Gauged $L_\mu - L_\tau$ with Large Muon Anomalous Magnetic Moment and the Bimaximal Mixing of Neutrinos

D. P. Roy; Ernest Ma; Sourov Roy

REVIEW

Gauged $L_\mu - L_\tau$ with Large Muon Anomalous Magnetic Moment and the Bimaximal Mixing of Neutrinos

Ernest Ma, D. P. Roy, Sourov Roy

High Energy Physics - Phenomenology · Submitted 11 Oct 2001 · 18 references

Pith's verdict: A solid, economical 2001 model paper: the g-2 piece is borrowed from Ref. [4], but the model tying it to bimaximal mixing and the collider study are real contributions, and the central bound survives the stress-test objection.

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arXiv IDhep-ph/0110146 (version 2)

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CitationD. P. Roy, Ernest Ma, Sourov Roy. "Gauged $L_\mu - L_\tau$ with Large Muon Anomalous Magnetic Moment and the Bimaximal Mixing of Neutrinos." arXiv:hep-ph/0110146 (2001). https://pith.science/paper/QMBEI2GN

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Short version: this is a competent, economical 2001 model-building paper. The X-boson contribution to g-2 is not new — it is Ref. [4] — but the model that ties it to bimaximal neutrino mixing is, and the collider study is a useful addition. I would send it out for refereeing rather than desk-reject it. What is actually new: two Higgs doublets with opposite U(1)_X charges, a charged singlet zeta, one right-handed neutrino, and a softly broken Z2. That yields a clean 3x3 mass matrix (Eq. 8): one seesaw mass m3 plus a radiative nu_e-nu_tau entry m'. The texture predicts |U_e3| around 0.22 and near-bimaximal mixing, which in 2001 was a real, checkable statement. The collider section runs from LEP-I through LC and LHC with sensible pT cuts and gives discovery reaches of a few hundred GeV for g_X = 1. Nothing fancy, but it is the kind of thing the L_mu - L_tau literature needed. Where it is soft: the agreement with data is a two-parameter fit. m3 = 0.05 eV and m' = 0.016 eV are chosen to land on the two measured splittings; Eqs. (13)-(14) then just invert the choice. The genuine predictions are the mixing pattern and |U_e3|, not the splittings. Second, bimaximal mixing needs f1 = f2, which is put in by hand, not derived from the interchange symmetry. Third, the stress-test note is right that v1 = v2 is approximate, but it is wrong that this threatens Eq. (3): the X contribution goes as m_mu^2/(24 pi^2 (v1^2 + v2^2)), so the lower bound survives any v1-v2 splitting. What does change is the X-Z mixing angle, which the paper does not estimate; it is probably small if the interchange breaking is soft, but 'probably' is doing work there. Fourth, the collider numbers are leading-order parton-level with no detector simulation and no shipped code — standard for the period, but reproduction takes effort. Retrospectively, |U_e3| around 0.22 is larger than what Daya Bay later found (theta_13 around 8.6 degrees), so that particular prediction did not quite land, though it was within the then-current CHOOZ bound. Who should read it: anyone working on gauged L_mu - L_tau, light Z-prime models, or radiative neutrino mass. It is a legitimate contribution and deserves a serious referee report.

Referee report

Major objections (4)

