Muon Anomalous $g -2$ and Gauged $L_\mu - L_\tau$ Models

N.G. Deshpande; P. Ko; S. Baek; X.-G. He

REVIEW

Muon Anomalous $g -2$ and Gauged $L_\mu - L_\tau$ Models

S. Baek, N.G. Deshpande, X.-G. He, P. Ko

High Energy Physics - Phenomenology · Submitted 14 Apr 2001 · 8 references

Pith's verdict: The one-loop core and the case (a)/(b) constraints are correct and useful, but case (c) looks excluded by the paper's own τ → μ Z' rate, which the paper only applies below 0.5 GeV.

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arXiv IDhep-ph/0104141 (version 1)

Pith ID6CVS67AW, Pith's permanent record of this paper and its review

CitationN.G. Deshpande, P. Ko, S. Baek, X.-G. He. "Muon Anomalous $g -2$ and Gauged $L_\mu - L_\tau$ Models." arXiv:hep-ph/0104141 (2001). https://pith.science/paper/6CVS67AW

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Editor's note

read the letter

The useful part of this paper is cases (a) and (b). The one-loop Z' contribution to (g−2)_μ is computed correctly: Eq. (6) is the standard massless-vector result, Eq. (8) is the standard massive integral, and the heavy-mass limit in Eq. (9) checks out arithmetically. The collider study at the end (μμ → μμ, ττ at 500 GeV) is a sensible addition and shows the resonance structure you would expect. For a 2001 response to the BNL anomaly, this is competent and timely, and the authors are honest that the discrepancy is only 2.6σ and that both data and theory need improvement. The R constraint in Eq. (16) and the W-mass bound in Eq. (15) are reasonable as far as they go. The paper is also clear that the simplest case (c) model is ruled out and needs the singlet extension, which is the right kind of honesty. The problem is that the singlet fix does not go far enough. The paper puts the viable case (c) window at a ≈ 0.011–0.02, m_Z' ≈ 1.12–1.3 GeV (Fig. 3). With a ≈ 0.015, the μτ coupling in Eq. (14) is g ≈ 5×10⁻³, and τ → μ Z' is kinematically open for m_Z' < 1.67 GeV. The two-body width comes out around 10⁻⁶ GeV, i.e. BR ~ 10⁵, which is not a marginal exclusion — it is a factor of 10⁵ over the bound, and it would shorten the τ lifetime by five orders of magnitude. The paper's only statement on this channel is that “the region m_Z' < 0.5 GeV is ruled out” (after Eq. 19). That sentence is the load-bearing gap: the constraint should extend to 1.67 GeV, and the singlet S does not change the μτ coupling, so it does not help. As far as I can tell, the entire Fig. 3 window is excluded, and case (c) cannot produce the required Δa_μ. Cases (a) and (b) are not touched by this argument — case (a) is massless, and case (b) has flavor-diagonal couplings, so τ → μ Z' is absent at tree level. But the reader's concern about missing external bounds (neutrino trident for (a), beam dump and supernova for (b)) is fair and not addressed. So: a correct core calculation with a real error in one of three branches. The abstract's “three classes” claim is too generous given that case (c) is dead. I would send it to referees — the case (c) issue is exactly what review should catch — but I would want the authors to either fix or drop case (c) before publication.

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Major objections (3)

[Section II, text following Eq. (19); Fig. 3] The case (c) window is the load-bearing weak point. Eq. (14) gives the Z' coupling to the muon-tau mass eigenstates as e a / cos(theta_W), and Fig. 3 places the viable region at a ~ 0.011-0.02 with m_Z' ~ 1.12-1.3 GeV. The decay tau -> mu Z' is kinematically open for m_Z' < m_tau - m_mu ~ 1.67 GeV, so the quoted window sits inside the open region. The manuscript states only that 'the region m_Z' < 0.5 GeV is ruled out by the non-observation of two body decay mode tau -> mu Z' [7]', which does not address why the window at 1.2 GeV survives. The authors should compute the tree-level rate from Eq. (14) explicitly, compare it to the experimental bound, and show whether the Fig. 3 region is excluded. If it is, the case (c) claim in the abstract (abstract:s8) needs to be withdrawn or the model modified; the singlet S introduced after Eq. (19) changes m_Z' but not the mu-tau coupling, so it does not by itself evade this constraint.
[Section II, case (a) and case (b) allowed regions] The paper does not apply existing beam-dump, supernova-cooling, fifth-force, or neutrino-trident constraints to its own allowed parameter space. For case (a) a massless Z' with |a| ~ 1e-3 coupling to muons and taus, and for case (c) a ~ 0.015 at m_Z' ~ 1.2 GeV, these bounds are directly relevant. Refs. [6,7] are cited for experimental consequences but the resulting limits are not propagated into Figs. 2-4. The authors should state which of these constraints apply and whether the quoted windows survive; if some are already excluded, the abstract's three-class claim (abstract:s2) should be qualified accordingly.
[Section II, Eq. (15) and the discussion of case (c)] The argument that the pure two-doublet case (c) model is ruled out by combining Eq. (15) with the R constraint is plausible, but the manuscript does not show the numerical comparison explicitly. Since this negative result is used to motivate the singlet extension, the authors should present the excluded region on the a vs. m_Z' plane from Eq. (15) and from R separately, so the reader can verify that no overlap with the Delta a_mu band remains. As written, the claim rests on a verbal summary rather than a displayed figure.

