The Ellipse of Muon Dipole Moments

Keith Hermanek; Navin McGinnis; Radovan Dermisek; Sangsik Yoon

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The Ellipse of Muon Dipole Moments

Radovan Dermisek, Keith Hermanek, Navin McGinnis, Sangsik Yoon

High Energy Physics - Phenomenology · Submitted 27 May 2022

full text compiled · 2026-09-24 · no language-model review

The authors' main claim We show that any new interaction resulting in a chirally-enhanced contribution to the muon magnetic moment necessarily modifies the decay rate of the Higgs boson to muon pairs or generates the muon electric dipole moment.

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What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.13 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.07 · mentions code or data availability 0.02.

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

We show that any new interaction resulting in a chirally-enhanced contribution to the muon magnetic moment necessarily modifies the decay rate of the Higgs boson to muon pairs or generates the muon electric dipole moment. These three observables are highly correlated, and near future measurements of $h\to μ^+μ^-$ will carve an ellipse in the plane of dipole moments for any such model. Together with the future measurements of the electric dipole moment many models able to explain the muon g-2 anomaly can be efficiently tested.

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 show that any new interaction resulting in a chirally-enhanced contribution to the muon magnetic moment necessarily modifies the decay rate of the Higgs boson to muon pairs or generates the muon electric dipole moment.	result 0.96	0.83	0.80	asserted 1.00
s1	These three observables are highly correlated, and near future measurements of $h\to μ^+μ^-$ will carve an ellipse in the plane of dipole moments for any such model.	result 0.55	0.70	0.34	asserted 0.91
s2	Together with the future measurements of the electric dipole moment many models able to explain the muon g-2 anomaly can be efficiently tested.	interpretation 0.94	0.22	0.21	asserted 0.55

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

What the paper reports

Result sentences with where each is established. A qualification the authors state beside a result is attached to it.

Further decreasing $k$ to about 2, even the $R_h→μ^+μ^- = 1 ±1%$ range extends to $d_μ = 0$.

simulation asserted Introduction p 0.91

We find that for hypercharge choices $±1/2$ and $±1$ of the scalar in FFS models or fermion in SSF models, $|𝒬|$ varies between 1/5 and 6.

derivation asserted Introduction p 0.88

In this Letter we show that any new interaction resulting in a chirally enhanced contribution to the muon magnetic moment necessarily modifies the muon Yukawa coupling, and thus the decay of the Higgs boson to muon pairs, or, if $h→μ^+μ^-$ is not modified, the muon electric dipole moment ($μ$EDM) of certain size must be generated (with one exception noted later).

derivation asserted Introduction p 0.86

However, the range of predicted $|d_μ|$ is also growing, and at some point, for $k ≲20$, it extends to $d_μ = 0$.

prediction asserted Introduction p 0.86

Thus, for these scenarios, the correlation of three observables requires deviations from SM predictions either in $R_μ$ or $d_μ$ that are observable in the near future.

prediction asserted Introduction p 0.85

Contours of constant $R_h→μ^+μ^- = 1$ for a few representative choices of smaller $k$ are shown in Fig. [ref] (bottom).

simulation asserted Introduction p 0.85

As $k$ decreases, the center of the ellipse moves to larger values of $Δa_μ$.

observation asserted Introduction p 0.81

Contours of $R_μ= 1±10%$ are now consistent with the whole $2σ$ range of $Δa_μ$.

observation asserted Introduction p 0.79

This allows us to write $λ_μμ^h$ and thus $R_h→μ^+μ^-$ in terms of electric and magnetic dipole moments: R_h→μ^+μ^-=(Δa_μ/2ω - 1)^2 + (m_μd_μ/eω)^2,

derivation asserted Introduction p 0.78

For example, for $𝒬= 1$, the range of $λ_YZ$ from $0.5$ to $√(4π)$ corresponds to $k = 1$ to $≃50$.

derivation asserted Introduction p 0.74

In fact, the consistency sharply requires values of $d_μ≃2.7-3.4×10^-22 e·cm$ ($𝒬=3$) and $d_μ≃3.6-5.1×10^-22 e·cm$ ($𝒬=5$), which are within the expected sensitivity of future measurements.

derivation asserted Introduction p 0.72

Thus, the correlation between $Δa_μ$, $d_μ$, and $R_h→μ^+μ^-$ can test most efficiently the high end of the spectrum that is far beyond the reach of currently envisioned future colliders.

interpretation asserted Introduction p 0.70

From Fig. [ref] we see that as $k$ is decreasing from the values typical for SM+VLs, the consistency of $Δa_μ$ with $R_h→μ^+μ^- = 1±10%$ requires larger $|d_μ|$.

