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arxiv: 2006.04822 · v2 · pith:EJQLP5KYnew · submitted 2020-06-08 · ✦ hep-ph · hep-ex· hep-lat· nucl-ex· nucl-th

The anomalous magnetic moment of the muon in the Standard Model

T. Aoyama , N. Asmussen , M. Benayoun , J. Bijnens , T. Blum , M. Bruno , I. Caprini , C. M. Carloni Calame
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M. C\`e G. Colangelo F. Curciarello H. Czy\.z I. Danilkin M. Davier C. T. H. Davies M. Della Morte S. I. Eidelman A. X. El-Khadra A. G\'erardin D. Giusti M. Golterman Steven Gottlieb V. G\"ulpers F. Hagelstein M. Hayakawa G. Herdo\'iza D. W. Hertzog A. Hoecker M. Hoferichter B.-L. Hoid R. J. Hudspith F. Ignatov T. Izubuchi F. Jegerlehner L. Jin A. Keshavarzi T. Kinoshita B. Kubis A. Kupich A. Kup\'s\'c L. Laub C. Lehner L. Lellouch I. Logashenko B. Malaescu K. Maltman M. K. Marinkovi\'c P. Masjuan A. S. Meyer H. B. Meyer T. Mibe K. Miura S. E. M\"uller M. Nio D. Nomura A. Nyffeler V. Pascalutsa M. Passera E. Perez del Rio S. Peris A. Portelli M. Procura C. F. Redmer B. L. Roberts P. S\'anchez-Puertas S. Serednyakov B. Shwartz S. Simula D. St\"ockinger H. St\"ockinger-Kim P. Stoffer T. Teubner R. Van de Water M. Vanderhaeghen G. Venanzoni G. von Hippel H. Wittig Z. Zhang M. N. Achasov A. Bashir N. Cardoso B. Chakraborty E.-H. Chao J. Charles A. Crivellin O. Deineka A. Denig C. DeTar C. A. Dominguez A. E. Dorokhov V. P. Druzhinin G. Eichmann M. Fael C. S. Fischer E. G\'amiz Z. Gelzer J. R. Green S. Guellati-Khelifa D. Hatton N. Hermansson-Truedsson S. Holz B. H\"orz M. Knecht J. Koponen A. S. Kronfeld J. Laiho S. Leupold P. B. Mackenzie W. J. Marciano C. McNeile D. Mohler J. Monnard E. T. Neil A. V. Nesterenko K. Ottnad V. Pauk A. E. Radzhabov E. de Rafael K. Raya A. Risch A. Rodr\'iguez-S\'anchez P. Roig T. San Jos\'e E. P. Solodov R. Sugar K. Yu. Todyshev A. Vainshtein A. Vaquero Avil\'es-Casco E. Weil J. Wilhelm R. Williams A. S. Zhevlakov
This is my paper

Pith reviewed 2026-05-24 12:46 UTC · model grok-4.3

classification ✦ hep-ph hep-exhep-latnucl-exnucl-th
keywords muon anomalous magnetic momentStandard Modelhadronic vacuum polarizationhadronic light-by-light scatteringdispersion relationslattice QCDelectroweak contributionsnew physics
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The pith

The Standard Model predicts the muon anomalous magnetic moment as 116591810(43) times 10 to the minus 11, 3.7 sigma below the Brookhaven measurement.

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

This review assembles the complete Standard Model value for the muon anomalous magnetic moment by combining the pure QED term evaluated to order alpha to the fifth, the electroweak term known to two loops, and the hadronic terms. The hadronic vacuum polarization at order alpha squared and the hadronic light-by-light scattering at order alpha cubed are computed with dispersion relations from experimental data and with lattice QCD. These nonperturbative pieces dominate the final uncertainty of 43 times 10 to the minus 11. The resulting prediction lies 3.7 standard deviations below the experimental average, and the paper notes that forthcoming Fermilab and J-PARC data will reduce the experimental error by up to a factor of four.