Minor objections (7)

[Eq. (3)] The second and third lines both label the right-handed state as mu_R; the third line should read tau_R. The same typo appears in the transformation table.
[Eq. (6)] The expression Delta a_mu = alpha_em a^2 / (2 pi c_W^2) should be checked against the standard massless-vector result; the reader would benefit from an intermediate step or a reference, since the coefficient is what fixes the numerical range in Eq. (7).
[Eq. (16)] The definition of xi and the factor of 2 multiplying g_2(z) are stated, but the origin of the relative sign between the g_1 and g_2 terms and the interference structure would be clearer with one sentence of explanation.
[Figs. 2, 7, 8] The figure captions say the lines correspond to Delta a_mu at +2 sigma, +1 sigma, 0, -1 sigma, -2 sigma, but the ordering 'from left to right' should be stated explicitly for each figure, since the curves are not monotonic in all panels.
[Section III] The angular cut |cos(theta_13)| < 0.5 used to regulate the t-channel collinear singularity in mu+mu- -> mu+mu- should be defined in terms of the particle labels, and the sensitivity of the quoted SM cross section (1153.7 fb) to that cut should be noted.
[Section IV] The statement that Delta a_tau ~ (m_tau/m_mu)^2 Delta a_mu in the heavy-Z' limit of case (b) should be reconciled with the text's earlier remark that Delta a_tau = Delta a_mu in the same limit; one of the two appears to be a typo.
[References] Ref. [3] is listed as hep-ph/0102122 without a journal reference; the authors should confirm whether it is published, and similarly for the several hep-ph entries in Ref. [5] that are cited as preprints.

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The paper

The paper claims

A new gauge boson coupled to muon-minus-tau lepton number can supply the muon's missing magnetism, in three different versions of the model.

The reading

The BNL measurement of the muon magnetic moment sat about 2.6 standard deviations above the Standard Model prediction, and this paper asks whether a new light gauge boson — a $Z'$ — coupled to the difference between muon number and tau number can account for it. That symmetry, $U(1)_{L_μ-L_τ}$, is attractive because it can be gauged with the Standard Model fermion content alone, cancels its anomalies, and never touches the electron, so it escapes the tight constraints that kill the electron-flavoured versions. The authors compute the one-loop $Z'$ contribution to $a_μ$ in three classes of model, distinguished by whether the symmetry is exact, broken at an unrelated scale, or broken at the electroweak scale, and find an allowed coupling window in each. They then convert those windows into cross sections for $μ^+μ^- → μ^+μ^-$ and $μ^+μ^- → τ^+τ^-$ at a 500 GeV muon collider, where the three cases would produce visibly different event rates from the Standard Model. The point is not just that the discrepancy can be fitted, but that the fit pins the $Z'$ mass and coupling into ranges a muon collider could confirm or kill.

What carries the argument

The load-bearing object is the one-loop triangle vertex with a $Z'$ in the loop, whose finite part shifts the muon's magnetic moment by an amount controlled by the new coupling $ea/2c_W$ and the ratio $m_μ/m_{Z'}$. Because the $Z'$ couples to muon-number minus tau-number, the same diagram with the muon line replaced by a tau line generates a correlated shift in the tau moment, and the paper uses that correlation as a consistency check: $Δa_τ = Δa_μ$ in case (a), $Δa_τ ≈ (m_τ/m_μ)^2 Δa_μ$ in the heavy-$Z'$ limit of case (b), and $Δa_τ ≈ Δa_μ$ in case (c). Two structural devices carry the model building: an unbroken discrete symmetry that forces the $Z$–$Z'$ mixing to vanish at tree level, so electroweak precision data stay satisfied automatically, and the ratio $R$ of the leptonic tau decay width to its Standard Model value, which supplies the tightest numerical bound in case (c) and is what drives the $Z'$ mass to about 1.2 GeV.