observation asserted Introduction p 0.69

For the FFS models and, in the limit of a common mass of all new particles, we find

derivation asserted Introduction p 0.69

This model (range of $k$) is somewhat special as, in spite of the large contribution from $C_μH$ to the muon mass and Yukawa coupling, the SM-like $R_h→μ^+μ^-$ and $d_μ = 0$ are consistent with $Δa_μ$ within $1σ$.[ This illustrates the only exception to generating non-zero $μ$EDM when $R_h→μ^+μ^-=1$, advertised in the introduction.

interpretation hedged possibility Introduction p 0.67

Conditions under which these results were obtained

Sentences the authors wrote about who was studied, how they were assigned, and what they received. Selected from the Methods; nothing inferred.

assumption or scope The discussion in this Letter has been limited to couplings necessary to generate a chirally-enhanced contribution to $Δa_μ$ through an interaction of the SM Higgs to new particles. Introduction · p 0.97

assumption or scope which remains a very good approximation for arbitrary splitting in the spectrum of new leptons and Higgs masses comparable to those of new leptons. Introduction · p 0.95

assumption or scope For the FFS models and, in the limit of a common mass of all new particles, we find Introduction · p 0.94

assumption or scope From the results of Refs. [ref] we can find that the modification to Eq. ([ref]), assuming a common mass for new leptons much larger than that of heavy Higgses, becomes Introduction · p 0.91

assumption or scope Finally, allowing for any $R_h→μ^+μ^-$ as a future possible measured value (up to the current limit), in Fig. ([ref]) we plot contours of $k$ in the $R_h→μ^+μ^-$ – $|d_μ|$ plane assuming the central value $Δa_μ$. Introduction · p 0.90

assumption or scope No matter what the quantum numbers of $X$, $Y$, and $Z$ particles are, as long as they can form the diagram on the left between $SU(2)$ doublet, $l_L$, and singlet, $μ_R$, leptons, the photon can be removed and the $Y$-$Z$-$H$ coupling and its conjugate can be used again to generate the diagram on the right top. Introduction · p 0.88

assumption or scope The boundary corresponds to the upper limit on possible $μ$EDM if $R_h→μ^+μ^- < 1$, [equation] Introduction · p 0.87

assumption or scope Effects of other possible dimension 6 operators involving muon fields, SM Higgs doublet and derivatives can be absorbed into the definition of the muon Yukawa coupling, $y_μ$, or are parametrically suppressed by $m_μ/v$, similar as in the discussion in Ref. [ref] . Introduction · p 0.87

assumption or scope For low $tanβ$ the results are similar as for the SM extensions with VLs discussed above. Introduction · p 0.85

assumption or scope This necessarily modifies the rate for $h→μ^+μ^-$, unless the modified Yukawa coupling has the same magnitude as that in the SM, which is possible with complex couplings that in turn predict a certain value of $μ$EDM. Introduction · p 0.84

assumption or scope As we will see, with complex couplings, predictions for $h→μ^+μ^-$ cannot be made based only on $Δa_μ$. Introduction · p 0.82

assumption or scope We also show corresponding $±10%$ and $±1%$ regions for cases when the region does not extend all the way to $d_μ = 0$ in the $1σ$ range of $Δa_μ$. Introduction · p 0.82

assumption or scope With order one couplings, the scale of new physics up to $∼10$ TeV is expected, and it further extends to $≳50$ TeV for couplings close to the perturbativity limit [ref] . Introduction · p 0.81

assumption or scope In addition, for models where $X$ is a scalar participating in electroweak symmetry breaking, for example, the SM Higgs boson, the same operator could be generated at tree level as in the diagram on the right bottom. Introduction · p 0.81

assumption or scope Although all the couplings in diagrams in Fig. [ref] can be complex, the same combination of couplings enter both $C_μγ$ and $C_μH$ for tree models, with an additional factor of $λ_YZ λ_YZ^*$ for loop models. Introduction · p 0.80

assumption or scope In such cases $R_h→μ^+μ^-$ still carves an ellipse in the plane of dipole moments but with the center shifted (to non-zero $d_μ$ for complex $k$) depending on the size of additional couplings. Introduction · p 0.78

assumption or scope In this Letter we show that any new interaction resulting in a chirally enhanced contribution to the muon magnetic moment necessarily modifies the muon Yukawa coupling, and thus the decay of the Higgs boson to muon pairs, or, if $h→μ^+μ^-$ is not modified, the muon electric dipole moment ($μ$EDM) of certain size must be generated (with one exception noted later). Introduction · p 0.77

