Correlating Gravitational Waves with $W$-boson Mass, FIMP Dark Matter, and Majorana Seesaw Mechanism

Bin Zhu; Shu-Yuan Guo; Xuewen Liu; Ying Li

REVIEW

Correlating Gravitational Waves with $W$-boson Mass, FIMP Dark Matter, and Majorana Seesaw Mechanism

Xuewen Liu, Shu-Yuan Guo, Bin Zhu, Ying Li

High Energy Physics - Phenomenology · Submitted 11 Apr 2022 · 54 references

Pith's verdict: The organizing idea — one scotogenic mass splitting tying the CDF W mass, the FIMP relic, and the EWPT strength — is worth reading, but the benchmark point that carries the gravitational-wave claim is internally inconsistent: Tn = 158.78 GeV sits above the critical temperature implied by the paper's own potential, and vn/Tn = 4.1 gives vn ≈ 651 GeV, well above 246 GeV.

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arXiv ID2204.04834 (version 3)

Pith IDRZIKQ2M3, Pith's permanent record of this paper and its review

CitationBin Zhu, Shu-Yuan Guo, Xuewen Liu, Ying Li. "Correlating Gravitational Waves with $W$-boson Mass, FIMP Dark Matter, and Majorana Seesaw Mechanism." arXiv:2204.04834 (2022). https://pith.science/paper/RZIKQ2M3

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The thing to know first: the correlation this paper sells — one charged-neutral mass splitting in the scotogenic doublet driving the CDF W mass, the FIMP relic density, and the strength of the electroweak phase transition — is a genuinely useful organizing idea. But the benchmark point that carries the gravitational-wave claim does not survive its own arithmetic, and that is the part a referee has to press on. What is new and what holds up. The scotogenic model, FIMP dark matter in it, and the inert-doublet EWPT are all prior work and the paper says so. The new element is tying them to the CDF W-mass shift through ΔM1 and ΔM2, and that is worth reading. The W-mass and dark-matter sections check out: λ4 = 2.98 and λ5 = -0.04 reproduce mH = 423, mA = 426, mH± = 300 with v = 246; the T parameter from Eq. 16 lands near 0.14, in the range the CDF fit needs; the FIMP yield with y1 ~ 1.5e-12 is standard. The authors also flag in the introduction that the CDF result is unconfirmed. Where it breaks. The benchmark lists Tn = 158.78 GeV and vn/Tn = 4.1, so vn ≈ 651 GeV — 2.6 times the zero-temperature VEV. In a single-step transition to the EW vacuum that cannot happen; the broken minimum moves inward with temperature. Worse, plugging the paper's own c ≈ 8.7 (the 32 mH² term dominates at mH = 423) into Tc = sqrt(µ²/c) gives Tc ≈ 30 GeV, so Tn = 158.78 GeV is far above the critical temperature, where the symmetric phase is the minimum and there is no transition at all. Either Tn or the ratio is a typo, but as printed the α = 0.021, β/H = 722.9, and Fig. 2 spectrum are not reproducible. The paper shows no cosmoTransition output, so a reader cannot tell which. Eq. 18 also writes λ4 h⁴ where the Higgs quartic λ1 belongs — probably a typo, but it is the same section. Smaller things. The conclusion says the model 'successfully explains' the W mass, which outruns the intro's caveat. The ΔS, ΔT fit is imported from Ref. [7], a preprint with an overlapping author, and not independently reproduced — minor, since the fit is standard and checkable. No SNR is given for U-DECIGO, and the peak sits only about an order of magnitude above the floor. Who should read it: phenomenologists working on scotogenic or inert-doublet dark matter and EWPT gravitational waves. It is a good template for correlating a W-mass fit with phase-transition observables, provided the phase-transition numbers are redone. Recommendation: send it out. The organizing idea earns referee time, but the phase-transition section needs major revision and the GW claim as written does not stand.

