Refinements in electroweak contributions to the muon anomalous magnetic moment

Andrzej Czarnecki; Arkady Vainshtein; William J. Marciano

REVIEW

Refinements in electroweak contributions to the muon anomalous magnetic moment

Andrzej Czarnecki, William J. Marciano, Arkady Vainshtein

High Energy Physics - Phenomenology · Submitted 16 Dec 2002 · 31 references

Pith's verdict: A careful, mostly convincing refinement of the electroweak piece of muon g-2; the weak spots are bounded and the authors know where they are.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on October 29, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 3 major objections · 7 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/0212229 (version 3)

Pith ID4JRMFGT7, Pith's permanent record of this paper and its review

CitationAndrzej Czarnecki, Arkady Vainshtein, William J. Marciano. "Refinements in electroweak contributions to the muon anomalous magnetic moment." arXiv:hep-ph/0212229 (2002). https://pith.science/paper/4JRMFGT7

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

This is the paper that settled how QCD enters the two-loop electroweak contribution to muon g-2, and it is worth your time if you care about that number. Three things are genuinely new. First, Sec. III.E.3 identifies what Knecht–Peris–Perrottet–de Rafael [18] left out of their OPE: the local part of the three-current expansion, i.e. the unit operator, which in their language is the dual field strength F-tilde. Restoring it recovers the ln m_Z terms in the transverse light-quark triangle that [18] had argued were damped away. That is a real correction to a published claim, argued cleanly, and the 2006 note records that the [18] authors eventually accepted it. Second, the (1−4 sin^2 theta_W)-suppressed two-loop pieces from gamma-Z mixing are computed explicitly (Eqs. 72–76), and the paper names the specific factor Q_f^2 vs Q_f Q_mu error in Eq. (23) of Degrassi–Giudice [15]. Third, the three-loop leading logs are redone, with two further specific corrections to [15]'s anomalous dimensions spelled out. The RG result is cross-checked against the explicit two-loop expressions, which is the right way to earn trust here. The headline shift, 152(4) to 154(1)(2), is modest and the error reduction is the real product. On the reader's weakest-assumption call: the two-pole rho-a1 model in Eq. (57) is indeed the softest object in the paper, and its own 1/Q^6 test misses by about a third. But the stress-test note is right that the reader overstates its role. The paper says plainly that the shift comes mainly from the longitudinal piece, which is anchored by 't Hooft matching and is the solid half of the analysis; the transverse model contributes about 0.24e-11 of model-dependent weight, and the authors' +/-0.2e-11 estimate is consistent with that. The three-loop section is the least satisfying: the answer depends on whether you use alpha(m_Z) or alpha(m_mu) in the two-loop piece at the 2e-11 level, and the resolution is a cancellation the authors themselves call a numerical coincidence. That is honest but not a derivation, and it is why the three-loop piece sits inside the +/-2 rather than standing on its own. Neither soft spot threatens 154(1)(2). This deserves referees, and I would cite it.

Referee report

Significance

The paper is a careful and influential reanalysis of a sub-leading but non-negligible piece of the Standard Model prediction for a_μ, at a time when the experimental error is comparable to the electroweak contribution itself. Its strengths are real and worth naming: the RG result in Eq. (91) is explicitly checked against the independent diagrammatic two-loop expressions of Eqs. (71) and (73); the mixing coefficient β_{V;μf} in Eq. (97) is verified against the explicit F7 diagram; the longitudinal sector is protected by 't Hooft matching and the Adler–Bardeen theorem rather than by a model; and the paper identifies concrete errors in two prior treatments (the Q_f² → Q_fQ_μ substitution in Eq. (23) of Ref. [15], and the omission of the local unit-operator piece in the OPE of Ref. [18]). The note added in May 2006 records that the authors of Ref. [18] accepted the OPE criticism, which is a meaningful external validation. The numerical shift is small but the uncertainty reduction and the clarification of the short-distance behaviour are the durable contributions.

Major objections (3)

[Sec. III.F, Eqs. (55)–(56), and the Note added] The Note added states that a mistake in Eq. (55) was pointed out by J. Erler and corrected in this version. Because Eq. (56) feeds Eq. (60), which in turn feeds the +1.7×10⁻¹¹ shift of Eq. (117) and the final Eq. (119), the reader needs an explicit statement that the downstream numbers were recomputed with the corrected Eq. (55) and are unchanged (or, if changed, by how much). It would also help to state in one sentence what the earlier erroneous form was, so that users who have taken the numerical value of Eq. (56) from the earlier version know whether their numbers are affected. This is the one place in the manuscript where a self-acknowledged error sits directly on the numerical chain leading to the headline result, so it should be closed explicitly rather than left to the Note added.
[Sec. III.F, Eqs. (57)–(59)] The transverse first-generation number Δa_μ^T[e,u,d] = −1.32×10⁻¹¹ rests on the two-pole ρ–a_1 ansatz of Eq. (57), with residues fixed by the leading 1/Q² and 1/Q⁴ OPE conditions. The authors' own 1/Q⁶ test gives −(0.96 GeV)⁴ against the OPE estimate −(0.71 GeV)⁴, a roughly 35% mismatch, which they describe as 'not extremely good'. The quoted ±0.2×10⁻¹¹ from varying m_ρ over 500–1000 MeV and m_a_1 over 900–2000 MeV is plausible given that the unambiguous logarithmic term supplies −1.08 of the −1.32, but the estimate would be more convincing with an independent handle on the transverse spectral function — for instance, using the measured vector spectral function for the ρ channel rather than a single pole, or imposing a third matching condition. I want to be clear that this concern is bounded: the shift of Eq. (117) is dominated by the longitudinal 't Hooft-matched piece, as the authors state in Sec. III.F, and the model dependence sits inside the quoted ±1×10⁻¹¹ hadronic error. It does not threaten the headline result, but the model-dependence discussion should say so explicitly rather than leave the reader to reconstruct it.
[Sec. IV.D, Eqs. (110)–(116)] The conclusion that the leading three-loop logs are 'essentially zero' rests on a cancellation that the authors themselves call 'a numerical coincidence', and the size of the three-loop term depends on whether α(m_μ) or α(m_Z) is used in the two-loop piece (0.4×10⁻¹¹ versus 2.4×10⁻¹¹). The paper argues that scale insensitivity is restored once the two-loop term is reevaluated with the shifted coupling, and that the residual is about 0.1×10⁻¹¹, which is consistent with the ±0.2×10⁻¹¹ assigned in Sec. V. Since this assignment is part of the second error bar in Eq. (119), it would strengthen the paper to show the scale-choice dependence explicitly in the error budget — for example, a short table of the three-loop plus shifted two-loop sum at μ = m_μ and μ = m_Z — so that the reader can see the ±0.2×10⁻¹¹ is not simply the smaller of the two numbers quoted in the text.

