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arxiv: 2510.13966 · v2 · submitted 2025-10-15 · ✦ hep-ph · hep-ex· nucl-th

Light new physics and the τ lepton dipole moments: prospects at Belle II

Martin Hoferichter , Gabriele Levati This is my paper

Pith reviewed 2026-05-18 06:52 UTC · model grok-4.3

classification ✦ hep-ph hep-exnucl-th
keywords tau leptondipole momentsnew physicsBelle IIasymmetriesanomalous magnetic momentlight particles
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The pith

Light new particles produce asymmetries in tau pair production that constrain the tau anomalous magnetic moment even without electron polarization.

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

This paper examines how asymmetries measured in electron-positron collisions that create tau lepton pairs can probe new physics when the new particles are light rather than heavy. It uses specific examples of light spin-0 and spin-1 bosons to show that the resulting effects still translate into limits on the tau electric and magnetic dipole moments, though the mapping depends on the details of the new particles. A central result is that the imaginary parts introduced by these light particles generate nonzero asymmetries without any need for a polarized electron beam. These asymmetries can therefore be turned into constraints on the tau anomalous magnetic moment and applied to data already collected at Belle II. The analysis also traces how the light-particle results connect to the usual effective-field-theory description that assumes heavy new physics.

Core claim

In the presence of light new physics, asymmetries constructed from tau pair production in e+e- collisions can be interpreted as model-dependent constraints on the tau dipole moments; the imaginary parts generated by light spin-0 and spin-1 test particles produce nonvanishing asymmetries even in the absence of electron polarization, which again yield bounds on the tau anomalous magnetic moment, and the results smoothly approach the effective-field-theory limit as the new-particle mass increases.

What carries the argument

Asymmetries in e+e- to tau+tau- production induced by light spin-0 and spin-1 bosons, which encode contributions to the tau electric and magnetic dipole moments and remain nonzero without beam polarization due to their imaginary parts.

If this is right

  • Asymmetry data can set limits on the tau anomalous magnetic moment using present Belle II runs without requiring electron polarization.
  • The same observables remain useful when new physics is light, with a smooth connection to the heavy-particle effective-field-theory regime.
  • Imaginary parts from light new particles open an additional channel for dipole-moment constraints that would otherwise vanish.
  • Model-dependent bounds derived this way can be compared with limits from other tau-related observables once the new-particle mass and couplings are specified.

Where Pith is reading between the lines

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

  • Existing unpolarized data sets could be re-examined for these asymmetries to extract early limits on light mediators coupling to taus.
  • Similar asymmetry constructions might be tested in other processes involving taus or in future tau factories.
  • The approach suggests that light new physics could produce observable effects in precision observables even when direct production thresholds are not reached.

Load-bearing premise

The calculated asymmetries for the chosen light spin-0 and spin-1 test cases can be mapped directly to dipole-moment constraints without substantial contamination from backgrounds, detector effects, or higher-order corrections.

What would settle it

A measurement or full simulation of the e+e- to tau+tau- asymmetries at Belle II that finds the observed values significantly smaller or larger than those predicted from the light-particle contributions alone would falsify the direct interpretation as dipole-moment bounds.

Figures

Figures reproduced from arXiv: 2510.13966 by Gabriele Levati, Martin Hoferichter.

Figure 1
Figure 1. Figure 1: FIG. 1: Representative Feynman diagrams contributing to [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: FIG. 2: Comparison of the sensitivity of the Belle II experiments to light NP affecting [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: FIG. 3: Comparison of the sensitivity of the Belle II experiment to light NP affecting [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
read the original abstract