Core claim

The Standard Model value is a_mu^SM equals 116591810(43) times 10 to the minus 11. This total is obtained after adding the dominant QED contribution, the suppressed electroweak contribution, and the hadronic vacuum polarization and light-by-light contributions that are evaluated nonperturbatively. The result differs from the Brookhaven experimental average by 3.7 sigma.

What carries the argument

The hadronic vacuum polarization and hadronic light-by-light scattering contributions, obtained through dispersion relations and lattice QCD, which supply almost the entire theoretical uncertainty.

If this is right

  • If both the calculated value and the experimental measurement hold, the discrepancy points to contributions from physics outside the Standard Model.
  • Further reduction of the hadronic uncertainty through improved lattice simulations or more precise e+e- data will be required to confirm the tension at higher significance.
  • The Fermilab experiment's expected factor-of-four reduction in experimental error will turn the present 3.7 sigma difference into either a clearer signal or a resolved agreement.
  • Similar methods applied to other low-energy observables can cross-check the same hadronic inputs used here.

Where Pith is reading between the lines

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

  • A persistent discrepancy after the new experiments would motivate targeted searches for TeV-scale particles whose loops could shift the muon moment without affecting other precision observables at the same level.
  • The same dispersion and lattice techniques used for the light-by-light term could be extended to calculate hadronic contributions to the electron anomalous moment or to rare meson decays.
  • If the tension is confirmed, global fits to beyond-Standard-Model parameters will need to incorporate this observable alongside Higgs and flavor data.

Load-bearing premise

The hadronic contributions are captured accurately enough by dispersion relations and lattice QCD that the quoted uncertainty of 43 times 10 to the minus 11 accounts for all relevant systematic effects.

What would settle it

A lattice QCD or dispersive re-evaluation that shifts the central hadronic contribution by more than 50 times 10 to the minus 11 while keeping a comparable uncertainty would remove the 3.7 sigma tension.

read the original abstract

We review the present status of the Standard Model calculation of the anomalous magnetic moment of the muon. This is performed in a perturbative expansion in the fine-structure constant $\alpha$ and is broken down into pure QED, electroweak, and hadronic contributions. The pure QED contribution is by far the largest and has been evaluated up to and including $\mathcal{O}(\alpha^5)$ with negligible numerical uncertainty. The electroweak contribution is suppressed by $(m_\mu/M_W)^2$ and only shows up at the level of the seventh significant digit. It has been evaluated up to two loops and is known to better than one percent. Hadronic contributions are the most difficult to calculate and are responsible for almost all of the theoretical uncertainty. The leading hadronic contribution appears at $\mathcal{O}(\alpha^2)$ and is due to hadronic vacuum polarization, whereas at $\mathcal{O}(\alpha^3)$ the hadronic light-by-light scattering contribution appears. Given the low characteristic scale of this observable, these contributions have to be calculated with nonperturbative methods, in particular, dispersion relations and the lattice approach to QCD. The largest part of this review is dedicated to a detailed account of recent efforts to improve the calculation of these two contributions with either a data-driven, dispersive approach, or a first-principle, lattice-QCD approach. The final result reads $a_\mu^\text{SM}=116\,591\,810(43)\times 10^{-11}$ and is smaller than the Brookhaven measurement by 3.7$\sigma$. The experimental uncertainty will soon be reduced by up to a factor four by the new experiment currently running at Fermilab, and also by the future J-PARC experiment. This and the prospects to further reduce the theoretical uncertainty in the near future-which are also discussed here-make this quantity one of the most promising places to look for evidence of new physics.

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 manuscript reviews the Standard Model calculation of the muon anomalous magnetic moment a_μ^SM, decomposed into QED (to O(α^5)), electroweak (to two loops), and hadronic (HVP at O(α^2) and HLbL at O(α^3)) contributions. The central result is a_μ^SM = 116591810(43) × 10^{-11}, 3.7σ below the Brookhaven measurement, with prospects for reduced experimental and theoretical uncertainties discussed.