Minor objections (7)

[Sec. III.E.2, after Eq. (46), and the Note added] The body text lists F̃_{αβ} Tr G_{μν}G^{μν} among the d = 6 operators, while the Note added states that the authors of Ref. [18] correctly emphasized that this operator does not appear in the OPE because of its chiral features. The body text should be corrected in place rather than patched only by the Note added, so that the operator list in Sec. III.E.2 is internally consistent with the note.
[Sec. II, Eq. (7) versus Sec. IV.A, Eq. (76)] The text states that Eq. (76) is 'slightly different than Eq. (7) in Sec. II, but equivalent'. A one-line demonstration of the equivalence, or a pointer to where the rearrangement is performed, would help readers who use Eq. (7) directly for the numerical value in Eq. (9).
[Sec. III.C, Eqs. (24)–(25)] The perturbative α_s uncertainty for the third generation is estimated with coefficients C_t and C_b 'of order ±1'. Since this estimate feeds the ±0.1×10⁻¹¹ quoted in Eq. (25), a sentence on the expected size of these coefficients (or on the range over which they were varied) would make the estimate reproducible.
[Sec. III.E.2, Eq. (49)] The d = 6 estimate neglects the FGG operators and the anomalous dimension of O_6, with the remark that the latter is 'rather large and positive'. Since Eq. (49) is used only as a test of the two-pole model, a brief statement of the expected size of the neglected terms would let the reader judge how much weight the 1/Q⁶ comparison can bear.
[Notation, Eqs. (74), (90), (107)] The brace notation {m_f, m_μ} ≡ max{m_f, m_μ} is introduced in Eq. (74) and then reused with three arguments in Eqs. (90) and (107). Defining the multi-argument form once, at first use, would avoid ambiguity.
[Abstract versus Sec. V] The abstract attributes the second error bar primarily to the allowed Higgs mass range, while Sec. V states that it also covers the top mass uncertainty and uncalculated three-loop effects. Aligning the two descriptions would be clearer.
[Typographical] There are several typographical slips that should be cleaned up: 'Upto n' in the author affiliation on the title page; 'translated them into into QED corrections' in Sec. II; 'similar to to one we did' in Sec. III.G; 'dominated by the the anomalous dimension term' in the text following Eq. (110); and stray spaces inside reference labels such as '[1 8]' and '[1 5]'.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

The electroweak part of the muon's anomalous magnetic moment comes out at $154(1)(2)times10^{-11}$ once strong-interaction effects on light-quark loops are treated with chiral effective field theory and operator-product constraints, roughly

The reading

The muon's anomalous magnetic moment is measured so precisely that every theoretical contribution has to be pinned down, and one of the awkward ones is the two-loop electroweak piece, because light quarks circulate in the relevant triangle diagrams where ordinary quark-mass perturbation theory is not trustworthy. This paper argues that strong interactions leave the short-distance logarithm in that piece untouched, and that the long-distance part can be computed with an effective field theory that preserves the chiral symmetry of QCD and is constrained by the operator product expansion. Carrying that out roughly halves the estimated contribution of the first fermion generation, shifts the total electroweak term upward by about $2times10^{-11}$, and shrinks its error bar. The authors also compute small previously neglected terms suppressed by $1-4sin^2theta_W$ and redo the leading three-loop logarithms, which turn out to cancel almost completely. The result is a Standard Model electroweak prediction of $a_mu^{rm EW}=154(1)(2)times10^{-11}$, where the first error is hadronic and the second covers the allowed Higgs mass range, the top mass and residual three-loop effects.

What carries the argument

The load-bearing device is the operator product expansion of the time-ordered product of the electromagnetic and axial currents, written so that the soft external photon enters the local operators explicitly through $tilde F_{alphabeta}$. That leading dimension-two operator carries the $1/Q^2$ large-momentum behaviour and its coefficient is just the one-loop triangle, which is how the paper restores the short-distance logarithms that an earlier treatment, which expanded the three-current product without the soft photon in the operator set, had dropped. Chiral symmetry then fixes the longitudinal channel completely (the $1/Q^2$ pole matches the pion, with $m_pi$ shifting the pole position), while the transverse channel is modelled as a sum of $rho(770)$ and $a_1(1260)$ poles whose residues are fixed by matching the $1/Q^2$ and $1/Q^4$ OPE coefficients, with the $1/Q^6$ term used as a check. A renormalization-group analysis of the dimension-five dipole operator $H$ and its mixing with four-fermion operators supplies the two- and three-loop leading logs, and the two-loop result reproduces the explicit diagrammatic calculation as a consistency check.

Extended reading notes

Core claim

The paper's central claim is that the two-loop electroweak contribution to $a_mu$ can be made both more accurate and better justified by handling the light-quark triangle diagrams correctly. Two things are asserted. First, the short-distance $ln m_Z$ terms are not modified by QCD: the longitudinal part of the $Zgammagamma^*$ amplitude is protected by the anomaly non-renormalization theorem, and the transverse part by the relation $w_T=w_L/2$ at vanishing external photon momentum, so the free-quark logarithmic behaviour survives and the logarithms cancel between leptons and quarks within a generation as they must. Second, the long-distance part is genuinely changed: using an operator product expansion in which the leading operator is the dual electromagnetic field strength $tilde F_{alphabeta}$, plus a two-pole $rho$–$a_1$ model for the transverse light-quark function fixed by OPE matching, the first generation contributes $-2.28times10^{-11}$ instead of the free-quark estimate of $-4.0times10^{-11}$, a shift of $+1.7times10^{-11}$ (Eqs. 60, 61, 117). The second generation is essentially unchanged at $-4.63times10^{-11}$. Adding the small $1-4sin^2theta_W$ terms, which shift the answer down by about $0.4times10^{-11}$, and finding the leading three-loop logs consistent with zero, the authors move the Standard Model electroweak value from $152(4)times10^{-11}$ to $154(1)(2)times10^{-11}$.

Load-bearing premise

The transverse light-quark function for $u$ and $d$ is not calculated from first principles but modelled as two poles with residues fixed by matching the leading operator-product coefficients, and the authors' own check against the next coefficient misses by about a third.