assumption or scope Defining the muon Yukawa coupling and the electric and magnetic dipole moments in terms of Dirac spinors in the basis where the muon mass, $m_μ$, is real and positive, Introduction · p 0.76

assumption or scope In Fig. [ref] (top), we show contours of constant $R_h→μ^+μ^-$ in the plane of the muon dipole moments for $k=64π^2$ which corresponds, for example, to the SM extended by a vectorlike doublet and singlet leptons whose quantum numbers mirror their respective SM counterparts, i.e., $𝒬=1$. Introduction · p 0.73

assumption or scope However, in contrast to the case with $𝒬=1$, consistency of $R_μ= 1±10%$ with $Δa_μ$ necessarily implies a nonzero value of $d_μ$. Introduction · p 0.73

Measurements

Numbers as the authors wrote them, bound to what they measure. Units, degrees of freedom and arithmetic checks are code, not the model.

Quantity	Value	Where	Checked by code
region where h→μ^+μ^- is found to be within	10% p 0.96	Introduction	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (Introduction)
d_μ = 0 are consistent with Δa_μ within	1σ p 0.94	Introduction	consistent number matches the authors' source text
large as the current upper limit when \|d_μ\|∼	1×10^-22 p 0.98	Introduction	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (Introduction)
Contours of R_μ=	1±10% p 0.92	Introduction	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (Introduction) consistent uncertainty is non-negative
R_μ= 1±10% are now consistent with the whole	2σ p 0.92	Introduction	consistent number matches the authors' source text
fact, the consistency sharply requires values of d_μ≃2.7	-3.4×10^-22 p 0.98	Introduction	consistent number matches the authors' source text not repeated same number stated elsewhere in the paper (stated once)
requires values of d_μ≃2.7-3.4×10^-22 e·cm (𝒬=3) and d_μ≃3.6	-5.1×10^-22 p 0.98	Introduction	consistent number matches the authors' source text not repeated same number stated elsewhere in the paper (stated once)
the way to d_μ = 0 in the	1σ p 0.82	Introduction	consistent number matches the authors' source text
We also show corresponding ±	10% p 0.82	Introduction	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (Introduction)
We also show corresponding ±10% and ±	1% p 0.82	Introduction	consistent number matches the authors' source text
SM+VLs, the consistency of Δa_μ with R_h→μ^+μ^- =	1±10% p 0.87	Introduction	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (Introduction) consistent uncertainty is non-negative
k to about 2, even the R_h→μ^+μ^- =	1 ±1% p 0.94	Introduction	consistent number matches the authors' source text consistent uncertainty is non-negative
for the scale of new physics to ∼	18 TeV p 0.98	Introduction	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (Introduction)
for the 2HDM [ref] and, for example, ∼	14 TeV p 0.98	Introduction	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (Introduction)
Improving the measurement of R_h→μ^+μ^- to within	1% p 0.97	Introduction	consistent number matches the authors' source text
will further reduce these upper limits to ∼	10 TeV p 0.97	Introduction	consistent number matches the authors' source text consistent same number stated elsewhere in the paper (Introduction)
these upper limits to ∼10 TeV and ∼	8 TeV p 0.97	Introduction	consistent number matches the authors' source text

Limitations the authors state

The discussion in this Letter has been limited to couplings necessary to generate a chirally-enhanced contribution to $Δa_μ$ through an interaction of the SM Higgs to new particles. Introduction · p 0.98
However additional couplings in a given model, not contributing to $Δa_μ$ might in principle enter the formula for $k$ (or even generate a complex $k$ parameter), for example scalar quartic couplings involving new scalars and the SM Higgs doublet [ref] . Introduction · p 0.98
While not a generic feature, in some models the dimension-5 operator $l_Ll_LHH$ may also be generated which would be subject to additional constraints from the neutrino sector. Introduction · p 0.95
Furthermore, in certain models there can be sizable contributions to $Δa_μ$ from other operators due to renormalization group mixing, for example from four-fermion operators in models with leptoquarks [ref] . Introduction · p 0.92
In such cases $R_h→μ^+μ^-$ still carves an ellipse in the plane of dipole moments but with the center shifted (to non-zero $d_μ$ for complex $k$) depending on the size of additional couplings. Introduction · p 0.69
Effects of other possible dimension 6 operators involving muon fields, SM Higgs doublet and derivatives can be absorbed into the definition of the muon Yukawa coupling, $y_μ$, or are parametrically suppressed by $m_μ/v$, similar as in the discussion in Ref. [ref] . Introduction · p 0.64

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Introduction	result 31 · setup 23 · interpretation 21 · background 9 · limitation 8 · other 5 · method 1 · future work 1

How this paper uses its references

35 references. For each citing sentence, the use is labeled and, where the cited paper has a compiled record, whether that paper's own main claim supports the use. 15 shown.

