Electroweak Phase Transition in 2HDM under Higgs, Z-pole, and W precision measurements

Huayang Song; Mengchao Zhang; Wei Su

REVIEW

Electroweak Phase Transition in 2HDM under Higgs, Z-pole, and W precision measurements

Huayang Song, Wei Su, Mengchao Zhang

High Energy Physics - Phenomenology · Submitted 11 Apr 2022 · 85 references

Pith's verdict: A competent, timely extension of the authors' own 2HDM phase-transition scan to include the CDF-II W mass; the physics story is sound, but the headline green region rests on two 95% cuts that should have been one joint fit.

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CitationHuayang Song, Mengchao Zhang, Wei Su. "Electroweak Phase Transition in 2HDM under Higgs, Z-pole, and W precision measurements." arXiv:2204.05085 (2022). https://pith.science/paper/OSLEM3FP

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The pitch is straightforward: take the 2HDM strong-first-order scan the same group published in 2021, add the CDF-II W mass as a constraint, and project onto future lepton-collider Higgs and Z-pole precision. The qualitative link is real and worth stating clearly — heavy-Higgs mass splitting controls the phase transition strength, the oblique parameters, and m_W, so the three are not independent knobs. The conclusion that a future lepton collider consistent with the SM would kill the CDF-II explanation while leaving SFOEWPT alive is a fair reading of their own figures, and it is the useful part of the paper. The scan is large (a billion points), BSMPT is the right tool, and the one-loop treatment of Higgs precision is not hand-waving. Credit where due: this is a clean, honest piece of phenomenology, and the authors are upfront about their simplifications rather than burying them. Section 2.4 says in plain text that a global fit combining Z-pole and m_W is needed and that they instead impose two separate measurements. That is the load-bearing soft spot, and the stress-test note is right about it: m_W in Eq. 2.12 is an explicit function of the same S,T,U that Table 1 constrains, so conjoining two 95% cuts is not the same as a joint chi-square, and the surviving green points sit exactly at the boundary where the two treatments diverge most. The authors flag it; they just don't quantify it. That is a fixable omission, not a fatal one, but the abstract's flat 'can explain at same time' should be softened to match the 'slight tension' language in Sections 1 and 3.3. Two smaller things. The ξ_c > 0.9 threshold in Eq. 2.15 is loosened from the standard >1 with a nod to Refs. [28,29] but no number attached to how much it buys. And Section 2.6 quotes a Type-II bound of m_H± > 580 GeV from b→sγ, while the Type-II allowed region reaches Δm_C = -200 GeV at m_H = 125 GeV; the text never says whether that bound was actually applied in the scan. Worth a referee question. Who should read it: anyone working on 2HDM electroweak baryogenesis or on CDF-II W mass explanations, and people preparing lepton-collider precision projections. It deserves referees — the fixes are within reach and the result is useful if the joint fit confirms it.

Referee report

Significance

The paper connects three normally separate threads (EWPT, electroweak precision obliques, and the CDF-II m_W anomaly) through a single set of 2HDM mass splittings, and it makes a falsifiable statement: if the CDF-II-compatible SFOEWPT region is real, CEPC/ILC/FCC-ee should see correlated deviations in Higgs and Z-pole observables, and if those measurements land on the SM the scenario is excluded. That is a useful, checkable target for the field, and the scan is broad enough to be a genuine global survey rather than a benchmark-point study. The result is, however, a statement about the intersection of several 95% CL windows whose statistical combination is not performed, so the quoted allowed ranges should be read as approximate until the points below are addressed.

Major objections (4)