Editorial extensions

If this is right

The hadronic uncertainty in the electroweak contribution drops to roughly $pm1times10^{-11}$, so any future discrepancy between measured and predicted $a_mu$ will have to be attributed to hadronic vacuum polarization, light-by-light scattering, or new physics rather than to this term.
Because QCD is argued not to renormalize the short-distance logarithms, the log-enhanced part of the electroweak correction can be trusted at higher orders, which legitimizes the renormalization-group resummation used here.
The leading three-loop logs come out consistent with zero, so the assigned $pm0.2times10^{-11}$ for uncalculated three-loop effects is defensible and naive log-counting estimates of higher orders overstate them.
The central value moves up by about $2times10^{-11}$ while the error shrinks by a factor of two, tightening the window in which any new-physics explanation of a muon $g-2$ deviation would have to fit.
The operator-product bookkeeping point — that the unit operator dressed by the soft photon field strength must be included — applies to any amplitude where a soft photon attaches to an anomalous triangle.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

The two-pole $rho$–$a_1$ ansatz is the piece most likely to move the central value; a first-principles lattice determination of the transverse light-quark invariant function over the relevant momentum range would turn the $+1.7times10^{-11}$ shift from a model estimate into a calculation and could plausibly move it by a comparable amount.
The same soft-photon-in-the-operator treatment should be transferable to other anomalous-triangle observables, such as radiative corrections to $Z$ couplings to leptons or precision hyperfine structure, wherever a light quark loop sits between a weak axial current and two photons.
The authors describe the near-total cancellation of the three-loop leading logs as a numerical coincidence; if so, it need not persist beyond leading log, and a complete three-loop next-to-leading-log calculation is the natural next target for anyone wanting the electroweak term at the $10^{-12}$ level.
Once the Higgs mass is measured, the second error quoted here collapses and the electroweak contribution becomes a fixed number with sub-$10^{-11}$ uncertainty, which sharpens the interpretation of any future $g-2$ anomaly.

Original abstract

Effects of strong interactions on the two loop electroweak radiative corrections to the muon anomalous magnetic moment, $a_\mu=(g_\mu-2)/2$, are examined. Short-distance logs are shown to be unaffected. Computation of long-distance contributions is improved by use of an effective field theory approach that preserves the chiral properties of QCD and accounts for constraints from the operator product expansion. Small, previously neglected, two loop contributions, suppressed by a $1-4\sin^2\theta_W$ factor, are computed and the complete three loop leading short-distance logs are reevaluated. These refinements lead to a reduction in uncertainties and a slight shift in the total electroweak contribution to $a_\mu^{\rm EW} = 154(1)(2)\times 10^{-11}$ where the first error corresponds to hadronic uncertainties and the second is primarily due to the allowed Higgs mass range.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,416 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.52 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.99 · compares with prior results 0.51 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v3. Results and the main claim are underlined; show every role.

Effects of strong interactions on the two loop electroweak radiative corrections to the muon anomalous magnetic moment, $a_\mu=(g_\mu-2)/2$, are examined. Short-distance logs are shown to be unaffected. Computation of long-distance contributions is improved by use of an effective field theory approach that preserves the chiral properties of QCD and accounts for constraints from the operator product expansion. Small, previously neglected, two loop contributions, suppressed by a $1-4\sin^2\theta_W$ factor, are computed and the complete three loop leading short-distance logs are reevaluated. These refinements lead to a reduction in uncertainties and a slight shift in the total electroweak contribution to $a_\mu^{\rm EW} = 154(1)(2)\times 10^{-11}$ where the first error corresponds to hadronic uncertainties and the second is primarily due to the allowed Higgs mass range.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	Effects of strong interactions on the two loop electroweak radiative corrections to the muon anomalous magnetic moment, $a_\mu=(g_\mu-2)/2$, are examined.	contribution 0.93	0.77	0.04	asserted 0.66
s1	Short-distance logs are shown to be unaffected.	result 1.00	0.83	0.04	asserted 1.00
s2	Computation of long-distance contributions is improved by use of an effective field theory approach that preserves the chiral properties of QCD and accounts for constraints from the operator product expansion.	method 0.96	0.90	0.07	asserted 1.00
s3	Small, previously neglected, two loop contributions, suppressed by a $1-4\sin^2\theta_W$ factor, are computed and the complete three loop leading short-distance logs are reevaluated.	contribution 0.96	0.93	0.08	asserted 1.00
s4	These refinements lead to a reduction in uncertainties and a slight shift in the total electroweak contribution to $a_\mu^{\rm EW} = 154(1)(2)\times 10^{-11}$ where the first error corresponds to hadronic uncertainties and the second is primarily due to the allowed Higgs mass range.	result 1.00	0.93	0.86	asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.53.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

full text
figures and tables
references and citing sentences
relations to other papers

levels run

P abstract

not run

S sections
T body sentences
C citations
R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

Figures

**Figure 1.** , were computed about 30 years ago [4–8]. They have the relatively simple form a EW µ (1-loop) = 5 Gµ m2 µ 24√ 2π 2 " 1 + 1 5 (1 − 4 sin2 θW ) 2 + O

Showing 1 of the paper's 9 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/0212229 by the authors.

References

Works cited (31)

[18]

M. Knecht, S. Peris, M. Perrottet and E. de Rafael, JHEP 0211, 003 (2002) [hep-ph/0205102]

View on Pith Pith review arXiv 2002
[15]

G. Degrassi and G. F. Giudice, Phys. Rev. D 58, 053007 (1998) [hep-ph/9803384]

View on Pith Pith review arXiv 1998
[1]

G. W. Bennett et al. [Muon g-2 Collaboration], Phys. Rev. Lett. 89, 101804 (2002) [hep- ex/0208001]

View on Pith 2002
[2]

M. Davier, S. Eidelman, A. Hocker and Z. Zhang, Confronting spectral functions from e+e− annihilation and tau decays: Consequences for the muon magne tic moment, hep-ph/0208177

View on Pith Pith review arXiv
[3]

K. Hagiwara, A. D. Martin, D. Nomura and T. Teubner, The SM prediction of g − 2 of the muon, hep-ph/0209187

View on Pith Pith review arXiv
[4]

K. Fujikawa, B. W. Lee and A. I. Sanda, Phys. Rev. D 6, 2923 (1972)

View on Pith 1972
[5]

R. Jackiw and S. Weinberg, Phys. Rev. D 5, 2396 (1972)

View on Pith 1972
[6]

G. Altarelli, N. Cabibbo and L. Maiani, Phys. Lett. B 40, 415 (1972)

View on Pith 1972
[7]

I. Bars and M. Yoshimura, Phys. Rev. D 6, 374 (1972)

View on Pith 1972
[8]

W. A. Bardeen, R. Gastmans and B. Lautrup, Nucl. Phys. B 46, 319 (1972)

View on Pith 1972
[9]

A. Ferroglia, G. Ossola, M. Passera and A. Sirlin, Phys. R ev. D 65, 113002 (2002) [hep-ph/0203224]

View on Pith Pith review arXiv 2002
[10]

T. V. Kukhto, E. A. Kuraev, A. Schiller and Z. K. Silagadz e, Nucl. Phys. B371, 567 (1992)

View on Pith 1992
[11]

E. D’Hoker, Phys. Rev. Lett. 69, 1316 (1992)

View on Pith 1992
[12]