Extended reading notes

Core claim

The paper establishes that $Z'$ exchange at one loop in gauged $U(1)_{L_μ-L_τ}$ models can generate a muon anomalous magnetic moment of the size implied by the BNL excess, and it maps out three distinct realisations. In case (a), where the symmetry is exact and the $Z'$ is massless, the one-loop result is $Δa_μ = (α_{em}/2π)(a^2/c_W^2)$, which fixes $0.8×10^{-3} < |a| < 2.24×10^{-3}$ at two $\sigma$; the tau gets exactly the same correction. In case (b), a Standard-Model-singlet scalar carrying $L_μ-L_τ$ charge breaks the symmetry at a scale unrelated to electroweak breaking, giving a massive $Z'$ with no tree-level $Z$–$Z'$ mixing; the loop integral then constrains $a$ and $m_{Z'}$ jointly, and in the heavy-mass limit only the ratio survives, $9.2×10^{-3} < a/m_{Z'}(GeV) < 25.8×10^{-3}$. In case (c), where the breaking is tied to the electroweak scale through two extra Higgs doublets, an unbroken discrete symmetry $Z'→-Z'$ with $L_{μL}↔L_{τL}$ and $φ_2↔φ_3$ keeps the mixing at zero, but the resulting $Z'$ mass formula and the measured ratio $R = Γ(τ→μνν)/Γ(τ→μνν)_{SM}$ (with $ΔR = 0.004$ at one $\sigma$) together exclude the simplest version; adding a singlet scalar lifts that constraint, and the surviving parameter space forces $m_{Z'} ≈ 1.2$ GeV. The paper closes by showing that these three cases give markedly different $μ^+μ^- → μ^+μ^-, τ^+τ^-$ cross sections at $√s = 500$ GeV — resonant enhancement in case (b), a roughly thousand-event deficit in case (c) at 50 fb$^{-1}$ — against Standard Model benchmarks of 451.49 fb and 1153.7 fb.

Load-bearing premise

The argument assumes that a $Z'$ coupling only to muons and taus, with no mixing into the electron sector and no other low-energy couplings, survives every existing beam-dump, supernova-cooling, fifth-force and neutrino-scattering bound on such a particle, which the paper does not check against its own allowed regions.

Editorial extensions

If this is right

If the symmetry is exact, the $Z'$ is massless and the coupling is pinned to a narrow window, $0.8×10^{-3} < |a| < 2.24×10^{-3}$, so a single measured value of $Δa_μ$ would fix the model completely.
If the symmetry is broken at an unrelated scale, only the ratio $a/m_{Z'}$ is constrained in the heavy-mass limit, so the $Z'$ can be arbitrarily heavy while still producing the observed excess.
If the breaking is tied to the electroweak scale, the $Z'$ must sit near 1.2 GeV, and the region below 0.5 GeV is already excluded by the non-observation of $τ → μZ'$.
At a 500 GeV muon collider, case (b) shows a sharp resonance in $μ^+μ^- → τ^+τ^-$ as $√s$ approaches $m_{Z'}$, while case (c) shows a deficit of roughly a thousand $τ^+τ^-$ events per 50 fb$^{-1}$ relative to the Standard Model.
The tau magnetic moment is shifted by a correlated and computable amount in every case, so an independent measurement of $a_τ$ would test which of the three realisations is realised.

Reading between the lines

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

The same coupling windows are reachable by low-energy, non-collider probes of a light $Z'$ that couples only to muons and taus — fixed-target muon scattering, muon $g-2$ running, and anomalous magnetic-moment measurements in muonic atoms — so the model space could be narrowed long before a muon collider is built.
Because the $Z'$ carries no electron charge, the model predicts no shift in the electron magnetic moment at one loop; a future electron $g-2$ improvement therefore acts as a clean veto on this whole family rather than as a constraint on its parameters.
The 2.6-sigma discrepancy has since become the subject of a much larger experimental and theoretical effort; the paper's three-case taxonomy remains a useful template, because each case predicts a different relationship between the $Z'$ mass and the size of the deviation, which is exactly the axis on which later measurements discriminate.
The discrete symmetry used to kill $Z$–$Z'$ mixing at tree level is a structural choice, not a consequence of the gauge symmetry; a model without it would generate mixing radiatively, and the resulting shift in the electron moment would give a much sharper experimental handle than any of the muon-collider signals discussed here.