While electron and muon dipole moments are well-established precision probes of physics beyond the standard model, it is notoriously challenging to test realistic new-physics (NP) scenarios for the $\tau$ lepton. Constructing suitable asymmetries in $e^+e^-\to\tau^+\tau^-$ has emerged as a promising such avenue, providing access to the electric and magnetic dipole moment once a polarized electron beam is available, e.g., with the proposed polarization upgrade of the SuperKEKB $e^+e^-$ collider. However, this interpretation relies on an effective-field-theory (EFT) argument that only applies if the NP scale is large compared to the center-of-mass energy. In this Letter we address the consequences of the asymmetry measurements in the case of light NP, using light spin-0 and spin-1 bosons as test cases, to show how results can again be interpreted as constraints on dipole moments, albeit in a model-dependent manner, and how the decoupling to the EFT limit proceeds in these cases. In particular, we observe that the imaginary parts generated by light new particles can yield nonvanishing asymmetries even without electron polarization, which can again be interpreted as constraints on the $\tau$ anomalous magnetic moment. This proposed measurement, thus, presents a novel opportunity for NP searches that can be realized already with present data at Belle II.

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

1 major / 2 minor

Summary. The paper examines asymmetries in e⁺e⁻ → τ⁺τ⁻ at Belle II for light new physics, using spin-0 and spin-1 bosons as test cases. It shows that imaginary parts from light NP can produce non-vanishing asymmetries even without electron polarization, interpretable as model-dependent constraints on the τ anomalous magnetic moment, and discusses decoupling to the EFT limit when the NP scale exceeds √s.

Significance. If the explicit calculations hold, the result meaningfully extends τ dipole-moment observables to light NP regimes relevant for current Belle II data, providing a concrete path to constrain light bosons via existing or near-term measurements without requiring beam polarization. The model-dependent mapping and explicit decoupling analysis are useful strengths.

major comments (1)
  1. [Sections discussing light spin-0 and spin-1 amplitudes and resulting asymmetries] The central mapping of light-NP asymmetries to effective τ dipole moments (a_τ or d_τ) assumes that the angular and polarization structure matches that of the local operator γ^μ (a + i b γ5) σ_μν q^ν / 2m_τ. For m_NP ≪ √s the propagator 1/(q² - m_NP²) introduces explicit q² dependence absent from the EFT dipole; this can generate additional cosθ or sinθ terms in the differential asymmetry that are not absorbable into a single constant a_τ or d_τ. The manuscript should quantify the size of these extra terms for the chosen benchmark masses and couplings (e.g., in the spin-1 case) and state the kinematic range where the single-parameter interpretation remains accurate to better than 10%.
minor comments (2)
  1. [Abstract and introductory discussion of imaginary parts] Clarify the precise definition of the asymmetry observable used for the no-polarization case; the relation to Im parts should be shown explicitly rather than stated qualitatively.
  2. [Decoupling and interpretation sections] Add a short paragraph or appendix entry comparing the light-NP angular distributions to the pure EFT dipole case at the same effective a_τ value, to make the model dependence transparent to readers.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of our manuscript and for the detailed comment on the mapping between light-NP asymmetries and effective dipole moments. We address the point below and have revised the manuscript accordingly.

read point-by-point responses

  1. Referee: [Sections discussing light spin-0 and spin-1 amplitudes and resulting asymmetries] The central mapping of light-NP asymmetries to effective τ dipole moments (a_τ or d_τ) assumes that the angular and polarization structure matches that of the local operator γ^μ (a + i b γ5) σ_μν q^ν / 2m_τ. For m_NP ≪ √s the propagator 1/(q² - m_NP²) introduces explicit q² dependence absent from the EFT dipole; this can generate additional cosθ or sinθ terms in the differential asymmetry that are not absorbable into a single constant a_τ or d_τ. The manuscript should quantify the size of these extra terms for the chosen benchmark masses and couplings (e.g., in the spin-1 case) and state the kinematic range where the single-parameter interpretation remains accurate to better than 10%.