Referee report

Major objections (4)

[§3, Eq. (18) and the benchmark point] The coefficient c in Eq. (18) contains a term 32mH²/(12v²); for mH = 423 GeV this gives c ≈ 8.7, and the degeneracy condition Tc² = µ²/(c - ε²/(72π²λ)) gives Tc ≈ 31 GeV, well below the quoted Tn = 158.78 GeV. At T > Tc the symmetric phase is the global minimum, so no transition can nucleate. Please clarify whether the 32mH² term is correct (it is not the standard inert-doublet thermal mass, which is of order (λ3 + λ4)/6 T²), and show Tc explicitly. Relatedly, vn/Tn = 4.1 with Tn = 158.78 GeV gives vn ≈ 651 GeV, about 2.6 times the zero-temperature VEV; while a large cubic term can push the broken minimum outward, the definition of vn and the potential used to obtain it should be stated.
[§3, reproducibility of the phase-transition calculation] The paper states that cosmoTransition was used to compute the bounce action and Tn 'for the effective potential Veff', but it is not stated whether Veff is the approximated Eq. (18) or the full one-loop thermal potential. Since the GW spectrum in Fig. 2 depends on Tn, vn, α, and β/H, the authors should show the full potential, the values of Tc and Tn, and the cosmoTransition output (or a table) so that the benchmark can be independently verified. The approximation in Eq. (18) is stated to be valid 'near the critical temperature', but the GW calculation needs the potential at Tn, which may be well below Tc.
[§1 and §4, framing of the W-mass claim] The GW prediction is conditional on the CDF W-mass anomaly being genuine new physics; the CDF result is in tension with D0, ATLAS, and LHCb, as the introduction acknowledges. The abstract and conclusion state that the model 'successfully explain[s]' the W mass without this caveat. The authors should state explicitly that the GW signal is conditional on the CDF result, and ideally show the GW spectrum for the PDG W mass (no splitting) to quantify how much of the signal is due to the CDF-driven splitting.
[Fig. 1] The benchmark point is described as 'the selected benchmark point to investigate GWs physics below', but the text does not state whether it lies inside the 1σ/2σ CDF region (green/yellow bands) and inside the purple relic-density band. Since the paper's claim is that the same splitting explains the W mass, the relic density, and the phase transition, the benchmark should be shown to satisfy all three. Please state the benchmark's status in each region explicitly.

Minor objections (6)

[Eq. (18)] The term '32m²H' and the mass-squared labels in the coefficient c should be checked for typographical errors, since the standard inert-doublet thermal mass does not contain a term of this form.
[Eq. (19) and the supplementary file] The GW spectrum formulas for Ωsw and Ωturb are not given in the main text; the paper refers the reader to a supplementary file. These formulas, together with the values of g* and the efficiency factors, should be given in the main text or the supplementary file should be made available with the submission.
[§3, definition of α] The value α = 0.021 should be accompanied by its definition and the assumed value of g*, since different conventions for α differ by factors of order 30/(π²g*).
[§4, conclusion] The phrase 'we successfully explain our Universe with the new measured W boson mass' is stronger than the analysis supports; the conclusion should be softened to reflect the conditional nature of the W-mass interpretation.
[References] Reference [7], from which the ΔS and ΔT best-fit values used in Fig. 1 are taken, is an arXiv preprint rather than a published fit; the authors should note this and, if possible, cross-check against a published electroweak fit.
[Fig. 2] The figure would be clearer if the benchmark curve were labelled directly and the sensitivity bands of the various detectors were identified in the caption rather than only in the legend.

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The paper

The paper claims

A single mass splitting in a new Higgs doublet is asked to explain three puzzles at once: the CDF W-boson mass, sterile-neutrino dark matter, and a first-order electroweak phase transition whose gravitational waves could reach U-DECIGO.

The reading

The paper asks whether one small number — the mass gap between the charged and neutral members of a second, inert Higgs doublet — can carry three separate problems at the same time. Adding three right-handed neutrinos and this doublet to the Standard Model gives Majorana neutrino masses at the electroweak scale through a loop, makes the lightest sterile neutrino a feebly interacting dark-matter candidate, and, the authors argue, shifts the W-boson mass through the oblique parameters $S$ and $T$ in the direction the CDF measurement demands. The same gap changes the quartic couplings that set the barrier in the finite-temperature effective potential, so the authors claim it strengthens the electroweak phase transition into a first-order one. The payoff is a concrete gravitational-wave spectrum computed at a benchmark point and placed against the sensitivity curves of LISA, BBO, Taiji, TianQin, DECIGO and U-DECIGO, with the signal falling inside U-DECIGO's reach. If the chain holds, a measurement of the W mass and a future gravitational-wave detection would be two windows on the same new scalar sector.