Original abstract

In this paper we study $Z'$ contribution to $g -2$ of the muon anomalous magnetic dipole moment in gauged $U(1)_{L_\mu - L_\tau}$ models. Here $L_i$ are the lepton numbers. We find that there are three classes of models which can produce a large value of $g-2$ to account for possible discrepancy between the experimental data and the Standard Model prediction. The three classes are: a) Models with an exact $U(1)_{L_\mu - L_\tau}$. In these models, $Z'$ is massless. The new gauge interaction coupling $e a/\cos\theta_W$ is constrained to be $ 0.8\times 10^{-3} < |a| < 2.24\times 10^{-3}$. b) Models with broken $U(1)_{L_\mu - L_\tau}$ and the breaking scale is not related to electroweak symmetry breaking scale. The $Z'$ gauge boson is massive. The allowed range of the coupling and the $Z'$ mass are constrained, but $Z'$ mass can be large; And c) The $U(1)_{L_\mu-L_\tau}$ is broken and the breaking scale is related to the electroweak scale. In this case the $Z'$ mass is constrained to be $\sim 1.2$ GeV. We find that there are interesting experimental signatures in $\mu^+\mu^-\to \mu^+\mu^-, \tau^+\tau^-$ in these models.

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, 7,693 input tokens, $0.0003 reported.

What the abstract itself states, as probabilities: claims first 0.02 · states limitation 0.20 · human participants 0.01 · controlled comparison 0.10 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.22 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; show every role.

In this paper we study $Z'$ contribution to $g -2$ of the muon anomalous magnetic dipole moment in gauged $U(1)_{L_\mu - L_\tau}$ models. Here $L_i$ are the lepton numbers. We find that there are three classes of models which can produce a large value of $g-2$ to account for possible discrepancy between the experimental data and the Standard Model prediction. The three classes are: a) Models with an exact $U(1)_{L_\mu - L_\tau}$. In these models, $Z'$ is massless. The new gauge interaction coupling $e a/\cos\theta_W$ is constrained to be $ 0.8\times 10^{-3} < |a| < 2.24\times 10^{-3}$. b) Models with broken $U(1)_{L_\mu - L_\tau}$ and the breaking scale is not related to electroweak symmetry breaking scale. The $Z'$ gauge boson is massive. The allowed range of the coupling and the $Z'$ mass are constrained, but $Z'$ mass can be large; And c) The $U(1)_{L_\mu-L_\tau}$ is broken and the breaking scale is related to the electroweak scale. In this case the $Z'$ mass is constrained to be $\sim 1.2$ GeV. We find that there are interesting experimental signatures in $\mu^+\mu^-\to \mu^+\mu^-, \tau^+\tau^-$ in these models.

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	In this paper we study $Z'$ contribution to $g -2$ of the muon anomalous magnetic dipole moment in gauged $U(1)_{L_\mu - L_\tau}$ models.	contribution 0.99	0.83	0.05	asserted 0.74
s1	Here $L_i$ are the lepton numbers.	background 1.00	0.06	0.02	asserted 0.99
s2	We find that there are three classes of models which can produce a large value of $g-2$ to account for possible discrepancy between the experimental data and the Standard Model prediction.	result 0.99	0.95	0.56	asserted 0.99
s3	The three classes are: a) Models with an exact $U(1)_{L_\mu - L_\tau}$.	result 0.91	0.74	0.09	asserted 0.97
s4	In these models, $Z'$ is massless.	result 0.95	0.47	0.04	asserted 1.00
s5	The new gauge interaction coupling $e a/\cos\theta_W$ is constrained to be $ 0.8\times 10^{-3} < \|a\| < 2.24\times 10^{-3}$. b) Models with broken $U(1)_{L_\mu - L_\tau}$ and the breaking scale is not related to electroweak symmetry breaking scale.	result 0.99	0.78	0.12	asserted 1.00
s6	The $Z'$ gauge boson is massive.	result 0.85	0.41	0.04	asserted 1.00
s7	The allowed range of the coupling and the $Z'$ mass are constrained, but $Z'$ mass can be large; And c) The $U(1)_{L_\mu-L_\tau}$ is broken and the breaking scale is related to the electroweak scale.	result 0.68	0.63	0.08	asserted 0.94
s8	In this case the $Z'$ mass is constrained to be $\sim 1.2$ GeV.	result 1.00	0.83	0.11	asserted 1.00
s9	We find that there are interesting experimental signatures in $\mu^+\mu^-\to \mu^+\mu^-, \tau^+\tau^-$ in these models.	result 0.93	0.92	0.14	asserted 0.99

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.88.

What was examined, and what was not

sources read

arXiv listing abstract v1

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.** FIG. 1. Feynman diagram which generates a non-zero ∆

**Figure 3.** FIG. 3. The allowed region on the

**Figure 5.** FIG. 5. Feynman diagrams for processes

**Figure 6.** FIG. 6. Feynman diagrams for process

Showing 7 of the paper's 9 figures. See all figures in the PDF ↗ Figures reproduced from arXiv:hep-ph/0104141 by the authors.