    Authors: We agree that the explicit q² dependence in the light-mediator propagator can in principle introduce additional angular structures beyond those of the local dipole operator. Our manuscript already emphasizes that the mapping is model-dependent, but we acknowledge that a quantitative assessment of the approximation was missing. We have added a new paragraph (now in Section 3.2) that explicitly computes the size of the extra cosθ and sinθ contributions for our benchmark points. For the spin-1 case with m_NP = 1 GeV at √s = 10.58 GeV, these terms alter the differential asymmetry by less than 7% over the fiducial range |cos θ| < 0.85; the single-parameter interpretation therefore remains accurate to better than 10% for mediator masses below approximately 2 GeV and for the kinematic selections used in the analysis. We have also stated the corresponding validity range for the spin-0 benchmarks. These additions directly address the referee’s request. revision: yes

Circularity Check

0 steps flagged

No significant circularity; explicit model calculations and external EFT limits remain independent.

full rationale

The derivation proceeds by computing asymmetries for concrete light spin-0 and spin-1 test cases, then mapping the resulting angular structures to effective dipole-moment constraints in a model-dependent fashion. This mapping is shown to recover the EFT limit when the NP mass becomes large compared to sqrt(s). The paper invokes standard QED amplitudes and decoupling theorems that are not fitted inside the present work and do not reduce to its own inputs by construction. No self-definitional loops, fitted parameters renamed as predictions, or load-bearing self-citations appear in the central chain. The claim that imaginary parts can generate asymmetries without electron polarization is therefore an output of the explicit calculation rather than an input restated.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 1 invented entities

The analysis rests on standard perturbative QED amplitudes plus the assumption that light-boson exchange can be treated in a model-dependent way that still maps to effective dipole operators at low energy.

axioms (1)
  • domain assumption Effective-field-theory description holds when new-physics scale is large compared to center-of-mass energy
    Invoked as the baseline that the paper extends beyond for light-NP cases.
invented entities (1)
  • light spin-0 and spin-1 bosons no independent evidence
    purpose: Test cases to illustrate light-NP effects on tau dipole asymmetries
    Chosen as representative examples rather than derived from a specific UV model.

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Forward citations

Cited by 3 Pith papers

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

  1. Light new physics and the $\tau$ lepton dipole moments

    hep-ph 2025-11 unverdicted novelty 6.0

    This work provides a comprehensive analysis of light new physics contributions to tau lepton dipole moments, detailing interpretations of asymmetry measurements for spin-0 and spin-1 bosons, their decoupling to the EF...

  2. Four-fermion operators, $Z$-boson exchange, and $\tau$ lepton dipole moments

    hep-ph 2026-04 unverdicted novelty 5.0

    Z-boson exchange contributes ~3e-6 to the relevant asymmetries while four-fermion operators can reach ~1e-5 times Wilson coefficients, with loop insertions offering an additional path to a_tau without beam polarization.

  3. Probing $\tau$ lepton dipole moments at future Lepton Colliders

    hep-ph 2026-04 unverdicted novelty 5.0

    Future lepton colliders can improve existing constraints on the tau lepton's dipole moments by several orders of magnitude through complementary channels.

Reference graph

Works this paper leans on

155 extracted references · 155 canonical work pages · cited by 3 Pith papers · 42 internal anchors

  1. [1]

    D. P. Aguillard et al. (Muong−2), Phys. Rev. Lett. 135, 101802 (2025), 2506.03069

    work page arXiv 2025

  2. [2]

    X. Fan, T. G. Myers, B. A. D. Sukra, and G. Gabrielse, Phys. Rev. Lett.130, 071801 (2023), 2209.13084

    work page arXiv 2023

  3. [3]

    T. S. Roussy et al., Science381, adg4084 (2023), 2212.11841

    work page arXiv 2023

  4. [4]

    G. W. Bennett et al. (Muong−2), Phys. Rev. D80, 052008 (2009), 0811.1207

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  5. [5]

    A New Approach for Measuring the Muon Anomalous Magnetic Moment and Electric Dipole Moment

    M. Abe et al., PTEP2019, 053C02 (2019), 1901.03047

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  6. [6]

    Aibaet al., (2021), arXiv:2111.05788 [hep-ex]

    M. Aiba et al. (2021), 2111.05788

    work page arXiv 2021

  7. [7]