[§2.4, Eq. (3.2), Fig. 3] The green region of Fig. 3 — the paper's headline result — is defined by conjoining two separate 95% CL cuts: the Table 1 S,T,U ellipsoid and the CDF-II window of Eq. (3.3). But Eq. (2.12) makes m_W^{2HDM} an explicit function of the same S,T,U that Table 1 constrains, so the model prediction links the two data sets even though the measurements are independent. The authors acknowledge this in §2.4 ('a global analysis to recast the S,T,U parameters is needed ... here for simplicity we just take them as two separate measurements') and note in §3.3 that the green points 'mainly locate around the boundary region' — precisely where a joint fit and two hard cuts diverge most. The manuscript should either perform the joint chi-square over (S,T,U) including both the Z-pole and CDF-II inputs, or at minimum quantify how the boundary of the green region moves under a joint treatment and state the sign of the effect. A related check is needed: if the S,T,U ranges of Table 1 (from Ref. [78]) were obtained from a fit that already used a measured m_W as input, then imposing the CDF-II m_W again in Eq. (3.2) partially double-counts the same observable. Please state explicitly which m_W value, if any, entered the Table 1 fit and how the double-counting is avoided.
[§2.7, Eq. (2.15)] The SFOEWPT criterion is loosened from the standard xi_c > 1 to xi_c > 0.9, justified by 'the uncertainty in xi_c calculation [28, 29]'. This choice is load-bearing: it directly determines which scan points enter the grey region of Fig. 3 and therefore which points can subsequently turn green. The manuscript should show the impact quantitatively — for example, the fraction of the grey and green samples that survive with xi_c > 1, and whether the quoted ranges Delta m_{A/C} in (-400, 400) GeV (Type-I) and (-200, 300) GeV (Type-II) shrink materially. If the allowed ranges are stable under the stricter cut, saying so strengthens the result considerably; if they are not, the abstract and Conclusion item 2 should quote the ranges obtained with the standard criterion.
[§2.6 and §3.1] §2.6 states that b -> s gamma disfavors m_H± < 580 GeV in Type-II 2HDM, but §3.1 lists 'B-physics' among the constraints applied without specifying which observables and which mass window, and the scan range of Eq. (3.1) allows m_H± down to 10 GeV. Since the Type-II allowed region quoted in the abstract extends to Delta m_C = -200 GeV with m_H as low as 125 GeV, whether the b -> s gamma cut is actually imposed changes the Type-II result. Please state explicitly which flavor observables are applied, with what numerical treatment (hard cut versus chi-square), and whether the 'can be alleviated with contributions from other sectors' caveat of §2.6 means the constraint was switched off in the scan. If it was switched off, the Type-II ranges should be labeled as flavor-independent upper bounds on the allowed parameter space.
[§3.3, Fig. 3, Table 1] The claim that future lepton colliders 'can exclude the region for m_W at CDF-II' rests on the red region being disjoint from the green one, which in turn depends on the assumed CEPC uncertainties in Table 1 and on the assumption that the future central values equal the SM predictions. The manuscript should quantify the robustness of this statement: how far must the CEPC central values move, or how much must the S,T,U uncertainties in Table 1 be relaxed, before the red and green regions overlap? It would also help to explain physically why the red points collapse onto Delta m_A = 0 or Delta m_C = Delta m_A, and to state whether this is simply the m_H± ~ m_H or m_H± ~ m_A requirement already noted in §2.4 or an independent effect of the one-loop Higgs-coupling fit.

Minor objections (8)

[Abstract and §3.2/Conclusion] The abstract states that 'O(100) GeV new scalars in 2HDMs are favored by SFOEWPT', but the quoted allowed regions extend to m_H ~ 900-1000 GeV. The phrasing should be softened to reflect the actual range, or the range should be tightened.
[§3.2 versus Conclusion item 2] The Type-I upper bound on m_H is quoted as 1000 GeV in §3.2 and as 950 GeV in Conclusion item 2. Please reconcile the two numbers.
[Eq. (3.2)] The denominator is written as a sum over sigma_mW^2 without defining the sum; presumably this is the combined experimental uncertainty. Please write it as a single combined variance and state its numerical value.
[Figs. 1 and 2] Both figures are drawn in the alignment limit cos(beta-alpha) = 0, while the scan of Eq. (3.1) allows |cos(beta-alpha)| < 0.5. Please state how sensitive the S,T,U and Delta m_W maps are to cos(beta-alpha) away from alignment, or note explicitly that the figures are illustrative.
[§3.1] The text says the Higgs precision study 'will deep into one-loop level' but does not describe the one-loop calculation or cite the specific expressions used. Please point to the source of the one-loop Higgs-coupling predictions (presumably Refs. [44, 79]) so the reader can reproduce the treatment.
[§3.1] Given roughly 10^9 scan points in six dimensions and about 10^6 surviving, please comment on whether the scan density is sufficient to resolve the boundaries quoted in the abstract, particularly the tan beta = 50 edge for Type-I and the Delta m_{A/C} extrema.
[Throughout] There are numerous typographical errors that should be corrected: 'letpon' in the abstract, 'diﬀernt' in §2.1, 'V acuum stability' in §2.2, 'can not be too heavy than EW scale' in §1, 'a certain mount of splitting' in §3.2, 'is is mainly because' in §3.3, 'than a clear deviation' in §1 (should be 'then'), and 'proprieties' in §3.3.
[Introduction] Ref. [27] (Su, Williams, Zhang) already studied SFOEWPT in the 2HDM against future Z and Higgs factory measurements, and the present work shares two authors with it. The Introduction should state explicitly what is new here relative to that reference — presumably the CDF-II m_W input and the joint SFOEWPT/m_W analysis — so the incremental contribution is clear.

