defined as the muon anomalous magnetic moment minus the electron anomalous magnetic moment scaled by the square of the muon-to-electron mass ratio. This rescaling produces an exact cancellation of short-distance contributions to the hadronic vacuum polarization. The surviving long-distance hadronic piece and its uncertainty therefore shrink by roughly 85 percent relative to the standard muon g-2. The resulting cleaner ultraviolet behavior turns a_{μ-e} into a dedicated low-energy observable for possible new physics that distinguishes muons from electrons or for light states below 1 GeV. Realizing this window requires improved experimental precision on the electron g-2 and the fine-structure constant.

Core claim

The central claim is that the linear combination a_{μ-e} ≡ a_μ − (m_μ/m_e)^2 a_e serves as a natural low-energy window quantity that directly probes the discrepancy between data-driven and lattice-QCD evaluations of hadronic contributions. The rescaling ensures an exact cancellation of the short-range effects, thereby improving the UV behavior and bypassing a number of issues that arise in a_μ or a_e separately. The hadronic-vacuum-polarization effect in a^{HVP}_{μ-e}, together with its uncertainty, is reduced as compared to a^{HVP}_μ by ∼85%. This is promising for tests of New Physics, conditional to significant improvements in experimental measurements of a_e and α, and opens a window to f

What carries the argument

The linear combination a_{μ-e} ≡ a_μ − (m_μ/m_e)^2 a_e, whose mass-squared rescaling produces exact cancellation of short-range hadronic vacuum polarization.

If this is right

  • The hadronic-vacuum-polarization contribution and its uncertainty in a^{HVP}_{μ-e} shrink by ∼85% compared with a^{HVP}_μ.
  • The combination provides a direct test of New Physics scenarios that exhibit some degree of flavor non-universality between muons and electrons.
  • It also constrains flavor-universal new states with masses below 1 GeV once experimental inputs improve.
  • Progress in measuring a_e and the fine-structure constant α directly tightens the sensitivity of this observable to new physics.

Where Pith is reading between the lines

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

  • The same rescaling technique could be applied to other lepton observables to isolate long-distance effects from short-distance contamination.
  • Agreement between data-driven and lattice evaluations in a_{μ-e} would indicate that the existing muon g-2 tension originates outside the hadronic sector.
  • Future experiments that measure both lepton moments to high precision could use this combination as a dedicated search channel for light new particles.

Load-bearing premise

Short-range hadronic effects remain identical for the muon and electron after the mass-squared rescaling so that they cancel exactly in the combination.

What would settle it

A high-precision determination of a_{μ-e} that shows a hadronic contribution larger than the predicted 15 percent remnant or that deviates from zero by an amount inconsistent with the expected New Physics window would falsify the claimed reduction and cancellation.

Figures

Figures reproduced from arXiv: 2606.08329 by Maxim Pospelov, Siyuan Li, Vladimir Pascalutsa.

Figure 1
Figure 1. Figure 1: FIG. 1: The leading-order HVP contribution to ( [PITH_FULL_IMAGE:figures/full_fig_p003_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: The kernel ratio, [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Two-pion contribution to the HVP in the VMD [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 5
Figure 5. Figure 5: FIG. 5: Pseudoscalar-meson contribution to [PITH_FULL_IMAGE:figures/full_fig_p004_5.png] view at source ↗
Figure 4
Figure 4. Figure 4: FIG. 4: The integrand of [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: FIG. 6: Exclusion plot for the dark-photon parameters. [PITH_FULL_IMAGE:figures/full_fig_p006_6.png] view at source ↗
read the original abstract

We propose the linear combination of the anomalous magnetic moments of the muon and electron, $a_{\mu-e} \equiv a_\mu - (m_\mu/m_e)^2 a_e$, as a natural low-energy window quantity that may directly probe the current discrepancy between the data-driven and lattice-QCD evaluations of hadronic contributions. The rescaling ensures an exact cancellation of the short-range effects, thereby improving the UV behavior and bypassing a number of issues that arise in $a_\mu$ or $a_e$ separately. The hadronic-vacuum-polarization effect in $a^{\rm HVP}_{\mu-e}$, together with its uncertainty, is reduced as compared to $a^{\rm HVP}_{\mu}$ by $\sim 85\%$. This is promising for tests of New Physics, conditional to significant improvements in experimental measurements of $a_e$ and $\alpha$. One can foresee the improvements in tests of New Physics with some degree of flavor non-universality, as well as for the flavor-universal sub-GeV states.