S. Peris, M. Perrottet and E. de Rafael, Phys. Lett. B 355, 523 (1995) [hep-ph/9505405]

View on Pith Pith review arXiv 1995
[13]

A. Czarnecki, B. Krause and W. J. Marciano, Phys. Rev. D 52, 2619 (1995) [hep-ph/9506256]

View on Pith Pith review arXiv 1995
[14]

A. Czarnecki, B. Krause and W. J. Marciano, Phys. Rev. Le tt. 76, 3267 (1996) [hep-ph/9512369]

View on Pith Pith review arXiv 1996
[16]

A. Czarnecki and W. J. Marciano, Phys. Rev. D 64, 013014 (2001) [hep-ph/0102122]

View on Pith Pith review arXiv 2001
[17]

A. Czarnecki and W. J. Marciano, Phys. Rev. D 53, 1066 (1996) [hep-ph/9507420]. 33

View on Pith Pith review arXiv 1996
[19]

S. L. Adler, Phys. Rev. 177, 2426 (1969)

View on Pith 1969
[20]

L. Rosenberg, Phys. Rev. 129, 2786 (1963)

View on Pith 1963
[21]

E. V. Shuryak and A. I. Vainshtein, Nucl. Phys. B 201, 141 (1982); V. A. Novikov, M. A. Shif- man, A. I. Vainshtein and V. I. Zakharov, Fortsch. Phys. 32, 585 (1985)

View on Pith 1982
[22]

S. L. Adler and W. A. Bardeen, Phys. Rev. 182, 1517 (1969)

View on Pith 1969
[23]

A. Vainshtein, Phys. Lett. B 569, 187 (2003) [hep-ph/0212231]

View on Pith Pith review arXiv 2003
[24]

G. ’t Hooft, in Recent Developments In Gauge Theories, Eds. G. ’t Hooft et al ., (Plenum Press, New York, 1980)

View on Pith 1980
[25]

B. L. Ioﬀe and A. V. Smilga, Nucl. Phys. B 232, 109 (1984)

View on Pith 1984
[26]

M. Gell-Mann, R. J. Oakes and B. Renner, Phys. Rev. 175, 2195 (1968)

View on Pith 1968
[27]

M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Sov. P hys. JETP 45, 670 (1977) [Zh. Eksp. Teor. Fiz. 72, 1275 (1977)]

View on Pith 1977
[28]

M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Phys. Rev. D 18, 2583 (1978) [Erratum-ibid. D 19, 2815 (1979)]

View on Pith 1978
[29]

B. Grinstein, R. P. Springer and M. B. Wise, Phys. Lett. B 202, 138 (1988)

View on Pith 1988
[30]

B. Grinstein, R. P. Springer and M. B. Wise, Nucl. Phys. B 339, 269 (1990)

View on Pith 1990
[31]

M. Ciuchini, E. Franco, L. Reina and L. Silvestrini, Nuc l. Phys. B 421, 41 (1994) [hep-ph/9311357]. 34

View on Pith Pith review arXiv 1994

Forward citations

Showing 60 of 71 Pith papers that cite this

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. See all 71 Pith citations

Precision evaluation of the $\eta$- and $\eta'$-pole contributions to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
hep-ph 2024-11 accept novelty 8.0 of 10

A new dispersive analysis of the eta and eta-prime transition form factors gives a_mu(eta-pole) = 14.7(9) x 10^-11 and a_mu(eta'-pole) = 13.5(7) x 10^-11, with combined pseudoscalar poles at 91.2(+2.9,-2.4) x 10^-11.
Light new physics and the $\tau$ lepton dipole moments: prospects at Belle II
hep-ph 2025-10 unverdicted novelty 7.0 of 10

Light new particles generate asymmetries in e+e- to tau+tau- that allow model-dependent constraints on tau dipole moments, including non-zero effects without electron polarization via imaginary parts.
Towards testing $(g-2)_\tau$ in $e^+e^-\to\tau^+\tau^-$: radiative corrections and projections for Belle II
hep-ph 2025-05 conditional novelty 7.0 of 10

A complete one-loop QED calculation for polarized e+e- to tau+tau- is implemented in the McMule Monte-Carlo code, showing that Belle II with a polarized beam could test the tau anomalous magnetic moment at the 10^-5 level.
Complete dispersive evaluation of the hadronic light-by-light contribution to muon $g-2$
hep-ph 2024-11 conditional novelty 7.0 of 10

Using a dispersive formalism with experimental transition form factors and short-distance constraints, the authors obtain a_mu^HLbL = 101.9(7.9) x 10^-11, halving the previous uncertainty.
A No-Lose Theorem for Discovering the New Physics of $(g-2)_\mu$ at Muon Colliders
hep-ph 2021-01 accept novelty 7.0 of 10

Under perturbative unitarity, flavour protection, and naturalness assumptions, the lightest new charged particle explaining the muon g-2 anomaly must lie below roughly 10 TeV, within reach of a proposed multi-TeV muon...

Show 55 more citing papers

Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD
hep-lat 2014-07 conditional novelty 7.0 of 10

A lattice QCD+QED calculation produces a statistically significant signal for the hadronic light-by-light form factor behind the muon g-2 anomaly, at unphysical masses and with only the connected quark-loop diagram.
BMW/DMZ calculation of the hadronic vacuum polarisation for the muon magnetic moment
hep-lat 2026-03 conditional novelty 6.0 of 10

A hybrid lattice-QCD plus e+e- data determination of the hadronic vacuum polarisation gives a Standard Model muon g-2 prediction 0.5σ from experiment, at 0.45% precision.
Light new physics and the $\tau$ lepton dipole moments
hep-ph 2025-11 unverdicted novelty 6.0 of 10

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...
Extracting the chiral anomaly from $e^+e^-\to 3\pi$
hep-ph 2025-04 conditional novelty 6.0 of 10

A dispersive fit to e+e−→3π data yields F3π = 33.1(1.7) GeV^-3, consistent with the chiral anomaly prediction at the 5% level.
Dispersion relation for hadronic light-by-light scattering: $\eta$ and $\eta'$ poles
hep-ph 2024-12 conditional novelty 6.0 of 10

A dispersive analysis of the eta and eta' transition form factors yields data-driven pole contributions to the muon g-2 of 14.7(9) x 10^-11 and 13.5(7) x 10^-11.
Dispersion relation for hadronic light-by-light scattering: subleading contributions
hep-ph 2024-11 conditional novelty 6.0 of 10

A dispersive evaluation gives a_mu^HLbL subleading = 33.2(7.2) x 10^-11 and total = 101.9(7.9) x 10^-11.
Hadronic light-by-light contribution to the muon anomaly from lattice QCD with infinite volume QED at physical pion mass
hep-lat 2023-04 conditional novelty 6.0 of 10