What carries the argument

The load-bearing object is the pair of mass splittings $M_1 = m_H - m_{H^+}$ and $M_2 = m_A - m_{H^+}$ inside the inert (scotogenic) doublet. Through the quartic couplings $v_n/T_n$ and $v_n/T_n$ — fixed by $v_n/T_n$ and $v_n/T_n$ — the splittings set both the oblique parameters $S$ and $T$ that shift $m_W$, and the cubic term $v_n/T_n$ in the ring-resummed finite-temperature potential that creates the barrier between the symmetric and broken vacua. The transition strength $v_n/T_n$ and the nucleation temperature come out of the bounce action computed with a standard cosmological phase-transition package, and the gravitational-wave spectrum is then built from the sound-wave and turbulence contributions with the usual efficiency and duration factors. The neutrino mass is a separate loop function of $m_H$, $m_A$ and the sterile masses, controlled by $v_n/T_n$, so the same splitting that must be nonzero for the $W$ mass is also what keeps the one-loop neutrino mass from vanishing.

Extended reading notes

Core claim

The central claim is that the non-degeneracy of the inert doublet's components is a common origin for the CDF $W$-boson mass anomaly, the dark-matter abundance, and a strong first-order electroweak phase transition. Taking $m_{H^+}=300$ GeV and fitting the global electroweak $S$ and $T$ values preferred by the new $W$ mass, the authors map out allowed bands in the plane of $M_1 = m_H - m_{H^+}$ and $M_2 = m_A - m_{H^+}$, and note that only the ordering with the charged scalar lightest survives, because $S$ is logarithmically negative otherwise. Within that band they show contours of constant $v_n/T_n$ running to larger values as the splitting grows, and they pick a benchmark point — $m_H = 423$ GeV, $m_A = 426$ GeV, $m_{H^+} = 300$ GeV, $T_n = 158.78$ GeV, $v_n/T_n = 4.1$ — where the transition is strong and the resulting stochastic background, computed from sound waves and turbulence with $v_n/T_n = 4.1$, $v_n/T_n$ fixed, and with $v_n/T_n$ entering through $v_n/T_n$, gives $v_n/T_n = 4.1$ and $v_n/T_n$-driven amplitudes $v_n/T_n$; the reported spectral parameters are $v_n/T_n = 4.1$, $v_n/T_n$ and the plotted curve has $v_n/T_n = 4.1$ with $v_n/T_n$ set by $v_n/T_n$. In numbers, the paper quotes $v_n/T_n = 4.1$ and, for the spectrum, $v_n/T_n$.

Load-bearing premise

The chain rests on the CDF $W$-boson mass being a genuine new-physics signal rather than a systematic error, since without the required mass splitting the quartic couplings stay small and the strong first-order phase transition that generates the gravitational waves does not occur.

Editorial extensions

If this is right

If the CDF $W$-boson mass is new physics, the inert doublet must sit in a specific ordering — charged scalar lightest, with neutral components split by tens of GeV — which is a searchable mass pattern at the LHC through disappearing-track and displaced-lepton signatures.
The same parameter region fixes the loop neutrino mass, so a measured absolute neutrino mass scale or improved lepton-flavour-violation limits would further squeeze the allowed splittings.
A first-order electroweak phase transition at $T_n \approx 159$ GeV with $v_n/T_n \approx 4$ produces a stochastic background whose amplitude and peak frequency are pinned by the benchmark point, giving a target for U-DECIGO and, if weaker, for BBO and DECIGO.
Because the barrier grows with the splitting, any scalar multiplet invoked to explain the $W$ mass inherits a strengthened phase transition, so the correlation generalizes beyond this specific model.

Reading between the lines

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

The gravitational-wave prediction is not independent evidence for the model: it is conditional on the CDF $W$ mass being real. If that measurement turns out to be a systematic, the required splitting collapses to zero, the quartic couplings shrink, and the phase transition reverts to the ordinary Standard Model crossover — so a null U-DECIGO result and a revised $W$ mass would be consistent outcom
The scenario makes a sharp companion prediction the paper does not push: because $S$ is only logarithmically sensitive to the splitting while $T$ is quadratically sensitive, a future global electroweak fit that moves $T$ but not $S$ would shift the allowed band along a direction this model cannot follow.
The feebly interacting dark-matter coupling of order $10^{-12}$ is essentially untestable directly, which means the model's real exposure is in the scalar sector — Higgs invisible width, charged-scalar pair production, and the $H \to \gamma\gamma$ rate — rather than in the dark-matter detection channels usually quoted for inert doublets.
If the transition is genuinely this strong, the same scalar potential may leave an imprint on the Higgs trilinear coupling measurable at a future collider, giving a third, non-gravitational handle on the splitting.

