REVIEW
Muon $g-2$ and $B$-anomalies from Dark Matter
High Energy Physics - Phenomenology · Submitted 7 Apr 2021 · 81 references
Pith's verdict: A tidy four-field classification that genuinely links DM, b→sμμ and g−2, but the simultaneous-fit claim rests on two benchmark points and an unstated fit criterion.
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Referee report
The paper
The paper claims
Four new fields beyond the Standard Model could simultaneously produce the muon's anomalous magnetic moment, the $B$-decay lepton-universality anomalies, and a thermal dark matter relic, with the Higgs vacuum expectation value supplying the
The reading
What carries the argument
The load-bearing object is the four-field loop of Figure 1: a quark line emits a mediator that turns into a lepton mediator which emits a muon pair, with the dark matter field running in the loop. Its two variants, a fermion mediator with two scalars and a scalar mediator with two fermions, define the classes F and S. Chirality enhancement is supplied by the mixing terms $a_H Φ_ℓ^† Φ'_ℓ H$ (scalar case) or $λ_{HL} Ψ P_L Ψ' H$, $λ_{HR} Ψ P_R Ψ' H$ (fermion case), which after electroweak symmetry breaking diagonalise into mass matrices whose off-diagonal entries scale with $v/√2$ rather than with $y_μ$. The loop integrals $F(x,y,z)$, $G(x,y,z)$ and the dipole functions $H(x)$, $H(x)$ convert those couplings and masses into the Wilson coefficients $δC_{9μ}$, $δC_{10μ}$ and into $Δa_μ$. The same couplings that set the $B$ anomalies also set the dark matter annihilation rate into muons, which is why the relic-density contours in the figures track the flavour fit rather than sitting independently of it.
Extended reading notes
Core claim
The paper's claim is a classification plus two demonstrations. The classification: requiring (i) a thermal dark matter candidate, (ii) loop contributions to $b$ to $s$ lepton-pair transitions of the size preferred by global fits, and (iii) a chirally-enhanced muon $g-2$, forces the new fields into a short list. A single choice of colour representation and three of weak isospin survive, and each minimal model contains exactly four fields: a quark-coupled mediator, a lepton-coupled mediator, a dark matter candidate, and one extra field that mixes with a mediator through the Higgs vacuum expectation value. The mixing is essential because the diagrams of the type that give $b$ to $s$ muon pairs with purely left-handed muons produce a dipole coefficient proportional to the muon Yukawa $y_μ$, which is far too small; the extra field allows a chirality flip inside the loop at the scale of the Higgs vacuum expectation value instead. The price is that the same mixing generates additional diagrams with right-handed muons, so the clean prediction $δC_{9μ} = -δC_{10μ}$ is only recovered in the limit where the mixing vanishes. The demonstrations: in model FIb, a singlet Majorana fermion mixed with an $SU(2)_L$ doublet, and in model FIIb, a real scalar singlet with two charged Dirac mediators, the authors show two-dimensional planes in which the $g-2$ band (at $1σ$), the $B$-anomaly region (at $2σ$), the correct thermal relic density, and the experimental exclusions all coexist.
Load-bearing premise
The overlap regions in the two benchmark figures are drawn for hand-picked values of the quark coupling product, the mediator masses and the muon couplings, and only two benchmark assignments per model are shown, so the claim that a joint fit is easily achieved rests on those choices being representative rather than tuned.
Editorial extensions
If this is right
- Because one set of couplings controls both the relic abundance and the $b$ to $s$ muon-pair Wilson coefficients, a measurement of either constrains the other; the two observables are not independent handles on the same sector.
- The models predict charged and neutral partners of the dark matter that decay into two or three leptons plus missing energy, giving LHC signatures that can be recast from existing three-lepton searches.
- Precision fits to $b$ to $s$ muon-pair angular observables can discriminate these models from purely left-handed leptoquark solutions, since the required mixing field necessarily induces right-handed muon couplings.