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

0 major / 3 minor

Summary. The manuscript proposes the linear combination a_{\mu-e} \equiv a_\mu - (m_\mu/m_e)^2 a_e as a low-energy window quantity to probe hadronic vacuum polarization (HVP) contributions. It claims that the mass-squared rescaling produces an exact cancellation of short-range HVP effects, improving UV behavior relative to a_\mu or a_e separately. The hadronic contribution and its uncertainty in a^{HVP}_{\mu-e} are stated to be reduced by \sim 85\% compared with a^{HVP}_\mu. This is presented as a potential probe of the data-driven versus lattice-QCD discrepancy in HVP and as a window to new physics with flavor non-universality or sub-GeV states, conditional on improved a_e and \alpha measurements.

Significance. If the cancellation and numerical reduction hold, the construction supplies a parameter-free observable that isolates the low-s regime of HVP more cleanly than the separate lepton moments. The absence of free parameters or fitted quantities, together with the direct use of the known UV asymptotics of the HVP kernel, is a clear strength. The approach could usefully complement existing g-2 analyses for testing non-universal new-physics scenarios, provided the required experimental advances in a_e materialize.

minor comments (3)
  1. [Abstract, §1] Abstract and §1: the statement that the rescaling 'bypasses a number of issues' would be clearer if the specific issues (e.g., UV sensitivity, scheme dependence) were enumerated explicitly rather than left implicit.
  2. The numerical claim of an ∼85% reduction is central to the quantitative appeal; a short table or paragraph breaking down the residual contribution by s-region (low-s vs. intermediate) would allow readers to verify the factor without re-deriving the integral.
  3. Notation: define a^{HVP}_{\mu-e} at first appearance and ensure consistent use of the superscript throughout; the current text occasionally reverts to a_{\mu-e} without the HVP label.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the supportive review and accurate summary of our proposal for the a_{\mu-e} combination. The recommendation of minor revision is noted; however, the report contains no specific major comments requiring point-by-point response.

Circularity Check

0 steps flagged

No significant circularity; derivation is self-contained

full rationale

The paper defines the quantity a_{\mu-e} explicitly as a linear combination chosen to exploit the known large-s asymptotic of the HVP kernel K(s/m_l^2) ~ m_l^2/s. This cancellation is a direct algebraic consequence of the definition and the standard kernel form, not a reduction to fitted inputs or self-citations. The ~85% reduction is presented as a numerical integral result over R(s) with the differing kernels; no parameters are fitted to data and then relabeled as predictions. No self-citation load-bearing steps, uniqueness theorems, or ansatze smuggled via prior work appear in the provided text. The construction is independent of the target discrepancy and remains falsifiable by external measurements of a_e and alpha.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Review limited to abstract; no free parameters or invented entities identified. One standard assumption extracted.

axioms (1)
  • standard math Short-range contributions to lepton anomalous magnetic moments scale proportionally to the square of the lepton mass
    Invoked to justify exact cancellation upon rescaling (abstract, sentence on rescaling).