Significance. If the result holds, the 3.7σ tension positions a_μ as a leading probe for beyond-Standard-Model physics, especially with the factor-of-four improvement expected from Fermilab and J-PARC data. The review's detailed compilation of dispersive and lattice-QCD methods for the hadronic terms provides a valuable reference for the field.

major comments (1)
  1. [Abstract / final numerical result] Abstract and final-result compilation: the total uncertainty of 43 × 10^{-11} is dominated by the hadronic vacuum polarization and light-by-light terms obtained by aggregating published dispersion-relation and lattice results; the text does not contain an explicit global error analysis showing how correlations across e+e− data sets, radiative corrections, and lattice systematics (finite-volume, chiral extrapolation) are combined, which is load-bearing for the quoted 3.7σ discrepancy.
minor comments (2)
  1. [Introduction] Notation for the separate QED, EW, and hadronic pieces is introduced in the abstract but would benefit from a single consolidated table early in the manuscript for quick reference.
  2. [Hadronic sections] Figure captions for the hadronic contributions should explicitly list the data sets or lattice ensembles used in each cited calculation.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript and for the recommendation of minor revision. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract / final numerical result] Abstract and final-result compilation: the total uncertainty of 43 × 10^{-11} is dominated by the hadronic vacuum polarization and light-by-light terms obtained by aggregating published dispersion-relation and lattice results; the text does not contain an explicit global error analysis showing how correlations across e+e− data sets, radiative corrections, and lattice systematics (finite-volume, chiral extrapolation) are combined, which is load-bearing for the quoted 3.7σ discrepancy.

    Authors: The manuscript is a review that compiles and summarizes the present status of the literature rather than performing a new global fit to the underlying data. The quoted central value and total uncertainty of 43 × 10^{-11} are taken directly from the consensus of published dispersion-relation and lattice-QCD results, each of which already incorporates its own treatment of experimental correlations, radiative corrections, and lattice systematics. A dedicated global error analysis that simultaneously reprocesses all e+e− data sets and lattice ensembles would constitute a separate research project beyond the scope of this review. The 3.7σ tension is therefore reported using the uncertainties as they appear in the current literature; we have added a clarifying sentence in the introduction to make this distinction explicit. revision: partial

Circularity Check

0 steps flagged

No circularity: review aggregates independent external calculations

full rationale

The manuscript is a review that compiles the muon g-2 result as a sum of QED (to O(α^5)), electroweak (to two loops), and hadronic (HVP via dispersion on e+e- data; HLbL via lattice or dispersive methods) contributions. Each component is taken from published, independent evaluations using external data or first-principles lattice simulations; the paper performs no new fit, no self-referential definition of a quantity in terms of itself, and no load-bearing uniqueness theorem imported from the same authors. The quoted central value and uncertainty are therefore not forced by construction within the review.

Axiom & Free-Parameter Ledger

2 free parameters · 2 axioms · 0 invented entities

The central numerical result depends on the accuracy of multiple independent calculations, particularly the non-perturbative hadronic ones that rely on experimental inputs and numerical simulations rather than first-principles derivations within the review.

free parameters (2)
  • hadronic vacuum polarization fit parameters
    Parameters fitted to experimental e+e- annihilation data in the dispersive approach.
  • lattice QCD parameters
    Various parameters in lattice simulations such as quark masses and lattice spacing.
axioms (2)
  • domain assumption The Standard Model Lagrangian is the correct effective theory at the relevant energy scales.
    The calculation assumes the validity of the SM without additional new physics contributions to a_μ.
  • domain assumption Dispersion relations and lattice QCD provide accurate non-perturbative evaluations of hadronic contributions.
    Invoked in the sections discussing hadronic vacuum polarization and light-by-light scattering.

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discussion (0)

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Reference graph

Works this paper leans on

300 extracted references · 300 canonical work pages · cited by 23 Pith papers · 195 internal anchors

  1. [1]

    G. W. Bennett et al. (Muon g− 2), Phys. Rev. D73, 072003 (2006), arXiv:hep-ex/0602035 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  2. [2]

    Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon g-2 and alpha(mZ) using newest hadronic cross-section data

    M. Davier, A. Hoecker, B. Malaescu, and Z. Zhang, Eur. Phys. J. C77, 827 (2017), arXiv:1706.09436 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  3. [3]