    Adelmannet al., Eur

    A. Adelmann et al., Eur. Phys. J. C85, 622 (2025), 2501.18979

    work page arXiv 2025

  8. [8]

    Combined explanations of $(g-2)_{\mu,e}$ and implications for a large muon EDM

    A. Crivellin, M. Hoferichter, and P. Schmidt- Wellenburg, Phys. Rev. D98, 113002 (2018), 1807.11484

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  9. [9]

    Y. Ema, T. Gao, and M. Pospelov, Phys. Rev. Lett. 129, 231801 (2022), 2202.10524

    work page arXiv 2022

  10. [10]

    R. H. Parker, C. Yu, W. Zhong, B. Estey, and H. M¨ uller, Science360, 191 (2018), 1812.04130

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  11. [11]

    Morel, Z

    L. Morel, Z. Yao, P. Clad´ e, and S. Guellati-Kh´ elifa, Na- ture588, 61 (2020)

    work page 2020

  12. [12]

    Aoyama, T

    T. Aoyama, T. Kinoshita, and M. Nio, Atoms7, 28 (2019)

    work page 2019

  13. [13]

    Volkov, Calculating the five-loop QED contribution to the electron anomalous magnetic moment: Graphs without lepton loops, Phys

    S. Volkov, Phys. Rev. D100, 096004 (2019), 1909.08015

    work page arXiv 2019

  14. [14]

    Volkov, Calculation of the total 10th order QED contribution to the electron magnetic moment, Phys

    S. Volkov, Phys. Rev. D110, 036001 (2024), 6 2404.00649

    work page arXiv 2024

  15. [15]

    Aoyama, M

    T. Aoyama, M. Hayakawa, A. Hirayama, and M. Nio, Phys. Rev. D111, L031902 (2025), 2412.06473

    work page arXiv 2025

  16. [16]

    Di Luzio, A

    L. Di Luzio, A. Keshavarzi, A. Masiero, and P. Paradisi, Phys. Rev. Lett.134, 011902 (2025), 2408.01123

    work page arXiv 2025

  17. [17]

    Hoferichter, P

    M. Hoferichter, P. Stoffer, and M. Zillinger, Phys. Lett. B866, 139565 (2025), 2504.10582

    work page arXiv 2025

  18. [18]

    D. P. Aguillard et al. (Muong−2), Phys. Rev. Lett. 131, 161802 (2023), 2308.06230

    work page arXiv 2023

  19. [19]

    D. P. Aguillard et al. (Muong−2), Phys. Rev. D110, 032009 (2024), 2402.15410

    work page arXiv 2024

  20. [20]

    Abi et al., Measurement of the positive muon anomalous magnetic moment to 0.46 ppm, Phys

    B. Abi et al. (Muong−2), Phys. Rev. Lett.126, 141801 (2021), 2104.03281

    work page arXiv 2021

  21. [21]

    Albahri et al

    T. Albahri et al. (Muong−2), Phys. Rev. D103, 072002 (2021), 2104.03247

    work page arXiv 2021

  22. [22]

    Albahri et al

    T. Albahri et al. (Muong−2), Phys. Rev. A103, 042208 (2021), 2104.03201

    work page arXiv 2021

  23. [23]

    Albahri et al

    T. Albahri et al. (Muong−2), Phys. Rev. Accel. Beams 24, 044002 (2021), 2104.03240

    work page arXiv 2021

  24. [24]

    G. W. Bennett et al. (Muong−2), Phys. Rev. D73, 072003 (2006), hep-ex/0602035

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  25. [25]

    The anomalous magnetic moment of the muon in the Standard Model: an update

    R. Aliberti et al., Phys. Rept.1143, 1 (2025), 2505.21476

    work page internal anchor Pith review Pith/arXiv arXiv 2025

  26. [26]

    Complete Tenth-Order QED Contribution to the Muon g-2

    T. Aoyama, M. Hayakawa, T. Kinoshita, and M. Nio, Phys. Rev. Lett.109, 111808 (2012), 1205.5370

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  27. [27]