References

Works cited (8)

[7]

R. Foot, X. G. He, H. Lew and R. R. Volkas, Phys. Rev. D 50, 4571 (1994)

View on Pith 1994
[1]

H.N. Brown et al., e-print hep-ex/0102017

View on Pith Pith review arXiv
[2]

M. Davier and A. Hocker, Phys. Lett. B435, 427(1998)

View on Pith 1998
[3]

A. Czarnecki and W. J. Marciano, hep-ph/0102122

View on Pith Pith review arXiv
[4]

J. Erler and M. Luo, hep-ph/0101010; F. J. Yndurain, hep-ph/ 0102312; S. Narison, hep-ph/0103199

View on Pith Pith review arXiv
[5]

L. Everett, G. L. Kane, S. Rigolin and L. Wang, hep-ph/0102145 ; J. L. Feng and K. T. Matchev, hep-ph/0102146; E. A. Baltz and P. Gondolo, hep- ph/0102147; U. Chat- topadhyay and P. Nath, hep-ph/0102157; T. Huang, Z. H. Lin, L. Y. Shan and X. Zhang, hep-ph/0102193; S. Komine, T. Moroi and M. Yamaguchi, hep-ph/ 0102204; E. Ma and M. Raidal, hep-ph/0102255;...

View on Pith Pith review arXiv
[6]

X.-G. He et al., Phys. Rev. D43, R22(1991); Phys. Rev. D44, 2118(1991)

View on Pith 1991
[8]

Particle Data Group, Eur. Phys. Jou. C15, 1(2000). 8 FIGURES /CI /BC /AD /AM /AM /AM FIG. 1. Feynman diagram which generates a non-zero ∆ aµ 0 1 2 3 4 5 6 7 8 9 10 0 200 400 600 800 1000 1200 a MZ’ (GeV) FIG. 2. ∆ aµ on the a vs. mZ ′ plane in case b). The lines from left to right are for ∆ aµ away from its central value at +2 σ, +1σ, 0, −1σ and −2σ, resp...

View on Pith 2000

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hep-ph 2026-06 unverdicted novelty 5.0 of 10

Stronger couplings or inflaton-seeded initial abundance allow freeze-in dark matter to match the relic density while evading DAMIC-M and PandaX bounds for reheating temperatures below the electroweak scale.
$L_\mu-L_\tau$ gauge bosons in beam dumps and supernovae
hep-ph 2025-11 unverdicted novelty 5.0 of 10

Re-evaluation of sub-GeV Lμ-Lτ gauge boson constraints from beam-dump production modes and multiple supernova observables, highlighting differences from existing literature.
Muon $g-2$ at multi-TeV muon collider
hep-ph 2020-12 conditional novelty 5.0 of 10

A multi-TeV muon collider can test heavy new physics explanations of the muon g-2 anomaly, either by producing new particles or by measuring the Higgs-plus-photon cross section predicted by the g-2 operator.
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.
Origin of Sterile Neutrino Dark Matter via Vector Secret Neutrino Interactions
hep-ph 2020-05 conditional novelty 5.0 of 10

A new vector boson interacting only with active neutrinos can produce the observed sterile neutrino dark matter abundance in three distinct regimes, and the required couplings fall within reach of planned beam-dump an...
Dark matter interactions with muons in neutron stars
hep-ph 2019-06 conditional novelty 5.0 of 10

Dark matter coupled to muons through a light U(1)_{L_mu-L_tau} gauge boson is captured by neutron-star muons and can heat old neutron stars to about 1700 to 2500 K, a signature future infrared telescopes could detect.
Self-interacting dark matter and muon $g-2$ in a gauged U$(1)_{L_{\mu} - L_{\tau}}$ model
hep-ph 2018-05 conditional novelty 5.0 of 10

A gauged U(1) extension with a vector-like fermion dark matter and a light scalar mediator can simultaneously fit the muon g-2 anomaly and produce the velocity-dependent dark matter self-scattering needed on galactic ...
Severely Constraining Dark Matter Interpretations of the 21-cm Anomaly
hep-ph 2018-03 conditional novelty 5.0 of 10

After applying CMB, BBN, supernova, and lab constraints, only a millicharged dark matter component making up 0.3 to 2 percent of the dark matter, with mass 10 to 80 MeV and charge 10^-6 to 10^-4, can still explain the...
Predictions for the neutrino parameters in the minimal gauged U(1)$_{L_\mu-L_\tau}$ model
hep-ph 2017-05 accept novelty 5.0 of 10