R. Dermisek, K. Hermanek and N. McGinnis, Phys. Rev. Lett. 126, no.19, 191801 (2021) [arXiv:2011.11812 [hep-ph]].

This immediately sets the upper bound for the scale of new physics to $∼18$ TeV for the 2HDM [ref] and, for example, $∼14$ TeV for FFS loop models with $SU(2)$ doublets and singlets and $𝒬 =1$. supports this paper p 0.61 · load-bearing 0.63 · Introduction

R. Dermisek, K. Hermanek and N. McGinnis, Phys. Rev. D 104, no.5, 055033 (2021) [arXiv:2103.05645 [hep-ph]].

This immediately sets the upper bound for the scale of new physics to $∼18$ TeV for the 2HDM [ref] and, for example, $∼14$ TeV for FFS loop models with $SU(2)$ doublets and singlets and $𝒬 =1$. supports this paper p 0.61 · load-bearing 0.62 · Introduction

G. Aad et al. [ATLAS], Phys. Lett. B 812, 135980 (2021) [arXiv:2007.07830 [hep-ex]].

The region outside $R_h→μ^+μ^-=2.2$ (shaded gray) is already ruled out by measurements of $h→μ^+μ^-$ [ref] . data used p 0.66 · load-bearing 0.58 · Introduction

R. Dermisek, K. Hermanek and N. McGinnis, Phys. Rev. D 104, no.5, 055033 (2021) [arXiv:2103.05645 [hep-ph]].

With order one couplings, the scale of new physics up to $∼10$ TeV is expected, and it further extends to $≳50$ TeV for couplings close to the perturbativity limit [ref] . supports this paper p 0.87 · load-bearing 0.57 · Introduction

L. Allwicher, L. Di Luzio, M. Fedele, F. Mescia and M. Nardecchia, Phys. Rev. D 104, no.5, 055035 (2021) [arXiv:2105.13981 [hep-ph]].

With order one couplings, the scale of new physics up to $∼10$ TeV is expected, and it further extends to $≳50$ TeV for couplings close to the perturbativity limit [ref] . supports this paper p 0.86 · load-bearing 0.56 · Introduction

R. Dermisek, K. Hermanek and N. McGinnis, Phys. Rev. Lett. 126, no.19, 191801 (2021) [arXiv:2011.11812 [hep-ph]].

With order one couplings, the scale of new physics up to $∼10$ TeV is expected, and it further extends to $≳50$ TeV for couplings close to the perturbativity limit [ref] . supports this paper p 0.84 · load-bearing 0.56 · Introduction

R. Capdevilla, D. Curtin, Y. Kahn and G. Krnjaic, Phys. Rev. D 105, no.1, 015028 (2022) [arXiv:2101.10334 [hep-ph]].

With order one couplings, the scale of new physics up to $∼10$ TeV is expected, and it further extends to $≳50$ TeV for couplings close to the perturbativity limit [ref] . supports this paper p 0.83 · load-bearing 0.55 · Introduction

A. Abada et al. [FCC], Eur. Phys. J. C 79, no.6, 474 (2019)

The $R_h→μ^+μ^-$ is expected to be measured with $∼10%$ precision at the LHC and $∼1%$ at the hadron version of the Future Circular Collider [ref] . data used p 0.54 · load-bearing 0.54 · Introduction

A. Adelmann, M. Backhaus, C. C. Barajas, N. Berger, T. Bowcock, C. Calzolaio, G. Cavoto, R. Chislett, A. Crivellin and M. Daum, et al. [arXiv:2102.08838 [hep-ex]].

The limits on $μ$EDM are expected to reach $|d_μ|∼1×10^-21 e·cm$ at the Muon $g-2$ experiment at Fermilab [ref] , and could reach $6×10^-23 e·cm$ at the Paul Scherrer Institute [ref] . data used p 0.64 · load-bearing 0.53 · Introduction

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The 4.2$σ$ deviation of the measured value of the muon anomalous magnetic moment from the SM prediction, $Δa_μ= (2.51 ±0.59)×10^-9$ [ref] , can be comfortably explained even by very heavy new particles as a result of the chiral enhancement from the Higgs coupling to new particles, see Fig. [ref] (left). data used p 0.98 · load-bearing 0.51 · Introduction

R. Chislett [Muon g-2], EPJ Web Conf. 118, 01005 (2016)

The limits on $μ$EDM are expected to reach $|d_μ|∼1×10^-21 e·cm$ at the Muon $g-2$ experiment at Fermilab [ref] , and could reach $6×10^-23 e·cm$ at the Paul Scherrer Institute [ref] . data used p 0.68 · load-bearing 0.49 · Introduction