A lattice QCD calculation at physical pion mass gives the hadronic light-by-light contribution to muon g-2 as 12.47(1.15)(0.95) x 10^-10, consistent with prior determinations.
Kaon electromagnetic form factors in dispersion theory
hep-ph 2022-02 conditional novelty 6.0 of 10

Combining dispersion relations with time- and spacelike kaon form-factor data gives charged and neutral kaon radii of 0.359(3) and -0.060(4) fm^2, phi parameters M = 1019.479(5) MeV and Gamma = 4.207(8) MeV, and kaon ...
Muonic Force Behind Flavor Anomalies
hep-ph 2021-07 conditional novelty 6.0 of 10

Among anomaly-free lepton-flavored U(1) extensions of the Standard Model with a muon-coupled leptoquark, only a few charge assignments survive all current constraints, with L_mu minus L_tau the cleanest survivor.
Consequences of chirally enhanced explanations of $(g-2)_\mu$ for $h\to \mu\mu$ and $Z\to \mu\mu$
hep-ph 2021-04 accept novelty 6.0 of 10

Matching simplified chiral-enhancement models for the muon g-2 anomaly onto SMEFT yields correlated, testable predictions for h to mu mu and Z to mu mu that sit below current precision but within reach of future colliders.
A Model of Muon Anomalies
hep-ph 2021-03 conditional novelty 6.0 of 10

A U(1)_{B-3L_mu} gauge symmetry with two scalar muoquarks fits the muon g-2, R_K(*), and b to s mu mu anomalies simultaneously while keeping proton decay at dimension six.
On the transition form factors of the axial-vector resonance $f_1(1285)$ and its decay into $e^+e^-$
hep-ph 2021-03 conditional novelty 6.0 of 10

Within a vector-meson-dominance model, the symmetric f1(1285) transition form factor is pinned to about 10 percent, while the two antisymmetric form factors stay weakly constrained and split into two solution branches.
Effective field theory interpretation of lepton magnetic and electric dipole moments
hep-ph 2021-02 conditional novelty 6.0 of 10

A complete one-loop effective-field-theory bookkeeping of lepton dipole moments shows that, for new physics above the electroweak scale, only the electroweak dipole operators and two semileptonic tensor operators can ...
The two-loop perturbative correction to the (g-2)$_{\mu}$ HLbL at short distances
hep-ph 2021-01 accept novelty 6.0 of 10

The two-loop QCD correction to the massless quark-loop term in the short-distance HLbL expansion is about minus ten percent of the leading term for photon virtualities above roughly one GeV.
Correlating $h\to\mu^+\mu^-$ to the Anomalous Magnetic Moment of the Muon via Leptoquarks
hep-ph 2020-08 accept novelty 6.0 of 10

Leptoquark explanations of the muon g-2 anomaly predict Higgs-to-muon-pair branching ratio shifts of a few percent up to a factor of three, and the recent ATLAS and CMS measurements already exclude part of the singlet...
A Guaranteed Discovery at Future Muon Colliders
hep-ph 2020-06 conditional novelty 6.0 of 10

A 10 TeV muon collider would find every singlet-model explanation of the muon g-2 anomaly, and a 40 to 60 TeV machine would find the electroweak-model explanations or empirically prove the Higgs and muon masses are tuned.
Hadronic vacuum polarization: $(g-2)_\mu$ versus global electroweak fits
hep-ph 2020-03 accept novelty 6.0 of 10

Modern electroweak precision data alone determine the hadronic running of alpha to 270.2(3.0) x 10^-4, below the e+e- value, so adjusting hadronic vacuum polarization to explain the muon anomaly would shift the tensio...
Beta decays as sensitive probes of lepton flavor universality
hep-ph 2020-02 accept novelty 6.0 of 10

Beta-decay data, reinterpreted through the muon-decay definition of the Fermi constant, tests lepton flavor universality in W-muon-neutrino couplings with a CKM enhancement of about twenty.
Axial vector transition form factors in holographic QCD and their contribution to the anomalous magnetic moment of the muon
hep-ph 2019-12 conditional novelty 6.0 of 10

Axial vector meson exchange, computed in holographic QCD with the full tower of states included, contributes roughly 2.2 to 4.1 x 10^-10 to the muon anomalous magnetic moment, several times larger than previous estimates.
Longitudinal short-distance constraints for the hadronic light-by-light contribution to $(g-2)_\mu$ with large-$N_c$ Regge models
hep-ph 2019-10 accept novelty 6.0 of 10

An infinite tower of excited pseudoscalars, constrained by QCD short-distance limits and matched to the perturbative quark loop, raises the hadronic light-by-light contribution to muon g-2 by 13(6) x 10^-11, well belo...
Short-distance constraints on hadronic light-by-light scattering in the anomalous magnetic moment of the muon
hep-ph 2019-10 conditional novelty 6.0 of 10

Implementing longitudinal short-distance constraints with a Regge tower of excited pseudoscalars raises the hadronic light-by-light contribution to muon g-2 by 13(6) x 10^-11, well below the ~38 x 10^-11 implied by th...
Axial-vector exchange contribution to the hadronic light-by-light piece of the muon anomalous magnetic moment
hep-ph 2019-10 conditional novelty 6.0 of 10

A resonance-chiral-theory evaluation puts the axial-vector contribution to the muon's hadronic light-by-light correction at roughly 0.8 x 10^-11, well below most recent estimates, with the spread driven by the assumed...
Short-distance constraints for the HLbL contribution to the muon anomalous magnetic moment
hep-ph 2019-08 conditional novelty 6.0 of 10

In the all-hard kinematic region of hadronic light-by-light scattering, the external-field OPE gives the perturbative quark loop as the leading term and a small 1/Q^4 magnetic-susceptibility correction.
EFT approach to the electron Electric Dipole Moment at the two-loop level
hep-ph 2018-10 conditional novelty 6.0 of 10

The authors derive two-loop anomalous dimensions of the electron EDM operators and use the ACME bound to set new limits on leptoquarks, heavy Higgs states, the MSSM and composite Higgs top partners.
Dispersion relation for hadronic light-by-light scattering: pion pole
hep-ph 2018-08 accept novelty 6.0 of 10

A dispersive reconstruction of the doubly-virtual pion transition form factor from e+e- to 3pi, pi0 to gamma gamma, and space-like data yields the pion-pole contribution to muon g-2 as 62.6 (+3.0/-2.5) x 10^-11.
Pion-pole contribution to hadronic light-by-light scattering in the anomalous magnetic moment of the muon
hep-ph 2018-05 conditional novelty 6.0 of 10

A dispersive reconstruction of the doubly-virtual pion transition form factor from e+e- to 3pi, e+e- to e+e-pi0, and pi0 to gamma gamma data yields the pion-pole contribution to muon g-2, 62.6 (+3.0/-2.5) x 10^-11, wi...
Renormalisation-group improved analysis of $\mu\to e$ processes in a systematic effective-field-theory approach
hep-ph 2017-02 accept novelty 6.0 of 10