[After Eq. (14), the sentence 'Note also that |U_e3| ≃ 0.22 (close to the maximum value allowed)'.] The predicted |U_e3| ≈ 0.22 should be compared quantitatively with the CHOOZ limit. For Δm^2_atm ≈ 2.6×10^-3 eV^2, CHOOZ gives sin^2(2θ13) < 0.1 at 90% CL, corresponding to |U_e3| < 0.16. The predicted value gives sin^2(2θ13) ≈ 0.18, which appears to be excluded. The authors should discuss whether the parameter choice (m', m3) can be adjusted to satisfy CHOOZ while maintaining the agreement with solar and atmospheric data, or whether this is a genuine tension.
[Eq. (16).] The squared decay amplitude for Z → ff̄X is dimensionally inconsistent as printed: the first term in the bracket, 1/(MZ-2E1)^2, has dimensions of inverse mass squared, while the second term, 4(1-cosθ)(MZ-2E1)(MZ-2E2){...}, has dimensions of mass squared. The derivation should be checked, and the LEP-I bound in Fig. 3 (MX > 50(70) GeV for g_X > 0.1(1)) may need revision.
[The paragraph beginning 'To obtain v1 = v2...' and Eq. (3).] The paper assumes v1 = v2 to eliminate X-Z mixing and derive Eq. (3). The η1-η2 interchange symmetry is broken by the Yukawa couplings in Eq. (4), and the paper does not quantify the resulting v1-v2 splitting or its effect on the X-Z mixing. While the lower bound itself is robust (it holds for any v1, v2 because v1^2+v2^2 ≤ (2√2G_F)^{-1}), the collider phenomenology (Z → ff̄X, e+e- → μ+μ-X) assumes no mixing, and the effect of a non-zero mixing angle on the LEP-I and LC bounds should be estimated.
[Fig. 2 and Eq. (15).] The charge flow in the radiative νeντ mass diagram should be clarified. With the stated U(1)_X charges (τ_R and ντ both -1, η1^0 +1), the τ_R → ντ transition via η1^0 appears forbidden; the diagram likely involves N_R or a different contraction. The derivation of Eq. (15) and the numerical value hλ = 0.8 MeV should be checked.

Minor objections (6)

[Eq. (9) and Eq. (14).] The sign of Δm^2_12 is negative (the eigenvalues are ±c m' with a common negative correction), but the paper writes it as positive. This is a minor sign convention issue.
[Eq. (16).] The notation E1, E2, θ should be defined more precisely (which particle is which, and in which frame).
[Fig. 3.] The caption says 'The region above the curves is excluded at 95% CL,' but the Z-decay and universality curves have different shapes; the reader would benefit from a clearer indication of which curve is which.
[The discussion of |U_e3|.] The paper should cite the CHOOZ experiment explicitly when discussing |U_e3|.
[Eq. (17).] Eq. (17) is cited to Carone-Murayama; the reader would benefit from a brief explanation of the origin of the correction.
[Conclusion.] The paper's conclusion says 'verifiable explanation' — the word 'verifiable' is appropriate given the collider predictions, but the |U_e3| tension should be addressed.

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The paper

The paper claims

One extra force could explain both the muon's magnetic excess and bimaximal neutrino mixing, if two new Higgs doublets get equal vacuum expectation values.

The reading

The paper asks whether a single extra force — a gauge symmetry acting on the difference between muon number and tau number, $L_μ - L_τ$ — can account for two otherwise unrelated puzzles at once: a muon magnetic moment that came out slightly larger than the standard-model prediction, and neutrino oscillation data that look like near-maximal mixing among all three flavours. The authors build an explicit model containing a new gauge boson $X$, two extra Higgs doublets of opposite charge, one heavy right-handed neutrino, and one charged singlet scalar. Their claim is that this field content, with no tuning beyond assuming the two new Higgs doublets receive equal vacuum expectation values $v_1 = v_2$, yields a calculable positive shift in the muon anomaly and a neutrino mass matrix whose texture is bimaximal. If right, the model makes sharp, checkable statements: a floor on the muon anomaly of $1.555×10^{-9}$, a smallest neutrino mixing element $|U_{e3}| ≈ 0.22$, and a new boson light enough to be found at the colliders then being planned.