- Invisible Higgs and invisible $Z$ widths impose a hard floor: a dark matter candidate lighter than half the relevant boson mass is excluded in the mixed cases, so the viable region is bounded from below as well as above.
- The large muon couplings required make these models a target for a multi-TeV muon collider, where the mediators would be produced directly.
Reading between the lines
- The classification tables are a reusable template rather than a one-off: any future anomaly in a different meson or a different lepton could be slotted into the same four-field scheme, so the paper's organising value may outlive the specific anomalies that motivated it.
- If the muon $g-2$ discrepancy is absorbed by improved hadronic vacuum-polarisation determinations, the chirality-flip machinery becomes an unnecessary complication and the surviving models reduce to the three-field versions of the authors' earlier work, which would still address dark matter and the $B$ anomalies.
- The same Higgs-vev mixing that produces the $g-2$ unavoidably generates right-handed muon couplings in $b$ to $s$ muon pairs, so a future precision extraction of the right-handed Wilson coefficient is a direct discriminator between this mechanism and leptoquark explanations, which need not produce it.
- The dark matter mass is not fixed by the anomalies; the relic-density strip moves with the mediator mass, so a null result from a more sensitive direct-detection experiment would push the mediator mass upward rather than close the scenario.
Original abstract
In the light of the recent result of the Muon g-2 experiment and the update on the test of lepton flavour universality $R_K$ published by the LHCb collaboration, we systematically build and discuss a set of models with minimal field content that can simultaneously give: (i) a thermal Dark Matter candidate; (ii) large loop contributions to $b\to s\ell\ell$ processes able to address $R_K$ and the other $B$ anomalies; (iii) a natural solution to the muon $g-2$ discrepancy through chirally-enhanced contributions.
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.
The abstract, sentence by sentence
In the light of the recent result of the Muon g-2 experiment and the update on the test of lepton flavour universality $R_K$ published by the LHCb collaboration, we systematically build and discuss a set of models with minimal field content that can simultaneously give: (i) a thermal Dark Matter candidate; (ii) large loop contributions to $b\to s\ell\ell$ processes able to address $R_K$ and the other $B$ anomalies; (iii) a natural solution to the muon $g-2$ discrepancy through chirally-enhanced contributions.
background contribution method result interpretation main claim
| # | sentence | role | the authors' own work | states the main conclusion | strength |
|---|---|---|---|---|---|
| s0 | In the light of the recent result of the Muon g-2 experiment and the update on the test of lepton flavour universality $R_K$ published by the LHCb collaboration, we systematically build and discuss a set of models with minimal field content that can simultaneously give: (i) a thermal Dark Matter candidate; (ii) large loop contributions to $b\to s\ell\ell$ processes able to address $R_K$ and the other $B$ anomalies; (iii) a natural solution to the muon $g-2$ discrepancy through chirally-enhanced contributions. | contribution 1.00 | 0.85 | 0.61 | asserted 0.68 |
What was examined, and what was not
- arXiv listing abstract v2
- full text
- figures and tables
- references and citing sentences
- relations to other papers
- P abstract
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- T body sentences
- C citations
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Figures
Figures reproduced from arXiv:2104.03228 by the authors.
References
How later papers used it
56 later papers cite it
1 later paper by other authors is listed below: 1 used its data or values.
Uses its data or values 1 of 3 papers with this label
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Focused on two benchmark points presented in this paper that can account for the muon g-2 and R_K(*) anomalies and the dark matter relic density while being compatible with direct search bounds.
Perturbative unitarity constraints on generic Yukawa interactions (2021) · 0.94 · paraphrased: the licence does not allow quoting
How the literature uses it
54 arXiv papers cite this in 66 sentences
Papers whose main result relates to this one's
States the same result 1 paper
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Motivated by the result of the Muon g-2 experiment and the long-standing anomalies in semileptonic $B$ meson decays, we systematically build a class of minimal models that can address both experimental results thanks to the contributions of a set of new fields that include a thermal Dark Matter candidate.