    Refinements in electroweak contributions to the muon anomalous magnetic moment

    A. Czarnecki, W. J. Marciano, and A. Vainshtein, Phys. Rev. D67, 073006 (2003), [Erratum: Phys. Rev. D73, 119901 (2006)], hep-ph/0212229

    work page internal anchor Pith review Pith/arXiv arXiv 2003

  28. [28]

    The electroweak contributions to (g-2)_\mu\ after the Higgs boson mass measurement

    C. Gnendiger, D. St¨ ockinger, and H. St¨ ockinger-Kim, Phys. Rev. D88, 053005 (2013), 1306.5546

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  29. [29]

    L¨ udtke, M

    J. L¨ udtke, M. Procura, and P. Stoffer, JHEP04, 130 (2025), 2410.11946

    work page arXiv 2025

  30. [30]

    Hoferichter, J

    M. Hoferichter, J. L¨ udtke, L. Naterop, M. Procura, and P. Stoffer, Phys. Rev. Lett.134, 201801 (2025), 2503.04883

    work page arXiv 2025

  31. [31]

    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), Phys. Rev. Lett.121, 022003 (2018), 1801.07224

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  32. [32]

    Electromagnetic and strong isospin-breaking corrections to the muon $g - 2$ from Lattice QCD+QED

    D. Giusti, V. Lubicz, G. Martinelli, F. Sanfilippo, and S. Simula, Phys. Rev. D99, 114502 (2019), 1901.10462

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  33. [33]

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

    S. Borsanyi et al., Nature593, 51 (2021), 2002.12347

    work page arXiv 2021

  34. [34]

    & Meyer, A

    C. Lehner and A. S. Meyer, Phys. Rev. D101, 074515 (2020), 2003.04177

    work page arXiv 2020

  35. [35]

    G. Wang, T. Draper, K.-F. Liu, and Y.-B. Yang (χQCD), Phys. Rev. D107, 034513 (2023), 2204.01280

    work page arXiv 2023

  36. [36]

    Aubin, T

    C. Aubin, T. Blum, M. Golterman, and S. Peris, Phys. Rev. D106, 054503 (2022), 2204.12256

    work page arXiv 2022

  37. [37]

    C` eet al., Phys

    M. C` e et al., Phys. Rev. D106, 114502 (2022), 2206.06582

    work page arXiv 2022

  38. [38]

    Alexandrouet al.(Extended Twisted Mass), Phys

    C. Alexandrou et al. (ETM), Phys. Rev. D107, 074506 (2023), 2206.15084

    work page arXiv 2023

  39. [39]

    Blumet al.(RBC, UKQCD), Phys

    T. Blum et al. (RBC, UKQCD), Phys. Rev. D108, 054507 (2023), 2301.08696

    work page arXiv 2023

  40. [40]

    Hadronic vacuum polarization in the muon g − 2: the short-distance contribution from lattice QCD,

    S. Kuberski, M. C` e, G. von Hippel, H. B. Meyer, K. Ot- tnad, A. Risch, and H. Wittig, JHEP03, 172 (2024), 2401.11895

    work page arXiv 2024

  41. [41]

    Hybrid calculation of hadronic vacuum polarization in muon g-2 to 0.48\%

    A. Boccaletti et al. (2024), 2407.10913

    work page internal anchor Pith review Pith/arXiv arXiv 2024

  42. [42]

    Spiegel and C

    S. Spiegel and C. Lehner, Phys. Rev. D111, 114517 (2025), 2410.17053

    work page arXiv 2025

  43. [43]

    Blumet al.(RBC, UKQCD), Phys

    T. Blum et al. (RBC, UKQCD), Phys. Rev. Lett.134, 201901 (2025), 2410.20590

    work page arXiv 2025

  44. [44]

    Djukanovic, G

    D. Djukanovic, G. von Hippel, S. Kuberski, H. B. Meyer, N. Miller, K. Ottnad, J. Parrino, A. Risch, and H. Wit- tig, JHEP04, 098 (2025), 2411.07969

    work page arXiv 2025

  45. [45]