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where $𝒬= 1$ for $X$ and $Y$ leptons in $2_-1/2⊕1_-1$ or $2_-1/2⊕ 3_0$ representations of $SU(2)×U(1)_Y$; $𝒬=3$ for $2_-3/2⊕1_-1$ or $2_-3/2⊕3_-1$; and $𝒬=5$ for $2_-1/2⊕3_-1$ [ref] . data used p 0.47 · load-bearing 0.48 · Introduction

R. Dermisek, K. Hermanek and N. McGinnis, Phys. Rev. D 104, no.5, 055033 (2021) [arXiv:2103.05645 [hep-ph]].

From the results of Refs. [ref] we can find that the modification to Eq. ([ref]), assuming a common mass for new leptons much larger than that of heavy Higgses, becomes data used p 0.54 · load-bearing 0.47 · Introduction

K. S. Babu, P. S. B. Dev, S. Jana and A. Thapa, JHEP 03, 179 (2021) [arXiv:2009.01771 [hep-ph]].

Possible correlations between $Δa_μ$ and $h→μ^+μ^-$ were pointed out before [ref] . background p 0.76 · load-bearing 0.45 · Introduction

R. Dermisek, K. Hermanek and N. McGinnis, Phys. Rev. D 104, no.9, L091301 (2021) [arXiv:2108.10950 [hep-ph]].

From the results of Refs. [ref] we can find that the modification to Eq. ([ref]), assuming a common mass for new leptons much larger than that of heavy Higgses, becomes data used p 0.51 · load-bearing 0.45 · Introduction

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Original abstract

We show that any new interaction resulting in a chirally-enhanced contribution to the muon magnetic moment necessarily modifies the decay rate of the Higgs boson to muon pairs or generates the muon electric dipole moment. These three observables are highly correlated, and near future measurements of $h\to \mu^+\mu^-$ will carve an ellipse in the plane of dipole moments for any such model. Together with the future measurements of the electric dipole moment many models able to explain the muon g-2 anomaly can be efficiently tested.

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References

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Cited by 5 Pith papers

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

On-shell Mass Renormalisation and RG-improved Effective Potential in Vector-like Lepton Models
hep-ph 2026-10 conditional novelty 6.0 of 10

The authors construct on-shell renormalization schemes and redundancy-free two-loop RGEs for six vector-like lepton models, then use the RG-improved effective potential to map vacuum instability scales across the para...
Taming lepton portal dark matter by a non-invertible selection rule
hep-ph 2026-08 conditional novelty 6.0 of 10

A non-invertible selection rule from Z2 gauging of Z5 enforces one-flavor dominance of lepton portal dark matter couplings while leaving the PMNS matrix unrestricted.
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.
Towards a Muon Collider
physics.acc-ph 2023-03 accept novelty 4.0 of 10

The International Muon Collider Collaboration reports no identified insurmountable obstacle to a 3 to 10 TeV muon collider, and lays out the cooling, magnet, detector and physics programme needed to demonstrate feasibility.
Muon Collider Forum Report
hep-ex 2022-09 conditional novelty 3.0 of 10

The report concludes that a 10 TeV muon collider is technically plausible on a roughly 20-year timescale and would deliver Higgs, dark-matter, and naturalness physics that no single proposed machine matches.

How the literature uses it

9 arXiv papers cite this in 23 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

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Uses its method or tool 1 paper

For a lepton $ℓ$, we match this result to the effective operator [ref] , [equation] We then obtain [equation] where $Q_ℓ= -1$ is the electric charge of the charged lepton.

Taming lepton portal dark matter by a non-invertible selection rule · Correction to photon coupling · 0.85

Cites it as background 5 papers

Dimension-six operators that modify the Higgs coupling to the muon as well as generate contributions to the muon's dipole moments via a chiral enhancement were studied extensively in [ref] .

Predictions for Muon Electric and Magnetic Dipole Moments from $h \rightarrow \mu^+ \mu^-$ in Two-Higgs-Doublet Models with New Leptons · 2HDM-II Effective Field Theory · 0.98
The structure of these correlations differs from the one in most other models where a BSM mass suppression would appear on the r.h.s. of Eq. [ref] instead of the loop suppression (for general discussions see Refs. [ref] and references therein).

From Higgs physics to lepton flavour violation: current bounds and future prospects for vector-like lepton models · Introduction · 0.87
This section reviews the findings of [ref] on this subject.

Towards a Muon Collider · The muon anomalous magnetic moment · 0.85

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