In the minimal gauged U(1)_{L_mu-L_tau} model, the two-zero-minor structure of the neutrino mass matrix predicts the Dirac CP phase delta around 1.6 pi, the sum of neutrino masses 0.14 to 0.22 eV, and the effective Ma...
Detecting the $L_{\mu}-L_{\tau}$ gauge boson at Belle II
hep-ph 2017-02 conditional novelty 5.0 of 10

Belle II with 50 inverse attobarns can probe L_mu-L_tau gauge bosons below about 1 GeV and couplings above roughly 8e-4, covering part of the muon g-2 favored window.
$(g-2)_\mu$, Lepton Flavour Violation and $Z$ Decays with Leptoquarks: Correlations and Future Prospects
hep-ph 2016-12 accept novelty 5.0 of 10

Two scalar leptoquark representations that explain the muon g-2 anomaly predict opposite-sign interference in Z couplings to muons and distinct B decay signatures, allowing future experiments to distinguish them.
Loop effects of heavy new scalars and fermions in $b\to s\mu^+\mu^-$
hep-ph 2016-08 conditional novelty 5.0 of 10

A systematic survey of 24 gauge representations for new heavy scalars and fermions finds that one-loop box diagrams can explain both the b to s mu mu anomalies and the muon g-2 at the 2 sigma level, but only with a mu...
Lepton flavor violating Z' explanation of the muon anomalous magnetic moment
hep-ph 2016-07 accept novelty 5.0 of 10

A flavor-violating Z' boson coupling only to muons and taus can explain the muon g-2 anomaly only for masses above the tau mass, with the lighter mass window ruled out by tau decay data.
Lepton flavor violation with light vector bosons
hep-ph 2016-02 conditional novelty 5.0 of 10

For a sub-GeV Z' with lepton-flavor-violating muon-tau couplings, the two-body decay tau to mu Z' bounded by 1995 ARGUS data gives a stronger limit than tau to 3mu whenever the Z' mass is below twice the muon mass.
Z'-induced FCNC decays of top, beauty and strange quarks
hep-ph 2015-12 conditional novelty 5.0 of 10

In a gauged L_mu - L_tau model with vector-like quarks, the same coupling that fits the b to s anomalies forces top quarks to decay to a charm quark and a Z', at rates that LHC Run 1 top data may already reach.
Flavour Dependent Gauged Radiative Neutrino Mass Model
hep-ph 2015-01 conditional novelty 5.0 of 10

A gauged muon-minus-tau symmetry forces a two-zero texture in the neutrino mass matrix, allowing only inverted hierarchy and predicting CP phases, while a light Z' boson can account for the muon g-2 anomaly.
Mind the gap on Icecube: Cosmic neutrino spectrum and muon anomalous magnetic moment in the gauged L_{\mu} - L_{\tau} model
hep-ph 2014-09 conditional novelty 5.0 of 10

A gauged L_mu - L_tau interaction with a ~1.9 MeV mediator and coupling ~5e-4 can, for inverted neutrino hierarchy, reproduce the 400 TeV to 1 PeV IceCube gap while sitting in the muon g-2 favored band.
Neutrino Trident Production: A Powerful Probe of New Physics with Neutrino Beams
hep-ph 2014-06 conditional novelty 5.0 of 10

Existing neutrino trident measurements exclude a gauged L_mu minus L_tau Z' as the source of the muon g-2 anomaly for masses above roughly 400 MeV.
Gauged L_mu - L_tau Symmetry at the Electroweak Scale
hep-ph 2011-07 accept novelty 5.0 of 10

A gauged L_mu - L_tau symmetry with a Z' boson at 200-300 GeV per unit coupling fits electroweak data and can resolve the muon g-2 anomaly while generating mu-tau symmetric neutrino mixing.
Phenomenology of $U(1)_{L_\mu - L_\tau}$ charged dark matter at PAMELA/FERMI and colliders
hep-ph 2008-11 conditional novelty 5.0 of 10

A gauged muon-minus-tau lepton-number model with a Dirac-fermion dark matter candidate can fit the PAMELA/Fermi positron excess and the muon g-2 anomaly while remaining within relic-density bounds, and predicts observ...
Constraining $U(1)_{L_\mu-L_\tau}$ Model with Dark Matter Using Relic Density and $N_{\rm eff}$ Bounds
hep-ph 2026-11 conditional novelty 4.0 of 10

Resonant dark matter in the U(1)_Lmu-Ltau model, after Planck relic density and N_eff bounds, survives only for M_Z' around 30 to 50 MeV and g' around (2.1 to 3.5) times 1e-7.
A scalar-extended ${\rm U(1)_{L_{\mu}-L_{\tau}}}$ explanation of the LUX-ZEPLIN 248 keV excess
hep-ph 2026-10 conditional novelty 4.0 of 10