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discussion (0)

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Reference graph

Works this paper leans on

41 extracted references · 18 linked inside Pith

  1. [1]

    X. Fan, T. G. Myers, B. A. D. Sukra, and G. Gabrielse, Measurement of the Electron Magnetic Moment, Phys. Rev. Lett.130, 071801 (2023), arXiv:2209.13084 [physics.atom-ph]

    arXiv 2023

  2. [2]

    D. P. Aguillardet al.(Muon g-2), Measurement of the Positive Muon Anomalous Magnetic Moment to 127 ppb, Phys. Rev. Lett.135, 101802 (2025), arXiv:2506.03069 [hep-ex]

    arXiv 2025

  3. [3]

    Melnikov and A

    K. Melnikov and A. Vainshtein,Theory of the muon anomalous magnetic moment, Springer Tracts Mod. Phys., Vol. 216 (2006) pp. 1–176

    2006

  4. [4]

    Jegerlehner,The Anomalous Magnetic Moment of the Muon, Springer Tracts Mod

    F. Jegerlehner,The Anomalous Magnetic Moment of the Muon, Springer Tracts Mod. Phys., Vol. 274 (2017) pp. 1–693

    2017

  5. [5]

    Aoyamaet al., The anomalous magnetic moment of the muon in the Standard Model, Phys

    T. Aoyamaet al., The anomalous magnetic moment of the muon in the Standard Model, Phys. Rept.887, 1 (2020), arXiv:2006.04822 [hep-ph]. 5 Generally, this feature should be derived via Schwinger’s sum rule, of which the dispersive representation for the HVP contri- bution is a particular case [38]

    Pith/arXiv arXiv 2020

  6. [6]

    Alibertiet al., The anomalous magnetic moment of the muon in the standard model: an update, Phys

    R. Alibertiet al., The anomalous magnetic moment of the muon in the standard model: an update, Phys. Rept. 1143, 1 (2025), arXiv:2505.21476 [hep-ph]

    Pith/arXiv arXiv 2025

  7. [7]

    G. F. Giudice, P. Paradisi, and A. Strumia, Correlation between the Higgs Decay Rate to Two Photons and the Muon g - 2, JHEP10, 186, arXiv:1207.6393 [hep-ph]

    Pith/arXiv arXiv

  8. [8]

    S. G. Karshenboim and V. A. Shelyuto, Hadronic vacuum-polarization contribution to various QED ob- servables, Eur. Phys. J. D75, 49 (2021)

    2021

  9. [9]

    Di Luzio, A

    L. Di Luzio, A. Keshavarzi, A. Masiero, and P. Paradisi, Model-Independent Tests of the Hadronic Vacuum Polar- ization Contribution to the Muon g-2, Phys. Rev. Lett. 134, 011902 (2025), arXiv:2408.01123 [hep-ph]

    arXiv 2025

  10. [10]

    Giusti and S

    D. Giusti and S. Simula, Ratios of the hadronic contributions to the leptong−2 from Lattice QCD+QED simulations, Phys. Rev. D102, 054503 (2020), arXiv:2003.12086 [hep-lat]

    arXiv 2020

  11. [11]

    Antognini, F

    A. Antognini, F. Hagelstein, and V. Pascalutsa, The pro- ton structure in and out of muonic hydrogen, Ann. Rev. Nucl. Part. Sci.72, 389 (2022), arXiv:2205.10076 [nucl- th]. 8

    arXiv 2022

  12. [12]

    T. Blum, P. A. Boyle, V. G¨ ulpers, T. Izubuchi, L. Jin, C. Jung, A. J¨ uttner, C. Lehner, A. Portelli, and J. T. Tsang (RBC, UKQCD), Calculation of the hadronic vac- uum polarization contribution to the muon anomalous magnetic moment, Phys. Rev. Lett.121, 022003 (2018), arXiv:1801.07224 [hep-lat]

    Pith/arXiv arXiv 2018

  13. [13]

    Boccalettiet al., Hybrid calculation of hadronic vac- uum polarization in muon g−2 to 0.48%, Nature653, 373 (2026), arXiv:2407.10913 [hep-lat]

    A. Boccalettiet al., Hybrid calculation of hadronic vac- uum polarization in muon g−2 to 0.48%, Nature653, 373 (2026), arXiv:2407.10913 [hep-lat]

    Pith/arXiv arXiv 2026

  14. [14]

    Borsanyiet al.(Budapest-Marseille-Wuppertal), Hadronic vacuum polarization contribution to the anomalous magnetic moments of leptons from first principles, Phys