What carries the argument

The load-bearing device is the charge assignment plus the equal-vev condition. Because only the muon and tau sectors are charged under the new $U(1)_X$, there are no flavour-changing couplings among charged leptons, and the $X$ couples to muons in a fixed, calculable way. The $η_1$–$η_2$ interchange symmetry enforces $v_1 = v_2$, which kills $X$–$Z$ mixing and makes the $g-2$ shift depend only on $v_1$ while leaving $M_X/g_X$ free — this is why the model can predict a floor on $Δa_μ$ and still allow the boson to be heavy. The same discrete structure, softly broken only by the trilinear scalar term, is what lets a single right-handed neutrino seed one heavy eigenstate while a radiative loop supplies the small $ν_e$–$ν_τ$ entry that tilts the matrix into bimaximal form.

Extended reading notes

Core claim

The central claim is a package deal. Gauging $L_μ - L_τ$, with $(ν_μ, μ)_L$ and $μ_R$ carrying charge $+1$ and the tau partners carrying $-1$, gives the $X$ boson a direct coupling to muons and therefore a one-loop contribution $Δa_μ = g_X^2 m_μ^2/(12π^2 M_X^2)$ to the muon anomalous magnetic moment. Adding two Higgs doublets $η_1$ (charge $+1$) and $η_2$ (charge $-1$) and setting $v_1 = v_2$ removes $X$–$Z$ mixing, fixes $M_X = 2g_X v_1$, and converts that contribution into a pure prediction, $Δa_μ = m_μ^2/(48π^2 v_1^2) > 1.555×10^{-9}$ — a lower bound, not a fit. The same doublets, together with one heavy right-handed singlet $N_R$ and a charged singlet $ζ^+$, generate neutrino masses: a seesaw mass $m_3$ for the combination $ν_3 = (f_1ν_μ + f_2ν_τ)/√(f_1^2+f_2^2)$, plus a radiative $ν_e$–$ν_τ$ entry $m'$ from soft breaking of a $Z_2$ symmetry by the trilinear term $λζ^-(η_1^+φ^0 - η_1^0φ^+)$. The resulting $3×3$ matrix, with $f_1 = f_2$ so that $s = c = 1/√2$, gives bimaximal mixing, and with $m_3 = 0.05$ eV and $m' = 0.016$ eV reproduces $Δm^2_{atm} ≈ 2.6×10^{-3}$ eV$^2$ and $Δm^2_{sol} ≈ 5.8×10^{-5}$ eV$^2$.

Load-bearing premise

Everything rests on the two new Higgs doublets having exactly equal vacuum expectation values, held in place by an interchange symmetry the authors themselves say cannot be exact, since the Yukawa couplings of Eq. (4) and standard-model terms break it and the size of that breaking is never quantified.

Editorial extensions

If this is right

The muon anomaly is bounded from below: any confirmed excess must exceed $1.555×10^{-9}$, so a smaller measured discrepancy would rule the model out rather than merely disfavour it.
The lightest neutrino mixing element is predicted near $|U_{e3}| ≈ 0.22$, close to the largest value then allowed, giving a definite target for reactor and long-baseline experiments.
The $X$ boson should appear as a peak in the $μ^+μ^-$ invariant mass inside 3-muon and 4-muon events, with discovery reach $M_X = 300\,(500)$ GeV at 500 (1000) GeV lepton colliders and 400 GeV at the LHC for $g_X = 1$.
LEP-I data already exclude $M_X < 50\,(70)$ GeV for $g_X \gtrsim 0.1\,(1)$ through the $Z → μ^+μ^- X$ channel, and the $Z$-pole universality constraint on $g_X$ is weak enough not to threaten the picture.
The soft-breaking coupling needed to fit solar data is small, $hλ = 0.8$ MeV for $m_ζ = 1$ TeV, so the discrete symmetry is broken by a technically natural amount.