Papers citing it · 32 sentences without a confident label
Uses its data or values 3 papers
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For what concerns the $b→sμ^+ μ^-$ observable, we now have no longer the $ΔC_9^μ=-ΔC_10^μ$ pattern, so that we take the 2D fit result from [ref] [equation] and the $ΔC_9^μ$ and $ΔC_10^μ$ expressions from [ref] .
Perturbative unitarity constraints on generic Yukawa interactions · The inclusion of right-handed couplings · 0.93
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The Fermilab-based Muon g-2 experiment has just reported a new result [ref] which, if combined with the BNL result reads $4.2σ$ deviation from the SM value[Recent measurement at the Fermilab has drawn some interests to our community [ref] .].
Magnetic Moments of Leptons, Charged Lepton Flavor Violations and Dark Matter Phenomenology of a Minimal Radiative Dirac Neutrino Mass Model · Anomalous magnetic moment and different LFV decays · 0.94
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Combining with the previous results by the Brookhaven National Lab (BNL) experiment, we have $4.2 σ$ deviation from the SM [ref] [equation] This finding suggests the new physics around 1 TeV and have generated flurry of activity [ref] .
Probing Relatively Heavier Right-Handed Selectron at the CEPC, $\rm\bf {FCC_{ee}}$ and ILC · Introduction · 0.88
Compares with it 3 papers
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It is to be mentioned that our results agree (with the exception of what is mentioned in footnote [ref]) with those presented in the past literature [ref] and in particular Refs. [ref] focussed on the analysis of the cancellation present in the $1$-loop CE contribution.
The Low-Scale Seesaw Solution to the $M_W$ and $(g-2)_\mu$ Anomalies · Muon magnetic dipole moment · 0.87
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It is evident that none of these completions is among the ones explored in Refs. [ref] and as such constitute novel extensions of the SM which can in principle contribute to $a_μ$.
A bridge to new physics: proposing new -- and reviving old -- explanations of $a_\mu$ · Three-field extensions · 0.81
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We close this section by noting that a comparison between our scenario and previous work [ref] is not a straightforward task.
Leptoquark manoeuvres in the dark: a simultaneous solution of the dark matter problem and the $R_{D^{(*)}}$ anomalies · Benchmark scenarios · 0.91
Cites it as background 26 papers
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The 3-field extensions with chirally enhanced contributions considered in Refs. [ref] generated the dipole operators through the box diagram, shown in Fig. [ref].
A bridge to new physics: proposing new -- and reviving old -- explanations of $a_\mu$ · Introduction · 0.84
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Among them there are models introducing DM candidates interacting with the SM leptons via leptophilic scalar [ref] , via generic scalar mediator [ref] and through vector mediator [ref] , emphasizing on the MAMM.
Light vector dark matter with scalar mediator and muon g-2 anomaly · Introduction · 0.95
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Many investigations have proposed models with direct modifications that enhance the muon magnetic moment (see e.g. [ref] ).
Resolving the muon $g-2$ tension through $Z'$-induced modifications to $\sigma_{\mathrm{had}}$ · Introduction · 0.94
What it cites · 63 sentences without a confident label
Builds on 2 papers
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This model is a generalisation of the model that in Ref. [ref] we called $ℱ_IA;0$ with Majorana DM $Ψ=(1,1,0)$ (previously studied also in Ref. [ref] ), to which we add a doublet fermion, $Ψ^'=(1,2,-1/2)=(Ψ^' 0,Ψ^' -)$.
Systematic approach to $B$-physics anomalies and $t$-channel dark matter · $ℱ_Ib$: Singlet-doublet fermionic DM · 0.98
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This model is a generalisation of the model that in Ref. [ref] we called $ℱ_IA;0$ with Majorana DM $Ψ=(1,1,0)$ (previously studied also in Ref. [ref] ), to which we add a doublet fermion, $Ψ^'=(1,2,-1/2)=(Ψ^' 0,Ψ^' -)$.