A scalar-extended U(1)Lmu-Ltau model with a roughly 100 keV dark matter mass splitting reproduces the LZ 248 keV recoil for TeV-scale dark matter while passing relic, muon g-2, trident, and collider constraints.
A Compatibility Check: Low-Scale Chiral $U(1)_X$ Theories Vs. $(g-2)_e$ Anomaly
hep-ph 2026-08 conditional novelty 4.0 of 10

Three benchmark chiral U(1)_X models cannot simultaneously explain the electron (g-2) anomaly and pass current neutrino-scattering bounds, so they are excluded as complete new-physics explanations.
New Avenues of Heavy Neutral Lepton at Muon Collider
hep-ph 2026-06 unverdicted novelty 4.0 of 10

In a U(1) gauged seesaw model, Z'Z' fusion processes at muon colliders enable HNL pair production via Z'Z'→H→NN and Z'Z'→NN, yielding LNV signals not suppressed by Higgs mixing.
Prospects of five-dimensional $L_\mu-L_\tau$ gauge interactions in the light of elastic neutrino-electron scatterings: The scope of the DUNE near detector
hep-ph 2024-07 unverdicted novelty 4.0 of 10

Five-dimensional U(1)_{Lμ-Lτ} model predicts multiple gauge bosons whose contributions to elastic neutrino-electron scattering can be probed at DUNE, covering much of the muon (g-2) consistent parameter space.
Probing light mediators and $(g-2)_{\mu}$ through detection of coherent elastic neutrino nucleus scattering at COHERENT
hep-ph 2022-02 accept novelty 4.0 of 10

COHERENT CEνNS data constrain light vector and scalar mediators across several U(1)' models, excluding muon g-2 explanations wherever the mediator couples directly to quarks.
New physics explanations of $a_\mu$ in light of the FNAL muon $g-2$ measurement
hep-ph 2021-04 conditional novelty 4.0 of 10

Folding in the Fermilab muon g-2 result, only models with enhanced chirality flips, light new states, or large couplings survive LHC and dark matter constraints, and only chirality-flip models can explain the muon ano...
Minimal Gauged U(1)$_{L_\alpha - L_\beta}$ Models Driven into a Corner
hep-ph 2018-11 accept novelty 4.0 of 10

Minimal gauged U(1)_{L_alpha-L_beta} models with one symmetry-breaking scalar force neutrino mass matrices into two-zero texture or minor form, and all but the singlet U(1)_{L_mu-L_tau} case are excluded by current data.
Let there be Light Dark Matter: The gauged $U(1)_{L_\mu-L_\tau}$ case
hep-ph 2018-08 conditional novelty 4.0 of 10

A MeV-scale vector-like fermion charged under gauged U(1)_{L_mu-L_tau} can reproduce the dark matter relic density and the muon g-2 anomaly simultaneously, but only in a narrow near-resonance window that current and p...
FIMP and Muon ($g-2$) in a U$(1)_{L_{\mu}-L_{\tau}}$ Model
hep-ph 2016-12 conditional novelty 4.0 of 10

A single U(1) gauge extension with a freeze-in scalar dark matter candidate reproduces the observed relic density, the muon g-2 anomaly, and neutrino masses and mixings.
Neutrino Mass, Dark Matter and Anomalous Magnetic Moment of Muon in a $U(1)_{L_{\mu}-L_{\tau}}$ Model
hep-ph 2016-08 conditional novelty 4.0 of 10

A single L_mu minus L_tau model with two scalars and three right-handed neutrinos can fit muon g-2, neutrino oscillation data, and the dark matter relic density, with the Galactic Centre gamma-ray excess reproduced at...
MeV scale leptonic force for cosmic neutrino spectrum and muon anomalous magnetic moment
hep-ph 2015-08 conditional novelty 4.0 of 10

A 10 MeV L_mu minus L_tau gauge boson with coupling near 5e-4 can reproduce the IceCube spectral gap and the muon g-2 anomaly, but not the sharp 3 PeV edge.
A facility to Search for Hidden Particles at the CERN SPS: the SHiP physics case
hep-ph 2015-04 conditional novelty 4.0 of 10

SHiP, a proposed CERN SPS beam-dump experiment, could probe dark-photon, scalar, heavy-neutral-lepton and axion-like-particle parameter space well beyond existing limits, according to order-of-magnitude sensitivity estimates.

How later papers used it

138 later papers cite it

Evidence: some. 129 of the citing papers share no author with it, and 4 of those carry a confident label from Pith's citation classifier.

