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arxiv: 2604.14891 · v1 · submitted 2026-04-16 · ✦ hep-ph

Status of the hadronic light-by-light contribution to the muon g-2 and holographic QCD predictions

Anton Rebhan , Luigi Cappiello , Josef Leutgeb , Jonas Mager This is my paper

Pith reviewed 2026-05-10 10:57 UTC · model grok-4.3

classification ✦ hep-ph
keywords hadronic light-by-lightmuon g-2holographic QCDtensor mesonstransition form factorsshort-distance constraintsaxial-vector mesons
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The pith

Holographic QCD predicts a sizable positive tensor-meson contribution to the hadronic light-by-light term that could resolve tensions in muon g-2 calculations.

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

The paper reviews how holographic models of QCD have produced larger estimates for axial-vector meson and short-distance pieces of the hadronic light-by-light contribution to the muon anomalous magnetic moment than the 2020 consensus. It introduces a new calculation focused on tensor mesons, which become relevant once the model is required to obey an additional symmetric longitudinal short-distance constraint. Under this matching the predicted tensor-meson transition form factors agree with singly virtual data, depart from the usual quark-model ansatz, and generate a sizable positive shift in the overall HLbL term. A reader would care because this shift offers a possible explanation for the remaining difference between lattice and data-driven evaluations of the same quantity. If the result holds, it would tighten the Standard Model prediction for the muon g-2 and sharpen the interpretation of any experimental discrepancy.

Core claim

When the holographic QCD model is tuned to satisfy the symmetric longitudinal short-distance constraint in addition to others, its predictions for tensor-meson transition form factors align with available singly virtual data, unlike traditional quark-model ansatzes, and generate a sizable positive contribution to the HLbL amplitude that may explain the remaining discrepancy between lattice QCD and data-driven results for the muon g-2.

What carries the argument

Holographic QCD model for tensor-meson transition form factors matched to the symmetric longitudinal short-distance constraint beyond the Melnikov-Vainshtein condition.

If this is right

  • Holographic QCD yields larger axial-vector meson contributions than the 2020 White Paper.
  • Tensor mesons supply a positive HLbL piece absent from conventional quark-model treatments.
  • The constrained form factors reproduce existing singly virtual data.
  • The added positive term can account for the current tension between lattice and data-driven HLbL values.
  • Short-distance constraints beyond the Melnikov-Vainshtein limit play an essential role in the holographic construction.

Where Pith is reading between the lines

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

  • If the holographic result is reliable, data-driven HLbL evaluations will need improved modeling of tensor-meson effects to match lattice numbers.
  • Future lattice work could isolate tensor-meson channels to test whether they produce the predicted positive increment.
  • Measurements of tensor-meson transition form factors at higher virtualities would directly confront the holographic curves.
  • The same short-distance matching technique might usefully be applied to other hadronic contributions in precision electroweak observables.

Load-bearing premise

The holographic QCD model accurately and uniquely captures tensor-meson physics while enforcing the short-distance constraints without extra parameter adjustments that could change the sign or size of the resulting contribution.

What would settle it

A precision lattice evaluation of the full HLbL contribution that shows no sizable positive tensor-meson shift, or new experimental data on doubly virtual tensor-meson form factors that deviates markedly from the holographic prediction.

Figures

Figures reproduced from arXiv: 2604.14891 by Anton Rebhan, Jonas Mager, Josef Leutgeb, Luigi Cappiello.

Figure 1
Figure 1. Figure 1: Hadronic light-by-light scattering contribution to aµ from single meson exchange HLbL contributions, with a special emphasis on checks on the data-driven approach that have been provided by holo￾graphic QCD (hQCD) models. The long-standing open is￾sue on the size of contributions from axial-vector mesons in single exchange diagrams like [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 3
Figure 3. Figure 3: The hQCD results for the a1 TFF of Ref. [17] (LMR22) with OPE fit (blue lines) and Fρ-fit (red lines) compared to the dispersive result of Ref. [21]. Dotted (and dash-dotted) lines show the LCE limit [47] without (and with) mass corrections. (Figure taken from [2]) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of hQCD result (HW) and quark model ansatz with Λ = Mρ [25] and MT [47, 57] for the singly-virtual tensor TFF for helicity λ = 2 with Belle data [58] for the f2(1270). (Figure adapted from Ref. [27]) A new open question appeared, however, concerning the role of tensor mesons. In the previous White Pa￾per, their contribution was estimated as [3, 35] a T,WP20 µ = 0.9(1) × 10−11, surprisingly small… view at source ↗
read the original abstract

We review the recent progress made with regard to the hadronic light-by-light (HLbL) contribution to the Standard Model prediction of the muon anomalous magnetic moment and how well this compares with predictions from holographic QCD models, which had predicted larger contributions from axial vector mesons and short-distance constraints than the White Paper of 2020. A new holographic prediction concerns tensor-meson contributions, which in holographic QCD play a significant role in short-distance constraints beyond the Melnikov-Vainshtein constraint. When matching also the symmetric longitudinal short-distance constraint, the resulting prediction for the tensor-meson transition form factors agree well with available singly virtual data, but lead to different results than the traditional quark-model ansatz and a sizable positive contribution that could explain the remaining current tension between lattice and data-driven results for the HLbL contribution.