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The paper

The paper claims

Under current data, both Type-I and Type-II two-Higgs-doublet models can simultaneously produce a strong first-order electroweak phase transition, satisfy Higgs and Z-pole precision measurements, and account for the CDF-II W boson mass, all

The reading

The paper asks whether the same new particles can do three jobs at once: make the early-universe electroweak transition strongly first order (the prerequisite for electroweak baryogenesis), stay consistent with the extremely precise Z-pole and Higgs measurements, and produce the heavier W boson reported by the CDF collaboration in 2022. The authors work in the two-Higgs-doublet models (2HDM), where a second Higgs doublet adds a neutral scalar $H$, a pseudoscalar $A$ and a charged scalar $H^+$, all light enough to be present during the transition. Their claim is that in both the Type-I and Type-II versions of the model there is a surviving region of parameter space that satisfies all of these at once, and that the same quantities, the mass splittings $|Delta m_A = m_A - m_H$ and $|Delta m_C = m_{H^+} - m_H$, control the phase transition, the oblique parameters $S,T,U$ and the W mass. If that is right, the W mass anomaly is not an isolated curiosity but a hint of new scalars near the electroweak scale, exactly the kind of spectrum baryogenesis needs. The paper then turns the argument around: because future lepton colliders will measure $S,T,U$ and the Higgs couplings far more precisely, they can either confirm this picture through a visible deviation from the Standard Model or shut it down.

What carries the argument

The load-bearing object is the pair of mass splittings $Delta m_A = m_A - m_H$ and $Delta m_C = m_{H^+} - m_H$. These enter the oblique parameters $S$, $T$ and $U$ through one-loop gauge-boson self-energies, and $T$ carries by far the tightest current bound, so the Z-pole data effectively pin the splitting pattern; the same $S,T,U$ then feed the 2HDM prediction for $m_W$ through the standard relation $m_W^2(1 - m_W^2/m_Z^2) = pi alpha/(sqrt(2) G_F)(1 + Delta r)$, with a small extra term from the modified triple-Higgs coupling. The phase transition side uses the finite-temperature effective potential, tree level plus Coleman-Weinberg plus counterterms plus thermal corrections, and the criterion that the minimum of the potential jump discontinuously as the temperature falls, with $v_c/T_c > 0.9$ to avoid washing out any generated baryon number. The numerical engine is BSMPT, which tracks the minima and reports the critical temperature and the strength of the transition.

Extended reading notes

Core claim

The central claim is a conjunction, established by a large numerical scan rather than by an analytic identity. The authors scan six 2HDM parameters (with $|cos(beta-alpha)| < 0.5$, $m_{A,H^+}$ and $m_H$ up to 1.5 TeV, $tan beta$ from 0.2 to 50), keep points that pass vacuum stability, unitarity, perturbativity, $B$-physics, LEP and LHC direct searches, and current Higgs and Z-pole precision data, and then require a strong first-order transition using the washout criterion $xi_c = v_c/T_c > 0.9$ computed with the public code BSMPT. On top of that they impose the CDF-II W mass at 95% confidence, which in their treatment corresponds to a shift $Delta m_W in (36.3, 103.4)$ MeV. The result is that a non-empty set of points survives all of it in both model types: roughly $m_H$ between 125 and 950 GeV with $tan beta$ from 1 to 50 and splittings $Delta m_{A/C}$ in $(-400, 400)$ GeV for Type-I, and $m_H$ between 125 and 900 GeV with $tan beta$ from 1 to 12 and splittings in $(-200, 300)$ GeV for Type-II. The authors also show the reverse side: if future CEPC-type measurements come out Standard-Model-like, the surviving region shrinks to slices at $Delta m_A = 0$ or $Delta m_C = Delta m_A$ that do not overlap the W-mass-compatible region, so the CDF-II explanation and a Standard-Model-consistent future cannot both hold in this model.

Load-bearing premise

The Z-pole oblique-parameter constraint and the CDF-II W mass are imposed as two separate 95% confidence cuts, which the authors themselves flag in Section 2.4 as a simplification standing in for a proper joint fit over correlated observables.

Editorial extensions

If this is right

If the paper is right, new scalars with masses of order 100 GeV to about 1 TeV, split by a few hundred GeV, are compatible with every current precision measurement while still driving a strong first-order electroweak transition.
The W mass, the Z-pole oblique parameters and the phase transition strength are then not independent observables: measuring any one of them constrains the other two through the shared splittings $Delta m_A$ and $Delta m_C$.
A future lepton collider measuring $S,T,U$ at the percent level and improving Higgs coupling precision would either observe a deviation from the Standard Model or exclude the region that explains the CDF-II W mass together with a strong first-order transition.
Conversely, if the CDF-II W mass is real and the 2HDM is the correct description, a deviation from Standard-Model predictions must appear at those future machines with high confidence.