    The muon $g-2$ and $\alpha(M_Z^2)$: a new data-based analysis

    A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D97, 114025 (2018), arXiv:1802.02995 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  4. [4]

    Two-pion contribution to hadronic vacuum polarization

    G. Colangelo, M. Hoferichter, and P. Sto ffer, JHEP 02, 006 (2019), arXiv:1810.00007 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  5. [5]

    Hoferichter, B.-L

    M. Hoferichter, B.-L. Hoid, and B. Kubis, JHEP 08, 137 (2019), arXiv:1907.01556 [hep-ph]

    work page arXiv 2019

  6. [6]

    Davier, A

    M. Davier, A. Hoecker, B. Malaescu, and Z. Zhang, Eur. Phys. J. C80, 241 (2020), [Erratum: Eur. Phys. J. C80, 410 (2020)], arXiv:1908.00921 [hep-ph]

    work page arXiv 2020

  7. [7]

    Keshavarzi, D

    A. Keshavarzi, D. Nomura, and T. Teubner, Phys. Rev. D101, 014029 (2020), arXiv:1911.00367 [hep-ph]

    work page arXiv 2020

  8. [8]

    A. Kurz, T. Liu, P. Marquard, and M. Steinhauser, Phys. Lett. B734, 144 (2014), arXiv:1403.6400 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  9. [9]

    Strong-isospin-breaking correction to the muon anomalous magnetic moment from lattice QCD at the physical point

    B. Chakraborty et al. (Fermilab Lattice, LATTICE-HPQCD, MILC), Phys. Rev. Lett.120, 152001 (2018), arXiv:1710.11212 [hep-lat]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  10. [10]

    Hadronic vacuum polarization contribution to the anomalous magnetic moments of leptons from first principles

    S. Borsanyi et al. (Budapest-Marseille-Wuppertal), Phys. Rev. Lett. 121, 022002 (2018), arXiv:1711.04980 [hep-lat]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  11. [11]

    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), arXiv:1801.07224 [hep-lat]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  12. [12]

    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 (ETM), Phys. Rev. D99, 114502 (2019), arXiv:1901.10462 [hep-lat]

    work page internal anchor Pith review Pith/arXiv arXiv 2019

  13. [13]

    Shintani and Y

    E. Shintani and Y . Kuramashi, Phys. Rev. D100, 034517 (2019), arXiv:1902.00885 [hep-lat]

    work page arXiv 2019

  14. [14]

    C. T. H. Davies et al. (Fermilab Lattice, LATTICE-HPQCD, MILC), Phys. Rev.D101, 034512 (2020), arXiv:1902.04223 [hep-lat]

    work page arXiv 2020

  15. [15]

    G ´erardin, M

    A. G ´erardin, M. C `e, G. von Hippel, B. H ¨orz, H. B. Meyer, D. Mohler, K. Ottnad, J. Wilhelm, and H. Wittig, Phys. Rev. D100, 014510 (2019), arXiv:1904.03120 [hep-lat]

    work page arXiv 2019

  16. [16]

    Aubin, T

    C. Aubin, T. Blum, C. Tu, M. Golterman, C. Jung, and S. Peris, Phys. Rev. D101, 014503 (2020), arXiv:1905.09307 [hep-lat]

    work page arXiv 2020

  17. [17]

    Giusti and S

    D. Giusti and S. Simula, PoS LA TTICE2019, 104 (2019), arXiv:1910.03874 [hep-lat]

    work page arXiv 2019

  18. [18]

    Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment revisited

    K. Melnikov and A. Vainshtein, Phys. Rev. D70, 113006 (2004), arXiv:hep-ph/0312226 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  19. [19]

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

    P. Masjuan and P. S ´anchez-Puertas, Phys. Rev. D95, 054026 (2017), arXiv:1701.05829 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  20. [20]

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

    G. Colangelo, M. Hoferichter, M. Procura, and P. Sto ffer, JHEP 04, 161 (2017), arXiv:1702.07347 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  21. [21]

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

    M. Hoferichter, B.-L. Hoid, B. Kubis, S. Leupold, and S. P. Schneider, JHEP 10, 141 (2018), arXiv:1808.04823 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  22. [22]