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 / 2 minor

Summary. The manuscript reviews recent progress on the hadronic light-by-light (HLbL) contribution to the muon g-2, contrasting data-driven, lattice, and holographic QCD results. It notes that holographic models predict larger axial-vector meson and short-distance contributions than the 2020 White Paper. The central new claim is that, after matching the symmetric longitudinal short-distance constraint, the holographic tensor-meson transition form factors agree with available singly-virtual data, differ from the traditional quark-model ansatz, and yield a sizable positive HLbL contribution capable of resolving the remaining tension between lattice and data-driven evaluations.

Significance. If the central claim holds, the work is significant for the muon g-2 program because it supplies an independent, non-perturbative framework that naturally incorporates short-distance constraints and tensor-meson degrees of freedom. The manuscript explicitly credits the new holographic prediction for tensor mesons and its consistency with singly-virtual data; these are concrete strengths that could help adjudicate the current lattice-versus-dispersive discrepancy.

major comments (2)
  1. [Abstract and tensor-meson section] The abstract states that matching the symmetric longitudinal short-distance constraint produces tensor-meson TFFs that 'lead to different results than the traditional quark-model ansatz and a sizable positive contribution.' This is load-bearing for the resolution-of-tension claim, yet the manuscript does not appear to supply a direct numerical comparison (e.g., the difference in the integrated HLbL contribution or the separate tensor-meson piece) with the quark-model baseline.
  2. [Tensor-meson TFFs and HLbL evaluation] The reader's assessment notes low confidence because full calculations, error estimates, and derivation details are not accessible. The paper must therefore include, in the section presenting the new TFFs, explicit uncertainty bands arising from the holographic parameters and from the extrapolation to the doubly-virtual kinematics relevant for g-2.
minor comments (2)
  1. [Abstract] The abstract is information-dense; splitting the review of prior holographic results from the new tensor-meson claim would improve readability.
  2. [Results section] A table summarizing the HLbL contributions (lattice, data-driven, holographic with and without the new tensor term) would make the size of the claimed resolution immediately visible.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. We address each major comment below.

read point-by-point responses

  1. Referee: [Abstract and tensor-meson section] The abstract states that matching the symmetric longitudinal short-distance constraint produces tensor-meson TFFs that 'lead to different results than the traditional quark-model ansatz and a sizable positive contribution.' This is load-bearing for the resolution-of-tension claim, yet the manuscript does not appear to supply a direct numerical comparison (e.g., the difference in the integrated HLbL contribution or the separate tensor-meson piece) with the quark-model baseline.

    Authors: We agree that a direct numerical comparison is needed to substantiate the claim. In the revised manuscript we will add, in the tensor-meson section, a table that reports the separate tensor-meson contribution to a_μ^HLbL obtained from our holographic TFFs and from the standard quark-model ansatz, together with the difference in the total HLbL value when each is used. revision: yes

  2. Referee: [Tensor-meson TFFs and HLbL evaluation] The reader's assessment notes low confidence because full calculations, error estimates, and derivation details are not accessible. The paper must therefore include, in the section presenting the new TFFs, explicit uncertainty bands arising from the holographic parameters and from the extrapolation to the doubly-virtual kinematics relevant for g-2.

    Authors: We acknowledge that explicit uncertainty bands and additional derivation details are required. In the revised version we will include, in the section on the new TFFs, uncertainty bands obtained by varying the holographic parameters (string tension and IR cutoff) and by propagating the extrapolation uncertainty to the doubly-virtual region; we will also expand the derivation appendix to make the steps more accessible. revision: yes

Circularity Check

0 steps flagged

No significant circularity; holographic predictions are independent of target HLbL quantity

full rationale

The paper reviews HLbL contributions and derives tensor-meson TFF predictions within holographic QCD after imposing symmetric longitudinal short-distance constraints. These are then compared to singly-virtual data and contrasted with quark-model results to estimate a positive HLbL term. No quoted equation or step shows the central prediction reducing by construction to a fit of the muon g-2 HLbL value itself, nor does any load-bearing premise collapse to a self-citation chain or ansatz smuggled from prior author work. The model is treated as an external framework whose parameters and matching are justified separately from the final HLbL number; uncertainties are acknowledged without circular closure. This is the typical self-contained case.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Insufficient information from abstract alone to identify specific free parameters, axioms, or invented entities; holographic QCD is a modeling framework whose internal parameters and assumptions are not detailed here.

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Reference graph

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