Reading between the lines

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

Because $m_W$ and the Z-pole observables are generated by the same radiative corrections, a genuine joint fit over both data sets would very likely shrink the region the paper calls allowed; the surviving slivers may partly reflect the choice to impose two separate 95% confidence cuts rather than one combined likelihood.
The paper's own logic makes the scenario fragile in a useful way: if an independent W mass measurement lands on the Standard-Model value, the W-compatible region empties and only the phase-transition-only region remains, which is a clean and near-term test of the whole construction.
The threshold $v_c/T_c > 0.9$ is a perturbative proxy for whether baryons survive the transition; a lattice or higher-order treatment of the 2HDM transition could move that boundary and therefore shift which mass splittings count as viable.
A first-order transition with these splittings would also source gravitational waves from bubble collisions and sound waves, so a stochastic background search offers a channel that is independent of the collider program described here.

Original abstract

In this work we revisit the existence of a strong first order electroweak phase transition (SFOEWPT) and recent $m_W$ precision measurement in the Type-I and Type-II 2HDMs. The O(100) GeV new scalars in 2HDMs are favored by SFOEWPT, which is necessary for electroweak baryogenesis, and observed $m_W$ shift as well. % We find that under current constraints, both Type-I and Type-II 2HDM can explain the SFOEWPT, Z-pole, Higgs precision measurements and $m_W$ precision measurement of CDF-II at same time, and all these precision measurements are sensitive to heavy Higgs mass splitting in 2HDM. The allowed regions are $\Delta m_{A/C} \in (-400, 400) GeV, \tanb\in(1,50)$, and $\Delta m_{A/C} \in (-200, 300) GeV, \tanb\in(1,12)$ for Type-I and Type-II 2HDM respectively. Furthermore future lepton collider measurements on Higgs and $Z$ boson properties can explore this scenario in more detail or even rule out it.

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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, 4,001 input tokens.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.41 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.98 · compares with prior results 0.16 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

In this work we revisit the existence of a strong first order electroweak phase transition (SFOEWPT) and recent $m_W$ precision measurement in the Type-I and Type-II 2HDMs. The O(100) GeV new scalars in 2HDMs are favored by SFOEWPT, which is necessary for electroweak baryogenesis, and observed $m_W$ shift as well. % We find that under current constraints, both Type-I and Type-II 2HDM can explain the SFOEWPT, Z-pole, Higgs precision measurements and $m_W$ precision measurement of CDF-II at same time, and all these precision measurements are sensitive to heavy Higgs mass splitting in 2HDM. The allowed regions are $\Delta m_{A/C} \in (-400, 400) GeV, \tanb\in(1,50)$, and $\Delta m_{A/C} \in (-200, 300) GeV, \tanb\in(1,12)$ for Type-I and Type-II 2HDM respectively. Furthermore future lepton collider measurements on Higgs and $Z$ boson properties can explore this scenario in more detail or even rule out it.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	In this work we revisit the existence of a strong first order electroweak phase transition (SFOEWPT) and recent $m_W$ precision measurement in the Type-I and Type-II 2HDMs.	contribution 0.99	0.69	0.06	unclear 0.59
s1	The O(100) GeV new scalars in 2HDMs are favored by SFOEWPT, which is necessary for electroweak baryogenesis, and observed $m_W$ shift as well. % We find that under current constraints, both Type-I and Type-II 2HDM can explain the SFOEWPT, Z-pole, Higgs precision measurements and $m_W$ precision measurement of CDF-II at same time, and all these precision measurements are sensitive to heavy Higgs mass splitting in 2HDM.	result 0.87	0.51	0.73	asserted 0.94
s2	The allowed regions are $\Delta m_{A/C} \in (-400, 400) GeV, \tanb\in(1,50)$, and $\Delta m_{A/C} \in (-200, 300) GeV, \tanb\in(1,12)$ for Type-I and Type-II 2HDM respectively.	result 1.00	0.86	0.24	asserted 1.00
s3	Furthermore future lepton collider measurements on Higgs and $Z$ boson properties can explore this scenario in more detail or even rule out it.	future work 0.98	0.16	0.06	hedged possibility 0.93

What kind of paper the classifier reports this is: theoretical result 0.88 · evidence from analysis of existing data 0.65.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