Reading between the lines

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

Because $Δa_μ$ depends on $v_1$ and not on $M_X$, a heavy or invisible $X$ does not weaken the $g-2$ prediction; the sharpest test of the model is therefore a precision magnetic-moment measurement, not a collider search.
The predicted $|U_{e3}| ≈ 0.22$ is the most exposed number in the paper: a substantially smaller measured value would require the radiative entry $m'$ to be far below the $0.016$ eV used to fit the solar splitting, which in turn would strain the loop estimate $m' ≈ hλ m_τ^2 v_1/(16π^2 v_0 m_ζ^2)$.
Since the $X$ carries muon number and not electron number, the model predicts suppressed but nonzero lepton-flavour violation in the charged sector at one loop; the charged singlet mass $m_ζ$ is the single knob that controls both this and the size of $m'$, so $τ → eν\bar{ν}$ and neutrino data are tied together.
The equal-vev assumption is the one place where the two halves of the argument meet: relaxing $v_1 = v_2$ reintroduces $X$–$Z$ mixing, which shifts the $g-2$ prediction and, through the same $η$ sector, the neutrino texture — so a future measurement of $Z$–$X$ mixing would test both claims at once.

Original abstract

We consider the gauging of $L_\mu - L_\tau$ as an explanation of a possibly large muon anomalous magnetic moment. We then show how neutrino masses with bimaximal mixing may be obtained in this framework. We study the novel phenomenology of the associated gauge boson in the context of present and future high-energy collider experiments.

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, 2,899 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.05 · compares with prior results 0.07 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; show every role.

We consider the gauging of $L_\mu - L_\tau$ as an explanation of a possibly large muon anomalous magnetic moment. We then show how neutrino masses with bimaximal mixing may be obtained in this framework. We study the novel phenomenology of the associated gauge boson in the context of present and future high-energy collider experiments.

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	We consider the gauging of $L_\mu - L_\tau$ as an explanation of a possibly large muon anomalous magnetic moment.	contribution 0.91	0.39	0.10	hedged possibility 0.97
s1	We then show how neutrino masses with bimaximal mixing may be obtained in this framework.	contribution 0.85	0.90	0.22	hedged possibility 0.66
s2	We study the novel phenomenology of the associated gauge boson in the context of present and future high-energy collider experiments.	contribution 1.00	0.82	0.10	asserted 0.83

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.90.

What was examined, and what was not

sources read

arXiv listing abstract v2

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.** Contribution of X to muon magnetic moment. νe τL τR ντ hη 0 1 i ζ + φ + hφ 0 i

**Figure 2.** Radiative contribution to the νeντ mass. 11

**Figure 3.** The LEP-I constraints on the mass and coupling of the

**Figure 4.** The X boson signal cross-section in the 4-muon channel at LEP and LC energies of 200, 500 and 1000 GeV for gX = 1. 13

**Figure 5.** The X boson signal cross-section in the 3-muon and 4-muons channels at the Tevatron and LHC energies for gX = 1. 14

Figures reproduced from arXiv:hep-ph/0110146 by the authors.

References

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J. A. M. Vermaseren, “New features of FORM”, math-ph/001 0025. 10 µ µ µ µ γ X Figure 1: Contribution of X to muon magnetic moment. νe τL τR ντ ⟨η01⟩ ζ + φ+ ⟨φ0⟩ Figure 2: Radiative contribution to the νeντ mass. 11 0 0.2 0.4 0.6 0.8 1 1.2 0 20 40 60 80 100 120 140 160 180 200 gX MX (GeV) Z-decay Universality Figure 3: The LEP-I constraints on the mass and...

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Hunting All the Hidden Photons
hep-ph 2018-03 accept novelty 5.0 of 10

The authors convert secluded hidden-photon limits into exclusion contours for U(1)_{B-L}, U(1)_{L_mu-L_e}, U(1)_{L_e-L_tau} and U(1)_{L_mu-L_tau} gauge bosons, adding loop-induced mixing, neutrino bounds, and white dw...
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...
$(g-2)_\mu$, 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.
Higgs $\to \mu \tau$ in Abelian and Non-Abelian Flavor Symmetry Models
hep-ph 2014-12 conditional novelty 5.0 of 10