    S. Borsanyiet al.(Budapest-Marseille-Wuppertal), Hadronic vacuum polarization contribution to the anomalous magnetic moments of leptons from first principles, Phys. Rev. Lett.121, 022002 (2018), arXiv:1711.04980 [hep-lat]

    Pith/arXiv arXiv 2018

  15. [15]

    Keshavarzi, D

    A. Keshavarzi, D. Nomura, and T. Teubner,g−2 of charged leptons,α(M 2 Z) , and the hyperfine split- ting of muonium, Phys. Rev.D 101, 014029 (2020), arXiv:1911.00367 [hep-ph]

    arXiv 2020

  16. [16]

    Bauer, M

    M. Bauer, M. Neubert, S. Renner, M. Schnubel, and A. Thamm, Axionlike Particles, Lepton-Flavor Violation, and a New Explanation ofa µ anda e, Phys. Rev. Lett. 124, 211803 (2020), arXiv:1908.00008 [hep-ph]

    arXiv 2020

  17. [17]

    Bauer, M

    M. Bauer, M. Neubert, S. Renner, M. Schnubel, and A. Thamm, The Low-Energy Effective Theory of Axions and ALPs, JHEP04, 063, arXiv:2012.12272 [hep-ph]

    arXiv 2012

  18. [18]

    A. M. Galda and M. Neubert, ALP-LEFT Interference and the Muon (g−2), JHEP11, 015, arXiv:2308.01338 [hep-ph]

    arXiv

  19. [19]

    Pustyntsev and M

    A. Pustyntsev and M. Vanderhaeghen, Implications of recent (g-2)µmeasurements for MeV-GeV dark sector searches, Phys. Rev. D112, 095001 (2025), arXiv:2506.17750 [hep-ph]

    arXiv 2025

  20. [20]

    Bouchiat and L

    C. Bouchiat and L. Michel, La r´ esonance dans la diffusion m´ esonπ— m´ esonπet le moment magn´ etique anormal du m´ esonµ, J. Phys. Radium22, 121 (1961)

    1961

  21. [21]

    S. J. Brodsky and E. de Rafael, Suggested boson-lepton pair couplings and the anomalous magnetic moment of the muon, Phys. Rev.168, 1620 (1968)

    1968

  22. [22]

    B. E. Lautrup and E. De Rafael, Calculation of the sixth- order contribution from the fourth-order vacuum polar- ization to the difference of the anomalous magnetic mo- ments of muon and electron, Phys. Rev.174, 1835 (1968)

    1968

  23. [23]

    Gourdin and E

    M. Gourdin and E. De Rafael, Hadronic contributions to the muon g-factor, Nucl. Phys. B10, 667 (1969)

    1969

  24. [24]

    Bernecker and H

    D. Bernecker and H. B. Meyer, Vector Correlators in Lat- tice QCD: Methods and applications, Eur. Phys. J. A47, 148 (2011), arXiv:1107.4388 [hep-lat]

    Pith/arXiv arXiv 2011

  25. [25]

    Beltran, A

    A. Beltran, A. Conigli, S. Kuberski, H. B. Meyer, K. Ot- tnad, and H. Wittig, Higher-order hadronic vacuum po- larization contribution to the muong−2 from lattice QCD (2026), arXiv:2603.06806 [hep-lat]

    Pith/arXiv arXiv 2026

  26. [26]

    M. E. Peskin and D. V. Schroeder,An Introduction to quantum field theory(Addison-Wesley, 1995)

    1995

  27. [27]

    Biloshytskyi, D

    V. Biloshytskyi, D. Erb, H. B. Meyer, J. Parrino, and V. Pascalutsa, Field-theoretic versus data-driven evalua- tions of electromagnetic corrections to hadronic vacuum polarization in (g−2) µ, Eur. Phys. J. C86, 497 (2026), arXiv:2509.08115 [hep-ph]

    Pith/arXiv arXiv 2026

  28. [28]

    Bauer, M

    M. Bauer, M. Neubert, and A. Thamm, LHC as an Ax- ion Factory: Probing an Axion Explanation for (g−2) µ with Exotic Higgs Decays, Phys. Rev. Lett.119, 031802 (2017), arXiv:1704.08207 [hep-ph]