    G ´erardin, H

    A. G ´erardin, H. B. Meyer, and A. Ny ffeler, Phys. Rev. D100, 034520 (2019), arXiv:1903.09471 [hep-lat]

    work page arXiv 2019

  23. [23]

    Bijnens, N

    J. Bijnens, N. Hermansson-Truedsson, and A. Rodr ´ıguez-S´anchez, Phys. Lett. B798, 134994 (2019), arXiv:1908.03331 [hep-ph]

    work page arXiv 2019

  24. [24]

    Colangelo, F

    G. Colangelo, F. Hagelstein, M. Hoferichter, L. Laub, and P. Sto ffer, JHEP 03, 101 (2020), arXiv:1910.13432 [hep-ph]

    work page arXiv 2020

  25. [25]

    Single meson contributions to the muon's anomalous magnetic moment

    V . Pauk and M. Vanderhaeghen, Eur. Phys. J.C74, 3008 (2014), arXiv:1401.0832 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  26. [26]

    Light-by-light scattering sum rules in light of new data

    I. Danilkin and M. Vanderhaeghen, Phys. Rev. D95, 014019 (2017), arXiv:1611.04646 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  27. [27]

    Jegerlehner, Springer Tracts Mod

    F. Jegerlehner, Springer Tracts Mod. Phys. 274, 1 (2017)

    work page 2017

  28. [28]

    Scalar Meson Contributions to a_\mu from Hadronic Light-by-Light Scattering

    M. Knecht, S. Narison, A. Rabemananjara, and D. Rabetiarivony, Phys. Lett. B787, 111 (2018), arXiv:1808.03848 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2018

  29. [29]

    Eichmann, C

    G. Eichmann, C. S. Fischer, and R. Williams, Phys. Rev. D101, 054015 (2020), arXiv:1910.06795 [hep-ph]

    work page arXiv 2020

  30. [30]

    Roig and P

    P. Roig and P. S ´anchez-Puertas, Phys. Rev. D101, 074019 (2020), arXiv:1910.02881 [hep-ph]

    work page arXiv 2020

  31. [31]

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

    G. Colangelo, M. Hoferichter, A. Ny ffeler, M. Passera, and P. Stoffer, Phys. Lett. B735, 90 (2014), arXiv:1403.7512 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  32. [32]

    T. Blum, N. Christ, M. Hayakawa, T. Izubuchi, L. Jin, C. Jung, and C. Lehner, Phys. Rev. Lett. 124, 132002 (2020), arXiv:1911.08123 [hep-lat]

    work page arXiv 2020

  33. [33]

    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), arXiv:1205.5370 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  34. [34]

    Aoyama, T

    T. Aoyama, T. Kinoshita, and M. Nio, Atoms 7, 28 (2019)

    work page 2019

  35. [35]

    Czarnecki, W

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

    work page arXiv 2003

  36. [36]

    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), arXiv:1306.5546 [hep-ph]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  37. [37]

    J. Z. Bai et al. (BES), Phys. Rev. Lett. 84, 594 (2000), arXiv:hep-ex/9908046 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  38. [38]

    R. R. Akhmetshin et al. (CMD-2), Phys. Lett. B476, 33 (2000), arXiv:hep-ex/0002017 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  39. [39]

    R. R. Akhmetshin et al. (CMD-2), Phys. Lett. B489, 125 (2000), arXiv:hep-ex/0009013 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2000

  40. [40]

    M. N. Achasov et al. (SND), Phys. Rev. D63, 072002 (2001), arXiv:hep-ex/0009036 [hep-ex]

    work page arXiv 2001

  41. [41]

    J. Z. Bai et al. (BES), Phys. Rev. Lett. 88, 101802 (2002), arXiv:hep-ex/0102003 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  42. [42]

    M. N. Achasov et al. (SND), Phys. Rev. D66, 032001 (2002), arXiv:hep-ex/0201040 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2002

  43. [43]

    R. R. Akhmetshin et al. (CMD-2), Phys. Lett. B578, 285 (2004), arXiv:hep-ex/0308008 [hep-ex]

    work page arXiv 2004

  44. [44]