B anomalies and dark matter: a complex connection · $ℱ_Ib$: Singlet-doublet fermionic DM · 0.98
Uses the method or tool of 1 paper
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In an analogous way as what done, e.g., in Ref. [ref] , we will trade in our numerical study the pair $(λ_HL,λ_HR)$ with the pair $(λ,θ)$, defined as: [equation] Furthermore we will assume all the parameters to be real.
Singlet-Doublet Model: Dark matter searches and LHC constraints · $ℱ_Ib$: Singlet-doublet fermionic DM · 0.95
Uses data or values from 4 papers
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Throughout our analyses we set the value of the product of the quark couplings $Γ^Q*_sΓ^Q_b = 0.15$, in accordance with the constraints imposed by $B_s-B̅_s$ oscillations as found in Ref. [ref] .
Systematic approach to $B$-physics anomalies and $t$-channel dark matter · $ℱ_Ib$: Singlet-doublet fermionic DM · 0.94
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The blue-hatched regions are excluded by constraints from XENON1T [ref] on DM SI interactions, while the gray regions corresponds to an invisible branching fraction of the Higgs above $11 %$ [ref] , or an invisible width of the $Z$ boson above $2.3$ [ref] .
The Higgs-portal for Dark Matter:effective field theories versus concrete realizations · $ℱ_Ib$: Singlet-doublet fermionic DM · 0.86
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The blue-hatched regions are excluded by constraints from XENON1T [ref] on DM SI interactions, while the gray regions corresponds to an invisible branching fraction of the Higgs above $11 %$ [ref] , or an invisible width of the $Z$ boson above $2.3$ [ref] .
Invisible Z-Boson Decays at e+e- Colliders · $ℱ_Ib$: Singlet-doublet fermionic DM · 0.86
Cites as support 12 papers
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Thus, a natural explanation of the muon $g-2$ anomaly requires a chiral enhancement, i.e. a chirality flip occurring inside the loop through a coupling to the SM Higgs field $≫y_μ$, see e.g. [ref] .
Generic Loop Effects of New Scalars and Fermions in $b\to s\ell^+\ell^-$, $(g-2)_\mu$ and a Vector-like $4^{\rm th}$ Generation · Setup · 0.97
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Thus, a natural explanation of the muon $g-2$ anomaly requires a chiral enhancement, i.e. a chirality flip occurring inside the loop through a coupling to the SM Higgs field $≫y_μ$, see e.g. [ref] .
Expectations for the muon g-2 in simplified models with dark matter · Setup · 0.97
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Thus, a natural explanation of the muon $g-2$ anomaly requires a chiral enhancement, i.e. a chirality flip occurring inside the loop through a coupling to the SM Higgs field $≫y_μ$, see e.g. [ref] .
Minimal Models for Dark Matter and the Muon g-2 Anomaly · Setup · 0.97
Cites as background 26 papers
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Subdominant contributions can be found e.g. in Ref. [ref] .
Generic Loop Effects of New Scalars and Fermions in $b\to s\ell^+\ell^-$, $(g-2)_\mu$ and a Vector-like $4^{\rm th}$ Generation · $ℱ_Ib$: Singlet-doublet fermionic DM · 0.81
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Subdominant contributions can be found e.g. in Ref. [ref] .
Minimal Models for Dark Matter and the Muon g-2 Anomaly · $ℱ_Ib$: Singlet-doublet fermionic DM · 0.81
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Again, the details of the DM phenomenology have been fully illustrated in Ref. [ref] and, hence, we will not discuss them in depth here.
Systematic approach to $B$-physics anomalies and $t$-channel dark matter · $ℱ_IIb$: Real scalar DM · 0.94
Discussion
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