Including one-loop (plus leading two-loop) renormalisation-group running between the electroweak scale and the muon scale converts previously unbounded four-fermion operators into tightly constrained ones.
Summary of the ATLAS experiment's sensitivity to supersymmetry after LHC Run 1 - interpreted in the phenomenological MSSM
hep-ex 2015-08 accept novelty 6.0 of 10

Across 310,327 pMSSM points, ATLAS Run 1 excludes about 41% and leaves viable low-fine-tuning spectra whose light top squarks should be reachable at Run 2.
Lepton-Specific Two Higgs Doublet Model as a Solution of Muon $g-2$ Anomaly
hep-ph 2015-04 conditional novelty 6.0 of 10

The leptonic tau decay excludes the 1σ explanation of the muon g-2 anomaly in the Type-X two Higgs doublet model, leaving a 2σ window with 10-30 GeV CP-odd Higgs, 200-350 GeV charged Higgs, and tanβ between 30 and 50.
Two-Loop Corrections to the Muon Magnetic Moment from Fermion/Sfermion Loops in the MSSM: Detailed Results
hep-ph 2013-11 conditional novelty 6.0 of 10

The full analytic two-loop fermion/sfermion-loop correction to the muon anomalous magnetic moment in the MSSM is derived, and it is logarithmically enhanced rather than decoupling when sfermions are heavy.
Magnetic susceptibility of QCD at zero and at finite temperature from the lattice
hep-lat 2012-09 conditional novelty 6.0 of 10

Dynamical lattice QCD at physical quark masses yields chi_u = -2.08(8), chi_d = -2.02(9), chi_s = -3.4(1.4) GeV^-2 at 2 GeV in MS-bar, showing the spin part of the QCD vacuum response to a magnetic field is diamagnetic.
Natural Priors, CMSSM Fits and LHC Weather Forecasts
hep-ph 2007-05 accept novelty 6.0 of 10

Rewriting the CMSSM prior in terms of mu and B, with a hierarchical same-order-of-magnitude assumption on all soft scales, removes the pseudoscalar-Higgs and focus-point fit regions and lowers predicted sparticle mass...
Hadronic light-by-light scattering contribution to the muon anomalous magnetic moment revisited
hep-ph 2003-12 conditional novelty 6.0 of 10

Matching the hadronic light-by-light amplitude to perturbative QCD at short distances raises the muon g-2 hadronic light-by-light contribution to 136(25) x 10^-11, about 50 percent above prior estimates.
Probing Bino Contribution to Muon g-2
hep-ph 2013-09 conditional novelty 5.5 of 10

Requiring the electroweak vacuum to be metastable caps the smuon and Bino masses that can explain the muon g-2 anomaly, giving concrete targets for LHC/ILC and for LFV/EDM searches.
An update of Euclidean windows of the hadronic vacuum polarization
hep-lat 2023-01 conditional novelty 5.0 of 10

A blinded, five-group lattice recomputation of the standard Euclidean window gives a_mu^W = 235.56(65)(50) x 10^-10, 3.8 sigma above the dispersive result of 229.4(1.4) x 10^-10.
$W$ boson mass and muon $g-2$ in a lepton portal dark matter model
hep-ph 2022-04 conditional novelty 5.0 of 10

Two vector-like leptons plus a scalar dark matter particle can jointly explain the CDF W mass shift, the muon g-2 anomaly, and the dark matter relic density, with the lightest new lepton below 200 GeV.
Hadronic Uncertainties versus New Physics for the $W$ boson Mass and Muon $g-2$ Anomalies
hep-ph 2022-04 conditional novelty 5.0 of 10

The CDF W mass and muon g-2 anomalies pull the common hadronic vacuum polarization correction in opposite directions, so hadronic uncertainties cannot resolve both, but a mixed scalar leptoquark model can.
The Tiny (g-2) Muon Wobble from Small-$\mu$ Supersymmetry
hep-ph 2021-04 conditional novelty 5.0 of 10

In the MSSM with a Bino-like dark matter candidate and opposite-sign Bino and Higgsino masses, the muon g-2 anomaly can be explained for Higgsino masses below about 500 GeV while satisfying current direct detection bounds.
Confirming $U(1)_{L_\mu-L_{\tau}}$ as a solution for $(g-2)_\mu$ with neutrinos
hep-ph 2021-04 conditional novelty 5.0 of 10

Combining muon-beam, neutrino-scattering, and dark-matter-detector data can distinguish a U(1)_{L_mu-L_tau} hidden photon from a muon-only U(1)_{L_mu} explanation of the muon g-2 anomaly, with a low-threshold DARWIN r...
Dark matter, fine-tuning and $(g-2)_{\mu}$ in the pMSSM
hep-ph 2021-04 conditional novelty 5.0 of 10

Within a pMSSM scan, the surviving spectra that explain the muon anomaly, saturate the relic density and stay minimally fine-tuned all have spin-dependent dark-matter-nucleon cross sections large enough for PICO-500 a...
Minimal models for $g-2$ and dark matter confront asymptotic safety
hep-ph 2020-12 conditional novelty 5.0 of 10

Coupling twelve muon g-2 and dark-matter models to asymptotically safe gravity fixes their Yukawa couplings and leaves five viable, each with a narrow predicted mass range for the new scalar and fermions.
Scalar Leptoquarks in Leptonic Processes
hep-ph 2020-10 accept novelty 5.0 of 10

A complete one-loop calculation of scalar leptoquark effects in leptonic observables, including Higgs-induced leptoquark mixing, for all five scalar representations.
Short-distance HLbL contributions to the muon anomalous magnetic moment beyond perturbation theory
hep-ph 2020-08 conditional novelty 5.0 of 10

The leading non-perturbative, non-mass-suppressed corrections to the short-distance hadronic light-by-light correlator are computed via a background-field OPE and found to be numerically negligible compared with the m...
Hadronic vacuum polarization and vector-meson resonance parameters from ${e^+e^-\to\pi^0\gamma}$
hep-ph 2020-07 conditional novelty 5.0 of 10

A dispersive analysis of e+e- to pi0 gamma gives a_mu^{pi0 gamma} = 43.8(6) x 10^-11 and combined omega/phi masses of 782.736(24) and 1019.457(20) MeV, consistent with 3pi and K-bar K data.
Solar neutrino probes of the muon anomalous magnetic moment in the gauged $U(1)_{L_\mu-L_\tau}$
hep-ph 2020-06 conditional novelty 5.0 of 10