    Study of e+e- --> pi+ pi- pi0 process using initial state radiation with BABAR

    B. Aubert et al. (BABAR), Phys. Rev.D70, 072004 (2004), arXiv:hep-ex/0408078 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2004

  45. [45]

    The $\epem\to\pi^+\pi^-\pi^+\pi^-$, $K^+K^-\pi^+\pi^-$, and $K^+K^- K^+K^- $ Cross Sections at Center-of-Mass Energies 0.5--4.5 \gev Measured with Initial-State Radiation

    B. Aubert et al. (BABAR), Phys. Rev.D71, 052001 (2005), arXiv:hep-ex/0502025 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  46. [46]

    A study of e+e- -> p anti-p using initial state radiation with BABAR

    B. Aubert et al. (BABAR), Phys. Rev.D73, 012005 (2006), arXiv:hep-ex/0512023 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  47. [47]

    The e+ e- --> 3(pi+pi-), 2(pi+pi-pi0) and K+K- 2(pi+pi-) Cross Sections at Center-of-Mass Energies from Production Threshold to 4.5 GeV Measured with Initial-State Radiation

    B. Aubert et al. (BABAR), Phys. Rev.D73, 052003 (2006), arXiv:hep-ex/0602006 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  48. [48]

    V . M. Aul’chenko et al. (CMD-2), JETP Lett. 82, 743 (2005), [Pisma Zh. Eksp. Teor. Fiz. 82, 841 (2005)], arXiv:hep-ex/0603021 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2005

  49. [49]

    M. N. Achasov et al. (SND), J. Exp. Theor. Phys. 103, 380 (2006), [Zh. Eksp. Teor. Fiz. 130, 437 (2006)], arXiv:hep-ex/0605013 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  50. [50]

    V . M. Aul’chenko et al. (CMD-2), JETP Lett. 84, 413 (2006), [Pisma Zh. Eksp. Teor. Fiz. 84, 491 (2006)], arXiv:hep-ex/0610016 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2006

  51. [51]

    R. R. Akhmetshin et al. (CMD-2), Phys. Lett. B648, 28 (2007), arXiv:hep-ex/0610021 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  52. [52]

    R. R. Akhmetshin et al. (CMD-2), Phys. Lett. B642, 203 (2006)

    work page 2006

  53. [53]

    The $e^+ e^-\to K^+ K^- \pi^+\pi^-$, $K^+ K^- \pi^0\pi^0$ and $K^+ K^- K^+ K^-$ Cross Sections Measured with Initial-State Radiation

    B. Aubert et al. (BABAR), Phys. Rev.D76, 012008 (2007), arXiv:0704.0630 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  54. [54]

    The $e^+ e^-\to 2(\pi^+\pi^-)\pi^0$, 2(\pi^+\pi^-)\eta$, $K^+ K^-\pi^+\pi^-\pi^0$ and $K^+ K^-\pi^+\pi^-\eta$ Cross Sections Measured with Initial-State Radiation

    B. Aubert et al. (BABAR), Phys. Rev.D76, 092005 (2007), [Erratum: Phys. Rev. D77, 119902 (2008)], arXiv:0708.2461 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  55. [55]

    Study of e+e- --> Lambda anti-Lambda, Lambda anti-Sigma0, Sigma0 anti-Sigma0 using Initial State Radiation with BABAR

    B. Aubert et al. (BABAR), Phys. Rev.D76, 092006 (2007), arXiv:0709.1988 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2007

  56. [56]

    Measurements of e+e- -> K+K-eta, K+K-pi0 and KsK+pi- Cross Sections Using Initial State Radiation Events

    B. Aubert et al. (BABAR), Phys. Rev.D77, 092002 (2008), arXiv:0710.4451 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  57. [57]

    R. R. Akhmetshin et al. (CMD-2), Phys. Lett. B669, 217 (2008), arXiv:0804.0178 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2008

  58. [58]

    Measurement of $\sigma(e^+e^-\to\pi^+\pi^-\gamma(\gamma))$ and the dipion contribution to the muon anomaly with the KLOE detector