Two electroweak-scale flavor models, A4 and gauged Lμ−Lτ, can reproduce the CMS h→μτ hint while predicting correlated rates for h→eτ, h→ττ, μ→eγ, τ→μγ, and neutrino-mixing correlations.
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.
Muon g-2 and LHC phenomenology in the $L_\mu-L_\tau$ gauge symmetric model
hep-ph 2013-11 conditional novelty 5.0 of 10

A U(1) gauge boson coupling only to muons and taus can account for the muon g-2 anomaly at 60 to 100 GeV mass, and existing ATLAS four-lepton data already exclude the 60 GeV case at coupling 0.3.
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...
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...
Gauged $U(1)_{L_\mu - L_\tau}$ model in light of muon $g-2$ anomaly, neutrino mass and dark matter phenomenology
hep-ph 2016-07 reject novelty 4.0 of 10

A U(1) muon-minus-tauon extension with a vector-like dark fermion and a doubly charged scalar is claimed to fit muon g-2, neutrino mass, relic density, and the AMS-02 positron excess, but the AMS-02 fit needs an unexp...
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.
The physics case of a 3 TeV muon collider stage
hep-ph 2022-03 accept novelty 3.0 of 10

A 3 TeV muon collider would improve Higgs coupling precision over HL-LHC, measure the Higgs trilinear coupling at 15 to 30 percent, and uniquely probe muon-flavored new physics behind the g-2 and B anomalies.
The Weak Gravity Conjecture: A Review
hep-th 2022-01 accept novelty 3.0 of 10

The Weak Gravity Conjecture and its stronger tower and sublattice forms hold in every consistent quantum gravity theory examined so far, but none of them has been derived from first principles.

How the literature uses it

104 arXiv papers cite this in 145 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 · 98 sentences without a confident label

Uses its data or values 3 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
The appropriate values for the case $M_Z'≫m_μ$ lie around $M_Z'/g' ∼[200]GeV$: [equation] The authors of Ref. [ref] also derive a direct detection limit of roughly $M_Z' >[50]GeV$, based on ALEPH measurements of the process $e^+ e^- →μμZ'^* →4μ$ [ref] (see Fig. [ref]) and under the assumption $M_Z'/g' ∼[200]GeV$.

Gauged L_mu - L_tau Symmetry at the Electroweak Scale · Gauge Sector · 0.86
For the $U(1)_L_μ-L_τ$ model, the LEP-1 measurement of the four-fermion final-state at the $Z$ pole [ref] was used to derive a constraint on $Z'$ from $Z→μ^+μ^-Z'$ decay, as well as from the universality of $Z→e^+e^-$ and $Z→μ^+μ^-$ [ref] , as collectively shown by the red curves in Fig. [ref] bottom panel.

Searching for Heavy Leptophilic $Z'$: from Lepton Colliders to Gravitational Waves · Current laboratory bounds on the model parameters · 0.91

Compares with it 2 papers

Other limits and projections are also shown for comparison, such as $e^+ e^- →μ^+ μ^- Z', Z' →μ^+ μ^-$ from the BaBar experiment [ref] , the LHC searches [ref] , the trident production in neutrino scattering experiments [ref] .

The physics case of a 3 TeV muon collider stage · Gauge $L_μ-L_τ$ Interactions · 0.99
Other limits and projections are also shown for comparison, such as $e^+ e^- →μ^+ μ^- Z', Z' →μ^+ μ^-$ from the BaBar experiment [ref] , the LHC searches [ref] , and the trident production in neutrino scattering experiments [ref] .

Towards a Muon Collider · Lepton Flavour Violation · 0.99

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 37 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
In this article, we focus on a particularly interesting solution proposed in terms of a new light mediator associated with a new gauge symmetry, which received a lot of attention over the last years [ref] .

Solar neutrino probes of the muon anomalous magnetic moment in the gauged $U(1)_{L_\mu-L_\tau}$ · Introduction · 0.81

Discussion

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