Reevaluated Borexino solar neutrino data exclude part of the parameter space in which a U(1)_{L_mu-L_tau} gauge boson explains the muon g-2 anomaly, and future xenon dark matter detectors can cover most of the remainder.
Probing $e\mu$ flavor-violating ALP at Belle II
hep-ph 2020-02 accept novelty 5.0 of 10

The muon g-2 favored region of an e-mu flavor-violating ALP is excluded by muonium-antimuonium oscillation data, but the electron g-2 region survives above 1.5 GeV and can be probed at Belle II.
On axials and pseudoscalars in the hadronic light-by-light contribution to the muon $(g-2)$
hep-ph 2019-12 conditional novelty 5.0 of 10

Within a holographic large-Nc model, the Melnikov-Vainshtein short-distance constraint on the hadronic light-by-light tensor is satisfied only by an infinite tower of axial-vector mesons, giving a combined pseudoscala...
A light complex scalar for the electron and muon anomalous magnetic moments
hep-ph 2018-10 conditional novelty 5.0 of 10

A complex scalar with a Peccei-Quinn-like symmetry can explain the opposite-sign electron and muon magnetic moment anomalies, with a light CP-odd component driving the electron deviation and a heavier CP-even componen...
The muon magnetic moment in the 2HDM: complete two-loop result
hep-ph 2016-07 conditional novelty 5.0 of 10

The complete two-loop bosonic contribution of the aligned two-Higgs-doublet model to the muon anomalous magnetic moment is computed and can reach (2 to 4) x 10^-10, at the scale of the planned Fermilab precision.
Towards an improved understanding of $\eta \to \gamma^* \gamma^*$
hep-ph 2015-09 conditional novelty 5.0 of 10

The a2 meson's exchange provides a natural but overly strong breaking of factorization in the doubly-virtual eta transition form factor, requiring additional physics to reconcile e+e- and eta decay data.
Muon g-2 vs LHC in Supersymmetric Models
hep-ph 2013-03 accept novelty 5.0 of 10

Reinterpreting ATLAS searches for electroweak supersymmetric particles, the authors show the LHC already excludes part of the supersymmetric parameter space that would explain the muon g-2 anomaly.
Reevaluation of the Hadronic Contributions to the Muon g-2 and to alpha(MZ)
hep-ph 2010-10 accept novelty 5.0 of 10

Updated hadronic vacuum-polarization integrals give a_mu(had,LO) = (692.3 +/- 4.2) x 10^-10 from e+e- data, raising the muon g-2 discrepancy to 3.6 sigma and shifting the fitted Higgs mass up by 7 GeV.
Muon lifetime and Fermi constant: an update
hep-ph 2026-07 accept novelty 4.5 of 10

Updated Δq = (−4 384 678 ± 34)×10^{-9} reduces theory error on the muon lifetime by an order of magnitude and gives G_F = 1.166 378 59(59)×10^{-5} GeV^{-2}.
Global analysis of a minimally extended scotogenic model
hep-ph 2026-06 unverdicted novelty 4.0 of 10

Numerical scan of minimally extended scotogenic model constrains fermionic DM to 120-350 GeV and CP-odd scalar to 350-600 GeV while noting DESI BAO data may rule out inverted neutrino hierarchy.
A model explaining the new CDF II W boson mass linking to muon $g-2$ and dark matter
hep-ph 2022-04 conditional novelty 4.0 of 10

A vector-like lepton plus inert-doublet model can accommodate the CDF II W mass shift, the muon g-2 anomaly, and a scalar dark matter candidate in a common parameter region.

See all 71 Pith citations

How later papers used it

255 later papers cite it

Evidence: substantial. 254 of the citing papers share no author with it, and 90 of those carry a confident label from Pith's citation classifier.

Pith read 18 of the 301 citing sentences, choosing only those whose citation markers point at this paper alone, and wrote the paraphrases from them. The summary, the counts, the evidence level, the links and the quotes come from code; the summary counts the papers listed below. A later paper is listed under a label when Pith's citation classifier gives one of its sentences that label at probability 0.8 or more (0.95 for support), Pith's reading finds that the citing paper itself did it, and a second check confirms the paraphrase against the sentence. This section lists uses only. It does not list criticism or disagreement, so their absence here says nothing about how the paper has been received. Papers that share an author with this one are listed apart, under "By the same authors". A quote is the citing authors' own sentence, shown when their paper's licence is CC BY, CC BY-SA or CC0. JSON

1 later paper by other authors is listed below: 1 compared its own results with it.

Compares with it 1 of 5 papers with this label

Reported that its results reduce the theoretical uncertainty on the first-family VVA contribution to a_mu compared to the analysis in this paper.

Dispersion relations for the hadronic VVA correlator (2024) · 1.00 · paraphrased: the licence does not allow quoting

How the literature uses it

245 arXiv papers cite this in 291 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 156 sentences without a confident label

Uses its method or tool 1 paper

We realized in [ref] that a similar problem had been solved earlier in the context of QCD sum rules for electromagnetic form-factors [ref] [We later realized that [ref] had used the same method for the electroweak two-loop contribution.].

Short-distance contributions to Hadronic-light-by-light for the muon $g-2$ · SD4 and SD3 · 0.80

Uses its data or values 85 papers

In this work we will discuss on the parameter spaces of a 2HDM satisfying the following experimental data: * $a_μ≡(g-2)_μ/2$ data has been updated from Ref. [ref] showing a deviation from the SM prediction of $a^SM_μ= 116591810(43)×10^-11$ [ref] combined from various different contributions based on the dispersion approach [ref] .

$(g-2)_{e,\mu}$ anomalies and decays $h\to e_a e_b$, $Z\to e_ae_b$, and $e_b\to e_a \gamma$ in a two Higgs doublet model with inverse seesaw neutrinos · Introduction · 1.00
[ref] , the contribution of light quarks in FQM is $a_μ^EW(2)(e,μ,u,c,d,s)=-(4.0+4.65)×10^-11=-8.65×10^-11$] in ref.

Numerical calculation of the full two-loop electroweak corrections to muon (g-2) · Results of our calculation · 0.99
Precision measurements of the muon anomalous magnetic moment [ref] yield a world average of [equation] while state-of-the-art SM calculations [ref] predict the value [ref] [equation] The difference between the theory prediction and measurement reads [equation] and corresponds to a significance of $5.1σ$.[Using recent lattice determinations of the hadronic vacuum polarisation significantly softens the tension between data and the SM [ref] .

Flavoured $(g-2)_\mu$ with Dark Lepton Seasoning · Theoretical Approach · 0.96

Compares with it 5 papers

Our results lead to a reduction of the theoretical uncertainty on the first-family VVA contribution to $a_μ$ compared to the analysis in Ref. [ref] .