    Pith/arXiv arXiv 2017

  29. [29]

    Bauer, M

    M. Bauer, M. Neubert, and A. Thamm, Collider Probes of Axion-Like Particles, JHEP12, 044, arXiv:1708.00443 [hep-ph]

    Pith/arXiv arXiv

  30. [30]

    Melnikov and A

    K. Melnikov and A. Vainshtein, Hadronic light-by-light scattering contribution to the muon anomalous mag- netic moment revisited, Phys. Rev.D 70, 113006 (2004), arXiv:hep-ph/0312226 [hep-ph]

    Pith/arXiv arXiv 2004

  31. [31]

    Bijnens, N

    J. Bijnens, N. Hermansson-Truedsson, and A. Rodr´ ıguez- S´ anchez, Short-distance constraints for the HLbL contri- bution to the muon anomalous magnetic moment, Phys. Lett.B798, 134994 (2019), arXiv:1908.03331 [hep-ph]

    arXiv 2019

  32. [32]

    Colangelo, F

    G. Colangelo, F. Hagelstein, M. Hoferichter, L. Laub, and P. Stoffer, Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic mo- ment of the muon, Phys. Rev. D101, 051501 (2020), arXiv:1910.11881 [hep-ph]

    arXiv 2020

  33. [33]

    I. R. Blokland, A. Czarnecki, and K. Melnikov, Pion pole contribution to hadronic light by light scattering and muon anomalous magnetic moment, Phys. Rev. Lett.88, 071803 (2002), arXiv:hep-ph/0112117

    Pith/arXiv arXiv 2002

  34. [34]

    Fayet, U-boson production in e+ e- annihilations, psi and Upsilon decays, and Light Dark Matter, Phys

    P. Fayet, U-boson production in e+ e- annihilations, psi and Upsilon decays, and Light Dark Matter, Phys. Rev. D75, 115017 (2007), arXiv:hep-ph/0702176

    Pith/arXiv arXiv 2007

  35. [35]

    Pospelov, Secluded U(1) below the weak scale, Phys

    M. Pospelov, Secluded U(1) below the weak scale, Phys. Rev. D80, 095002 (2009), arXiv:0811.1030 [hep-ph]

    Pith/arXiv arXiv 2009

  36. [36]

    Arkani-Hamed and N

    N. Arkani-Hamed and N. Weiner, LHC Signals for a SuperUnified Theory of Dark Matter, JHEP12, 104, arXiv:0810.0714 [hep-ph]

    Pith/arXiv arXiv

  37. [37]

    Gabrielse and G

    G. Gabrielse and G. Venanzoni, Measured Lepton Mag- netic Moments (2025), arXiv:2507.11268 [hep-ex]

    arXiv 2025

  38. [38]

    Hagelstein and V

    F. Hagelstein and V. Pascalutsa, Dissecting the Hadronic Contributions to (g−2)µ by Schwinger’s Sum Rule, Phys. Rev. Lett.120, 072002 (2018), arXiv:1710.04571 [hep- ph]

    Pith/arXiv arXiv 2018

  39. [39]

    P. J. Mohr, D. B. Newell, B. N. Taylor, and E. Tiesinga, CODATA recommended values of the fundamental physi- cal constants: 2022*, Rev. Mod. Phys.97, 025002 (2025), arXiv:2409.03787 [hep-ph]

    arXiv 2022

  40. [40]

    Morel, Z

    L. Morel, Z. Yao, P. Clad´ e, and S. Guellati-Kh´ elifa, De- termination of the fine-structure constant with an accu- racy of 81 parts per trillion, Nature588, 61 (2020)

    2020

  41. [41]

    R. H. Parker, C. Yu, W. Zhong, B. Estey, and H. M¨ uller, Measurement of the fine-structure constant as a test of the Standard Model, Science360, 191 (2018), arXiv:1812.04130 [physics.atom-ph]

    Pith/arXiv arXiv 2018