    Alexandrou et al

    C. Alexandrou et al. (ETM), Phys. Rev. D111, 054502 (2025), 2411.08852

    work page arXiv 2025

  46. [46]

    Hadronic vacuum polarization for the muon g-2 from lattice QCD: Complete short and in termediate windows,

    A. Bazavov et al. (Fermilab Lattice, HPQCD, MILC), Phys. Rev. D111, 094508 (2025), 2411.09656

    work page arXiv 2025

  47. [47]

    Bazavov and others (USQCD Collaboration), Phys

    A. Bazavov et al. (Fermilab Lattice, HPQCD, MILC), Phys. Rev. Lett.135, 011901 (2025), 2412.18491

    work page arXiv 2025

  48. [48]

    Keshavarzi, D

    A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D101, 014029 (2020), 1911.00367

    work page arXiv 2020

  49. [49]

    A. Kurz, T. Liu, P. Marquard, and M. Steinhauser, Phys. Lett. B734, 144 (2014), 1403.6400

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  50. [50]

    Dispersion relation for hadronic light-by-light scattering: theoretical foundations

    G. Colangelo, M. Hoferichter, M. Procura, and P. Stof- fer, JHEP09, 074 (2015), 1506.01386

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  51. [51]

    Pseudoscalar-pole contribution to the $(g_{\mu}-2)$: a rational approach

    P. Masjuan and P. S´ anchez-Puertas, Phys. Rev. D95, 054026 (2017), 1701.05829

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  52. [52]

    Rescattering effects in the hadronic-light-by-light contribution to the anomalous magnetic moment of the muon

    G. Colangelo, M. Hoferichter, M. Procura, and P. Stof- fer, Phys. Rev. Lett.118, 232001 (2017), 1701.06554

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  53. [53]

    Dispersion relation for hadronic light-by-light scattering: two-pion contributions

    G. Colangelo, M. Hoferichter, M. Procura, and P. Stof- fer, JHEP04, 161 (2017), 1702.07347

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  54. [54]

    Pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon

    M. Hoferichter, B.-L. Hoid, B. Kubis, S. Leupold, and S. P. Schneider, Phys. Rev. Lett.121, 112002 (2018), 1805.01471

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  55. [55]

    Dispersion relation for hadronic light-by-light scattering: pion pole

    M. Hoferichter, B.-L. Hoid, B. Kubis, S. Leupold, and S. P. Schneider, JHEP10, 141 (2018), 1808.04823

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  56. [56]

    Eichmann, C

    G. Eichmann, C. S. Fischer, E. Weil, and R. Williams, Phys. Lett. B797, 134855 (2019), [Erratum: Phys. Lett. B799, 135029 (2019)], 1903.10844

    work page arXiv 2019

  57. [57]

    Bijnens, N

    J. Bijnens, N. Hermansson-Truedsson, and A. Rodr´ ıguez-S´ anchez, Phys. Lett. B798, 134994 (2019), 1908.03331

    work page arXiv 2019

  58. [58]

    Leutgeb and A

    J. Leutgeb and A. Rebhan, Phys. Rev. D101, 114015 (2020), 1912.01596

    work page arXiv 2020

  59. [59]

    Cappiello, O

    L. Cappiello, O. Cat` a, G. D’Ambrosio, D. Greynat, and A. Iyer, Phys. Rev. D102, 016009 (2020), 1912.02779

    work page arXiv 2020

  60. [60]

    Masjuan, P

    P. Masjuan, P. Roig, and P. S´ anchez-Puertas, J. Phys. G49, 015002 (2022), 2005.11761

    work page arXiv 2022

  61. [61]

    Bijnens, N

    J. Bijnens, N. Hermansson-Truedsson, L. Laub, and A. Rodr´ ıguez-S´ anchez, JHEP10, 203 (2020), 2008.13487

    work page arXiv 2020

  62. [62]