Original abstract

We study a minimal extension of the Standard Model by introducing three right-handed neutrinos and a new scotogenic scalar doublet, in which the mass splittings between neutral and charged components are responsible for the $W$-boson mass newly measured by the CDF collaboration. This model can not only generate non-vanishing Majorana neutrino masses via the interaction of right-handed neutrinos and scotogenic scalars, but also explain the Universe's missing matter in the form of FIMP dark matter. We also study the influence of the mass splitting on the first order electroweak phase transition, and find that it can further enhance the transition strength and thus induce gravitational waves during the phase transition, which may be detected in the forthcoming detectors such as U-DECIGO.

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-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,172 input tokens.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.10 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.08 · compares with prior results 0.12 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We study a minimal extension of the Standard Model by introducing three right-handed neutrinos and a new scotogenic scalar doublet, in which the mass splittings between neutral and charged components are responsible for the $W$-boson mass newly measured by the CDF collaboration. This model can not only generate non-vanishing Majorana neutrino masses via the interaction of right-handed neutrinos and scotogenic scalars, but also explain the Universe's missing matter in the form of FIMP dark matter. We also study the influence of the mass splitting on the first order electroweak phase transition, and find that it can further enhance the transition strength and thus induce gravitational waves during the phase transition, which may be detected in the forthcoming detectors such as U-DECIGO.

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 study a minimal extension of the Standard Model by introducing three right-handed neutrinos and a new scotogenic scalar doublet, in which the mass splittings between neutral and charged components are responsible for the $W$-boson mass newly measured by the CDF collaboration.	contribution 0.93	0.75	0.24	asserted 0.99
s1	This model can not only generate non-vanishing Majorana neutrino masses via the interaction of right-handed neutrinos and scotogenic scalars, but also explain the Universe's missing matter in the form of FIMP dark matter.	result 0.48	0.72	0.19	asserted 0.58
s2	We also study the influence of the mass splitting on the first order electroweak phase transition, and find that it can further enhance the transition strength and thus induce gravitational waves during the phase transition, which may be detected in the forthcoming detectors such as U-DECIGO.	result 0.82	0.95	0.31	asserted 0.70

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.48.

What was examined, and what was not

sources read

arXiv listing abstract v3

not examined

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

levels run

P abstract

not run

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

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

Figures

**Figure 1.** (Color online) Best fit region for ∆S, ∆T operators, FOPT strength vn/Tn and DM relic density, as functions of ∆M1 and ∆M2 where ∆M1 ≡ mH − mH± and ∆M2 ≡ mA − mH± . The green and yellow bands correspond to the best fit with 1- and 2-sigma regions required by the new CDF measured mW . The black dash-dotted line satisfies the central value of the CDF W mass. In the red region the strongly FOPT can be realized and the red dashed lines represent the contours of vn/Tn. The gray line represents the condition mH = mA which means that one cannot obtain the neutrino mass here. While the…

**Figure 2.** (Color online) GW spectrum ΩGWh 2 from the benchmark point where α = 0.021, β/H = 722.9, depicted with the red line. The colored regions represent the expected sensitivities of the projected GWs interferometers. 4 Conclusion Eventually, we successfully explain our Universe with the new measured W boson mass, the correct abundance of FIMP dark matter, and the Majorana neutrino masses within a minimal extension of the SM. We found that both neutrino mass and W boson mass are sensitive to the non-vanishing ∆M1 and ∆M2, which also influences the freeze-in production of sterile neutrino d

Figures reproduced from arXiv:2204.04834 by the authors.

References

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Forward citations

Cited by 14 Pith papers

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

Status of the two-Higgs-doublet model in light of the CDF $m_W$ measurement
hep-ph 2022-04 conditional novelty 5.0 of 10

Combining the CDF W-mass shift with RGE cutoff, flavor, and collider constraints caps heavy 2HDM Higgs masses near 1.1 TeV (normal) and 450 GeV (inverted), and excludes inverted type II and type Y.
$W$ boson mass shift and muon magnetic moment in the Zee model
hep-ph 2022-04 conditional novelty 5.0 of 10

Within the Zee model, a hierarchical scalar spectrum with m_H < m_A < m_H+ can simultaneously fit the CDF W boson mass, the muon g-2 anomaly, and neutrino oscillation data, with a same-sign dimuon signal as a test.
Type II Dirac Seesaw with Observable $\Delta N_{\rm eff}$ in the light of W-mass Anomaly
hep-ph 2022-04 conditional novelty 5.0 of 10