    F. Ambrosino et al. (KLOE), Phys. Lett. B670, 285 (2009), arXiv:0809.3950 [hep-ex]. 182

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  59. [59]

    $R$ value measurements for $e^+e^-$ annihilation at 2.60, 3.07 and 3.65 GeV

    M. Ablikim et al. (BES), Phys. Lett. B677, 239 (2009), arXiv:0903.0900 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  60. [60]

    Precise measurement of the e+ e- to pi+ pi- (gamma) cross section with the Initial State Radiation method at BABAR

    B. Aubert et al. (BABAR), Phys. Rev. Lett.103, 231801 (2009), arXiv:0908.3589 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2009

  61. [61]

    Measurement of sigma(e+ e- -> pi+ pi-) from threshold to 0.85 GeV^2 using Initial State Radiation with the KLOE detector

    F. Ambrosino et al. (KLOE), Phys. Lett. B700, 102 (2011), arXiv:1006.5313 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2011

  62. [62]

    J. P. Lees et al. (BABAR), Phys. Rev.D86, 012008 (2012), arXiv:1103.3001 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  63. [63]

    J. P. Lees et al. (BABAR), Phys. Rev.D85, 112009 (2012), arXiv:1201.5677 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  64. [64]

    J. P. Lees et al. (BABAR), Phys. Rev.D86, 032013 (2012), arXiv:1205.2228 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2012

  65. [65]

    Precision measurement of $\sigma(e^+e^-\rightarrow\pi^+\pi^-\gamma)/\sigma(e^+e^-\rightarrow \mu^+\mu^-\gamma)$ and determination of the $\pi^+\pi^-$ contribution to the muon anomaly with the KLOE detector

    D. Babusci et al. (KLOE), Phys. Lett. B720, 336 (2013), arXiv:1212.4524 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  66. [66]

    R. R. Akhmetshin et al. (CMD-3), Phys. Lett. B723, 82 (2013), arXiv:1302.0053 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  67. [67]

    J. P. Lees et al. (BABAR), Phys. Rev.D87, 092005 (2013), arXiv:1302.0055 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  68. [68]

    J. P. Lees et al. (BABAR), Phys. Rev.D88, 072009 (2013), arXiv:1308.1795 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2013

  69. [69]

    J. P. Lees et al. (BABAR), Phys. Rev.D89, 092002 (2014), arXiv:1403.7593 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  70. [70]

    M. N. Achasov et al. (SND), Phys. Rev. D90, 112007 (2014), arXiv:1410.3188 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2014

  71. [71]

    V . M. Aulchenko et al. (SND), Phys. Rev. D91, 052013 (2015), arXiv:1412.1971 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2015

  72. [72]

    R. R. Akhmetshin et al. (CMD-3), Phys. Lett. B759, 634 (2016), arXiv:1507.08013 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  73. [73]

    Ablikim et al

    M. Ablikim et al. (BESIII), Phys. Lett. B753, 629 (2016), arXiv:1507.08188 [hep-ex]

    work page arXiv 2016

  74. [74]

    D. N. Shemyakin et al. (CMD-3), Phys. Lett. B756, 153 (2016), arXiv:1510.00654 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  75. [75]

    V . V . Anashinet al. (KEDR), Phys. Lett. B753, 533 (2016), arXiv:1510.02667 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  76. [76]

    M. N. Achasov et al. (SND), Phys. Rev. D93, 092001 (2016), arXiv:1601.08061 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  77. [77]

    M. N. Achasov et al. (SND), Phys. Rev. D94, 112006 (2016), arXiv:1608.08757 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2016

  78. [78]

    J. P. Lees et al. (BABAR), Phys. Rev.D95, 092005 (2017), arXiv:1704.05009 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  79. [79]

    R. R. Akhmetshin et al. (CMD-3), Phys. Lett. B773, 150 (2017), arXiv:1706.06267 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

  80. [80]

    J. P. Lees et al. (BABAR), Phys. Rev.D96, 092009 (2017), arXiv:1709.01171 [hep-ex]

    work page internal anchor Pith review Pith/arXiv arXiv 2017

Showing first 80 references.