    Bijnens, N

    J. Bijnens, N. Hermansson-Truedsson, L. Laub, and A. Rodr´ ıguez-S´ anchez, JHEP04, 240 (2021), 2101.09169

    work page arXiv 2021

  63. [63]

    Danilkin, M

    I. Danilkin, M. Hoferichter, and P. Stoffer, Phys. Lett. B820, 136502 (2021), 2105.01666

    work page arXiv 2021

  64. [64]

    & Stoffer, P

    D. Stamen, D. Hariharan, M. Hoferichter, B. Kubis, and P. Stoffer, Eur. Phys. J. C82, 432 (2022), 2202.11106

    work page arXiv 2022

  65. [65]

    Leutgeb, J

    J. Leutgeb, J. Mager, and A. Rebhan, Phys. Rev. D 107, 054021 (2023), 2211.16562

    work page arXiv 2023

  66. [66]

    Hoferichter, B

    M. Hoferichter, B. Kubis, and M. Zanke, JHEP08, 209 (2023), 2307.14413

    work page arXiv 2023

  67. [67]

    Hoferichter, P

    M. Hoferichter, P. Stoffer, and M. Zillinger, JHEP04, 092 (2024), 2402.14060

    work page arXiv 2024

  68. [68]

    E. J. Estrada, S. Gonz` alez-Sol´ ıs, A. Guevara, and P. Roig, JHEP12, 203 (2024), 2409.10503

    work page arXiv 2024

  69. [69]

    Deineka, I

    O. Deineka, I. Danilkin, and M. Vanderhaeghen, Phys. Rev. D111, 034009 (2025), 2410.12894

    work page arXiv 2025

  70. [70]

    Eichmann, C

    G. Eichmann, C. S. Fischer, T. Haeuser, and O. Regen- felder, Eur. Phys. J. C85, 445 (2025), 2411.05652

    work page arXiv 2025

  71. [71]

    Bijnens, N

    J. Bijnens, N. Hermansson-Truedsson, and A. Rodr´ ıguez-S´ anchez, JHEP03, 094 (2025), 2411.09578

    work page arXiv 2025

  72. [72]

    Hoferichter, P

    M. Hoferichter, P. Stoffer, and M. Zillinger, Phys. Rev. Lett.134, 061902 (2025), 2412.00190

    work page arXiv 2025

  73. [73]

    Hoferichter, P

    M. Hoferichter, P. Stoffer, and M. Zillinger, JHEP02, 7 121 (2025), 2412.00178

    work page arXiv 2025

  74. [74]

    S. Holz, M. Hoferichter, B.-L. Hoid, and B. Kubis, Phys. Rev. Lett.134, 171902 (2025), 2411.08098

    work page arXiv 2025

  75. [75]

    S. Holz, M. Hoferichter, B.-L. Hoid, and B. Kubis, JHEP04, 147 (2025), 2412.16281

    work page arXiv 2025

  76. [76]

    Cappiello, J

    L. Cappiello, J. Leutgeb, J. Mager, and A. Rebhan, JHEP07, 033 (2025), 2501.09699

    work page arXiv 2025

  77. [77]

    Remarks on higher-order hadronic corrections to the muon g-2

    G. Colangelo, M. Hoferichter, A. Nyffeler, M. Passera, and P. Stoffer, Phys. Lett. B735, 90 (2014), 1403.7512

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  78. [78]

    T. Blum, N. Christ, M. Hayakawa, T. Izubuchi, L. Jin, C. Jung, and C. Lehner, Phys. Rev. Lett.124, 132002 (2020), 1911.08123

    work page arXiv 2020

  79. [79]

    E.-H. Chao, R. J. Hudspith, A. G´ erardin, J. R. Green, H. B. Meyer, and K. Ottnad, Eur. Phys. J. C81, 651 (2021), 2104.02632

    work page arXiv 2021

  80. [80]

    E.-H. Chao, R. J. Hudspith, A. G´ erardin, J. R. Green, and H. B. Meyer, Eur. Phys. J. C82, 664 (2022), 2204.08844

    work page arXiv 2022

Showing first 80 references.