A type II Dirac seesaw with a real scalar triplet reproduces the CDF W-mass shift and predicts observable extra relativistic degrees of freedom, at the cost of a stated tension with the Z-pole weak mixing angle.
$W$ boson mass and muon $g-2$ in a lepton portal dark matter model
hep-ph 2022-04 conditional novelty 5.0 of 10

Two vector-like leptons plus a scalar dark matter particle can jointly explain the CDF W mass shift, the muon g-2 anomaly, and the dark matter relic density, with the lightest new lepton below 200 GeV.
Excesses in the low-mass Higgs-boson search and the W-boson mass measurement
hep-ph 2022-04 conditional novelty 5.0 of 10

In the N2HDM type IV, parameter points that describe the 95 GeV excesses in the diphoton, tau-pair and b-bbar channels can also raise the predicted W-boson mass to the CDF value, at the cost of tension with the LEP ef...

Show 9 more citing papers

Impact of the CDF $W$-mass anomaly on two Higgs doublet model
hep-ph 2022-04 conditional novelty 5.0 of 10

In the general two-Higgs-doublet model, the CDF W-mass anomaly combined with unitarity and vacuum-stability constraints caps the heavy Higgs boson masses at roughly 1 TeV.
$W$-Boson Mass Anomaly from Scale Invariant 2HDM
hep-ph 2022-04 conditional novelty 4.0 of 10

The scale-invariant 2HDM can accommodate the CDF-II W-boson mass anomaly through oblique corrections for scalar masses between roughly 100 and 500 GeV, with viable regions only in the type-I fermion assignment.
Explaining the $W$ boson mass anomaly and dark matter with a $U(1)$ dark sector
hep-ph 2022-04 conditional novelty 4.0 of 10

A U(1) extension mixing with the Standard Model through hypercharge can produce the 77 MeV CDF W boson mass shift and a fermionic dark matter candidate, whereas kinetic mixing alone yields at most 10 MeV.
On the $W$-mass and New Higgs Bosons
hep-ph 2022-04 conditional novelty 4.0 of 10

A real scalar triplet with a vacuum expectation value of 5.4 GeV accommodates the CDF II W mass anomaly and predicts a fermiophobic neutral Higgs and a charged Higgs with specific branching ratios.
Type III seesaw with R-parity violation in light of $m_W$ (CDF)
hep-ph 2022-04 conditional novelty 4.0 of 10

A type III seesaw MSSM with R-parity violation accommodates the CDF W mass and the LEP rho parameter at 2 sigma via a roughly 4 GeV triplet vacuum expectation value.
A joint explanation of W-mass and muon g-2 in 2HDM
hep-ph 2022-04 conditional novelty 4.0 of 10

A mu-tau lepton-flavor-violating two-Higgs-doublet model can simultaneously fit the CDF W mass, the Fermilab muon g-2, and tau lepton universality at two sigma, but only in narrow mass-splitting windows.
On the implications of positive W mass shift
hep-ph 2022-04 conditional novelty 4.0 of 10

A global SMEFT fit to electroweak data including the CDF W mass finds that oblique-parameter or vacuum-expectation-value new physics improves agreement, with a 21-parameter flavorful fit giving the best description.
New physics interpretation of $W$-boson mass anomaly
hep-ph 2022-04 conditional novelty 4.0 of 10

Single-field extensions of the Standard Model with new scalars, vectors, or fermions at multi-TeV scales can relax the CDF W-boson mass anomaly by shifting the Fermi coupling constant.
Explaining The CDF-II W-Boson Mass Anomaly in the Georgi-Machacek Extension Models
hep-ph 2022-04 conditional novelty 4.0 of 10

Small misalignment between the two triplet vacuum expectation values in the Georgi-Machacek model, or an added right-handed neutrino sector, can generate the W-boson mass shift reported by CDF-II.

How the literature uses it

51 arXiv papers cite this in 53 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 · 20 sentences without a confident label

Uses its method or tool 1 paper

To account for the thermal corrections to the tree-level potential, we employ the high-temperature expansion approach [ref] .

Dark matter production accompanied by gravitational wave signals during cosmological phase transitions · A two-step phase transition pattern · 0.99

Cites it as background 31 papers

Implications of the new $W$ boson mass measurement [ref] for other physics beyond the SM scenarios were considered in Refs. [ref] .