Dispersion relations for the hadronic VVA correlator · Introduction · 1.00
This result is almost $1σ$ larger than the previous evaluation from Refs. [ref] , with changes primarily driven by (i) dispersive evaluation of the $VVA$ correlator for the first generation ($+0.20$), (ii) $η$–$η'$ mixing in $w_L^s$ ($+0.14$), (iii) $α_s$ and non-perturbative corrections for charm loop ($+0.48$), and all these effects happen to go in the same direction.

Improved evaluation of the electroweak contribution to muon $g-2$ · Introduction · 1.00
[ref] ) gives the contribution of the third generation [ref] , [equation] in agreement with the result first published in [ref] and recently checked in an automated calculation [ref] .

Top-quark loops and the muon anomalous magnetic moment · Top loop diagrams · 0.84

Cites it as background 34 papers

There is the long-standing discrepancy in the anomalous magnetic moment ($$) of muon between the Standard Model (SM) prediction [ref] and the experimental measurement [ref] .

Semi-visible dark photon in a model with vector-like leptons for the $(g-2)_{e,\mu}$ and $W$-boson mass anomalies · Introduction · 0.84
Vainshtein asked himself a question [ref] (see also [ref] ) whether the transverse part of the triangle graphs is also constrained.

QCD Sum Rules: Bridging the Gap between Short and Large Distances · Can holography help? · 0.87
The OPE for the VVA correlator has been discussed in Refs. [ref] .

Dispersion relations for the hadronic VVA correlator · Review of OPE constraints · 1.00

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [18]

M. Knecht, S. Peris, M. Perrottet and E. de Rafael, JHEP 0211, 003 (2002) [hep-ph/0205102]

View on Pith Pith review arXiv 2002

[2] [15]

G. Degrassi and G. F. Giudice, Phys. Rev. D 58, 053007 (1998) [hep-ph/9803384]

View on Pith Pith review arXiv 1998

[3] [1]

G. W. Bennett et al. [Muon g-2 Collaboration], Phys. Rev. Lett. 89, 101804 (2002) [hep- ex/0208001]

View on Pith 2002

[4] [2]

M. Davier, S. Eidelman, A. Hocker and Z. Zhang, Confronting spectral functions from e+e− annihilation and tau decays: Consequences for the muon magne tic moment, hep-ph/0208177

View on Pith Pith review arXiv

[5] [3]

K. Hagiwara, A. D. Martin, D. Nomura and T. Teubner, The SM prediction of g − 2 of the muon, hep-ph/0209187

View on Pith Pith review arXiv

[6] [4]

K. Fujikawa, B. W. Lee and A. I. Sanda, Phys. Rev. D 6, 2923 (1972)

View on Pith 1972

[7] [5]

R. Jackiw and S. Weinberg, Phys. Rev. D 5, 2396 (1972)

View on Pith 1972

[8] [6]

G. Altarelli, N. Cabibbo and L. Maiani, Phys. Lett. B 40, 415 (1972)

View on Pith 1972

[9] [7]

I. Bars and M. Yoshimura, Phys. Rev. D 6, 374 (1972)

View on Pith 1972

[10] [8]

W. A. Bardeen, R. Gastmans and B. Lautrup, Nucl. Phys. B 46, 319 (1972)

View on Pith 1972

[11] [9]

A. Ferroglia, G. Ossola, M. Passera and A. Sirlin, Phys. R ev. D 65, 113002 (2002) [hep-ph/0203224]

View on Pith Pith review arXiv 2002

[12] [10]

T. V. Kukhto, E. A. Kuraev, A. Schiller and Z. K. Silagadz e, Nucl. Phys. B371, 567 (1992)

View on Pith 1992

[13] [11]

E. D’Hoker, Phys. Rev. Lett. 69, 1316 (1992)

View on Pith 1992

[14] [12]

S. Peris, M. Perrottet and E. de Rafael, Phys. Lett. B 355, 523 (1995) [hep-ph/9505405]

View on Pith Pith review arXiv 1995

[15] [13]

A. Czarnecki, B. Krause and W. J. Marciano, Phys. Rev. D 52, 2619 (1995) [hep-ph/9506256]

View on Pith Pith review arXiv 1995

[16] [14]

A. Czarnecki, B. Krause and W. J. Marciano, Phys. Rev. Le tt. 76, 3267 (1996) [hep-ph/9512369]

View on Pith Pith review arXiv 1996

[17] [16]

A. Czarnecki and W. J. Marciano, Phys. Rev. D 64, 013014 (2001) [hep-ph/0102122]

View on Pith Pith review arXiv 2001

[18] [17]

A. Czarnecki and W. J. Marciano, Phys. Rev. D 53, 1066 (1996) [hep-ph/9507420]. 33

View on Pith Pith review arXiv 1996

[19] [19]

S. L. Adler, Phys. Rev. 177, 2426 (1969)

View on Pith 1969

[20] [20]

L. Rosenberg, Phys. Rev. 129, 2786 (1963)

View on Pith 1963

[21] [21]

E. V. Shuryak and A. I. Vainshtein, Nucl. Phys. B 201, 141 (1982); V. A. Novikov, M. A. Shif- man, A. I. Vainshtein and V. I. Zakharov, Fortsch. Phys. 32, 585 (1985)

View on Pith 1982

[22] [22]

S. L. Adler and W. A. Bardeen, Phys. Rev. 182, 1517 (1969)

View on Pith 1969

[23] [23]

A. Vainshtein, Phys. Lett. B 569, 187 (2003) [hep-ph/0212231]

View on Pith Pith review arXiv 2003

[24] [24]

G. ’t Hooft, in Recent Developments In Gauge Theories, Eds. G. ’t Hooft et al ., (Plenum Press, New York, 1980)

View on Pith 1980

[25] [25]

B. L. Ioﬀe and A. V. Smilga, Nucl. Phys. B 232, 109 (1984)

View on Pith 1984

[26] [26]

M. Gell-Mann, R. J. Oakes and B. Renner, Phys. Rev. 175, 2195 (1968)

View on Pith 1968

[27] [27]

M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Sov. P hys. JETP 45, 670 (1977) [Zh. Eksp. Teor. Fiz. 72, 1275 (1977)]

View on Pith 1977

[28] [28]

M. A. Shifman, A. I. Vainshtein and V. I. Zakharov, Phys. Rev. D 18, 2583 (1978) [Erratum-ibid. D 19, 2815 (1979)]

View on Pith 1978

[29] [29]

B. Grinstein, R. P. Springer and M. B. Wise, Phys. Lett. B 202, 138 (1988)

View on Pith 1988

[30] [30]

B. Grinstein, R. P. Springer and M. B. Wise, Nucl. Phys. B 339, 269 (1990)

View on Pith 1990

[31] [31]

M. Ciuchini, E. Franco, L. Reina and L. Silvestrini, Nuc l. Phys. B 421, 41 (1994) [hep-ph/9311357]. 34

View on Pith Pith review arXiv 1994