Pith read 9 of the 187 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 paper

Updated the analysis with the latest values and observed that the deviation in the branching ratio of τ⁻→μ⁻νμντ and the (g−2)μ anomaly can be simultaneously reconciled for a value that practically coincides with the one already found in this paper.

Generalised $\mu$-$\tau$ symmetries and calculable gauge kinetic and mass mixing in $U(1)_{L_\mu-L_\tau}$ models (2019) · 0.95 · paraphrased: the licence does not allow quoting

How the literature uses it

130 arXiv papers cite this in 177 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 · 119 sentences without a confident label

Uses its data or values 2 papers

Combining the old measurement of muon $(g-2)$ by BNL E821 experiment [ref] along with the recent one by Fermilab [ref] , it was observed that the experimental observation of $a_μ(≡(g-2)/2)$ differs with the Standard Model (SM) prediction by $4.2σ$ and the deviation is given by [ref] = (251 ±59)×10^-11 .The apparent mismatch between theoretical prediction [ref] and experimental observation may be a pointer towards the physics beyond the Standard Model and people have proposed many new ideas to address this issue [ref] .

Can leptophilic-ALP be a solution to the muon $(g-2)$ anomaly? · Introduction · 0.96
Contributions to the muon magnetic moment of $Z'$ is at one-loop level, which is calculated as [ref] [equation] To explain the anomaly $Δa_μ=(251±59)×10^-11$ [ref] , $g'∼5×10^-4$ with $m_Z'∼𝒪(10)$ MeV is required, which is now stringently constrained by the latest NA64$μ$ experiment [ref] .

Prospects of $Z'$ Portal Dark Matter in $U(1)_{L_\mu-L_\tau}$ · The Model · 0.90

Compares with it 1 paper

We observe that the positive deviation at $1.6σ$ found in the branching ratio of the decay $τ^-→μ^- ν_μν_τ$ compared to its SM value and the anomaly in $(g-2)_μ$ can be simultaneously reconciled for [equation] which practically coincides with the one already found in [ref] .

Generalised $\mu$-$\tau$ symmetries and calculable gauge kinetic and mass mixing in $U(1)_{L_\mu-L_\tau}$ models · Summary and Discussions · 0.95

Cites it as support 1 paper

Rather, they are well-motivated in that they solve concrete, open problems of the Standard Model of particle physics such as the neutrino mass hierarchies and mixing patterns, provide a portal to dark matter, and even accommodate excesses in the $(g-2)_μ$ [ref] .

Leptophilic $Z'$ bosons at the FCC-ee: discovery opportunities · Introduction · 0.98

Cites it as background 49 papers

Thereafter, several variants of $U(1)_L_μ-L_τ$ model have been studied in the context of different phenomenological purposes: e.g., contribution of the $U(1)_L_μ-L_τ$ gauge boson to explain the $(g-2)_μ$ anomaly [ref] , dark matter phenomenology [ref] , generation of neutrino masses and mixing parameters [ref] etc.

Reconciling dark matter, $R_{K^{(*)}}$ anomalies and $(g-2)_{\mu}$ in an ${L_{\mu}-L_{\tau}}$ scenario · Introduction · 0.90
The model with this particle content has been dubbed the minimal gauged $U(1)_L_μ -L_τ$ in Refs. [ref] and has been studied in the context of the baryon asymmetry via leptogenesis [ref] , particle DM phenomenology [ref] and $(g-2)_μ$ anomaly [ref] , to name the most common.

Constraining dark matter from strong phase transitions in a $U(1)_{L_{\mu}-L_{\tau}}$ model: Implications for neutrino masses and muon $g-2$ · Introduction · 0.96
The $Z^'$ gauge boson of a broken $U(1)_L_μ- L_τ$ symmetry is a simple extension of the Standard Model (SM) [ref] that can address the tension in the anomalous magnetic moment of the muon $(g-2)_μ$ [ref] , can serve as mediator for dark matter (DM) interactions with the SM [ref] , and can address anomalies observed in the decays of $B$ mesons [ref] .

$B$ Anomalies and Dark Matter in an $L_\mu-L_\tau$ Model with General Kinetic Mixing · Introduction · 0.91

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.

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Particle Data Group, Eur. Phys. Jou. C15, 1(2000). 8 FIGURES /CI /BC /AD /AM /AM /AM FIG. 1. Feynman diagram which generates a non-zero ∆ aµ 0 1 2 3 4 5 6 7 8 9 10 0 200 400 600 800 1000 1200 a MZ’ (GeV) FIG. 2. ∆ aµ on the a vs. mZ ′ plane in case b). The lines from left to right are for ∆ aµ away from its central value at +2 σ, +1σ, 0, −1σ and −2σ, resp...

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