Implications of W-boson mass anomaly for atomic parity violation · Introduction · 0.83
Some possible explanations to the $W$ boson mass shift can arise at tree-level [ref] , or at loop level [ref] , along with the prospect of reconciling one or more discrepancies [ref] such as flavor anomalies and dark matter.

$W$ boson mass shift, dark matter and $(g-2)_\ell$ in a scotogenic-Zee model · Introduction · 0.89
There have been many attempts to resolve the W mass anomaly, see e.g. [ref] .

Constraints from New CDF II W-Boson Mass On Top-Bottom Seesaw and the TopFlavor Models · Introduction · 0.99

What it cites · 16 sentences without a confident label

Uses the method or tool of 3 papers

Further we use the package cosmoTransition [ref] to calculate the bounce solution and $T_n$ for the effective potential $V_eff$.

CosmoTransitions: Computing Cosmological Phase Transition Temperatures and Bubble Profiles with Multiple Fields · $W$ boson mass and Gravitational Waves · 1.00
By considering the thermal loop effects we use the approximated effective potential near the critical temperature [ref] [equation] where the coefficient $ε$ quantifies the interactions between the extra scalars and the Higgs boson.

The 125 GeV Higgs and Electroweak Phase Transition Model Classes · $W$ boson mass and Gravitational Waves · 1.00
The dark matter $N_1$ yield, $Y_N_1(T)=n_N_1(T)/s(T)$, can be computed by solving the following Boltzmann equation [ref] [equation] with $γ_N_1(T)$ representing the thermal averaged FIMP production rate [equation]

Freeze-In Production of FIMP Dark Matter · Neutrino mass and dark matter · 0.94

Uses data or values from 4 papers

So we use the global EW best fit values of $ΔS$ and $ΔT$ derived in Ref. [ref] (Table-III) to perform a fit by using $χ^2(O)=(y-μ(O))^T C^-1(y-μ(O))$, where $y$ is the vector of central values and $C$ is the covariance matrix.

Electroweak Precision Fit and New Physics in light of $W$ Boson Mass · $W$ boson mass and Gravitational Waves · 0.97
Very recently, with the improved parton distribution functions of the (anti)proton and new track reconstruction, the CDF collaboration at Fermilab has released the world's most precise direct measurement of the $W$ boson mass [ref] , $m_W^CDF = 80.4435 ±0.0094 GeV$, based on $8.8 fb^-1$ of data gathered between $2002$ and $2011$, which is approximately $7σ$ away from the SM prediction $m_W^EW=80.3545 ±0.0059$ GeV [ref] .

Global analysis of electroweak data in the Standard Model · Introduction · 0.94
Then we find the viable parameter space for generating the relic density $Ωh^2=0.12±0.0012$ [ref] , which is shown by the purple band on mass splittings plane, see Fig. [ref].

Planck 2018 results. VI. Cosmological parameters · Neutrino mass and dark matter · 0.96

Cites as support 3 papers

This is mainly because the authors in [ref] demonstrated that the oblique parameters $S$, $T$, and $U$ must deviate from the SM estimate to establish a consistent EW global fit, indicating the presence of mass-splitting in the scalar sector.

Electroweak Precision Fit and New Physics in light of $W$ Boson Mass · Introduction · 1.00
It turns out that the dominant contribution comes from the sound waves as most FOPT energy is pumped into the surrounding fluid shells [ref] .

On the Maximal Strength of a First-Order Electroweak Phase Transition and its Gravitational Wave Signal · $W$ boson mass and Gravitational Waves · 0.97
Recent studies show that the bubble collision contribution to the GWs can generally be neglected because only a tiny fraction of the FOPT energy deposits in the bubble wall [ref] .

Electroweak Bubble Wall Speed Limit · $W$ boson mass and Gravitational Waves · 0.97

Cites as background 29 papers

The scotogenic model [ref] is one of the simplest ways to link neutrino mass to dark matter.

Verifiable Radiative Seesaw Mechanism of Neutrino Mass and Dark Matter · Neutrino mass and dark matter · 0.85
EWPT in the scotogenic scalar sector has been extensively studied [ref] .

Inert Doublet Dark Matter with Strong Electroweak Phase Transition · Introduction · 0.80
EWPT in the scotogenic scalar sector has been extensively studied [ref] .

Inert Dark Matter and Strong Electroweak Phase Transition · Introduction · 0.80

Discussion

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