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

levels run

P abstract

not run

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

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

Figures

**Figure 1.** Current oblique constraints S, T, U in the plane of ∆mA − ∆mC with mH = 700 GeV, tan β = 3 in the alignment limit cos(β − α) = 0. The colors are for corresponding parameter value. – 5 –

**Figure 2.** , it is clear that the uplifted mW is consistent with SFOEWPT requirement. 3.3 SFOEWPT under Higgs, Z and W precision measurements As discussed above, SFOEWPT, Higgs precision measurements at one-loop level, and Z-pole physics (oblique parameter S, T, U) are all connected by heavy Higgs mass splitting. In more detail,

**Figure 3.** The allowed parameter space in the plane of mH − tan β (left), ∆mA − ∆mC (right). The grey points survive all theoretical constraints, current experimental constraints, and the conditions of SFOEWPT. The top and bottom panels are for Type-I and Type-II respectively. The green ones are able to provide a mW by CDF-II, while the red ones are allowed by future Higgs and Z-pole precision measurements from CEPC. The red and green points do not cover each other. To incorporate in the mW at CDF-II, here in the 2HDM based on Eq. (2.12), we take the mW data at 95% Confidence Level (C.L.) with…

Figures reproduced from arXiv:2204.05085 by the authors.

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Forward citations

Cited by 15 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.
Combined explanation of $W$-mass, muon $g-2$, $R_{K^{(*)}}$ and $R_{D^{(*)}}$ anomalies in a singlet-triplet scalar leptoquark model
hep-ph 2022-04 conditional novelty 5.0 of 10

A singlet-triplet scalar leptoquark model with Higgs-portal mixing can simultaneously fit the W mass, muon g-2, R_K(*), and R_D(*) anomalies for leptoquark masses between about 1.5 and 8 TeV.
$W$ 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.

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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...
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.
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.
Implications of the new CDF-II $W$-boson mass on two-Higgs-doublet models
hep-ph 2022-04 conditional novelty 4.0 of 10

The two-Higgs-doublet model can reproduce the CDF-II W mass through oblique corrections from scalar mass splittings, favoring a scenario where the observed 125 GeV Higgs is the lighter CP-even state.
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

63 arXiv papers cite this in 70 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 · 32 sentences without a confident label

Cites it as background 37 papers

Extensive studies have been carried out in the literature to explain the CDF-2 $W$-boson mass anomaly with low-dimensional scalar multiplets, which include a scalar singlet [ref] , a second Higgs doublet [ref] , and a scalar triplet [ref] .

$W$-boson Mass Anomaly from High-Dimensional Scalar Multiplets · Introduction · 0.90
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 · 51 sentences without a confident label

Uses the method or tool of 1 paper

This method has been numerically implemented in public package $$ [ref] .

BSMPT - Beyond the Standard Model Phase Transitions -A Tool for the Electroweak Phase Transition in Extended Higgs Sectors · Phase transition in the 2HDM · 1.00

Uses data or values from 4 papers

Here $m_W^SM=80.357 GeV ±4_inputs ±$ $4_theory MeV$ [ref] , $S, T, U$ are oblique parameters in the 2HDM [ref] , and $δρ^2HDM =|λ_hhh^2HDM|^2/16 π^2 m_h^2$ are higher order 2HDM effects from enhanced Higgs boson self-interactions.

Type-II 2HDM under the Precision Measurements at the $Z$-pole and a Higgs Factory · $m_W$ in the 2HDM · 1.00
We adopt the Higgs measurements results presented in Table 3 in Ref. [ref] .

Type-I 2HDM under the Higgs and Electroweak Precision Measurements · Z-pole and Higgs precision measurements · 1.00
The search for pair-produced charged Higgs bosons at the Large Electron-Positron Collider (LEP) imposes a lower bound of 80 on the mass of the charged Higgs boson [ref] , and LEP searches for $AH$ production constrain the sum of the masses $m_H + m_A > 209$ [ref] .

Search for Charged Higgs bosons: Combined Results Using LEP Data · Direct searches at LEP and LHC · 0.94

Cites as support 3 papers

Furthermore, these light extra scalar can induce a positive $m_W$ shift [ref] and modify the predictions on the Z-pole observables like the oblique parameters $S$, $T$ and $U$ via one-loop contributions to the $W$ and $Z$ self-energies.

Delta r in the Two-Higgs-Doublet Model at full one loop level -- and beyond · Introduction · 0.99
Therefore the EW phase transition can be first order and strong enough for the baryogenesis [ref] .

Strong first order electroweak phase transition in 2HDM confronting future Z & Higgs factories · Introduction · 0.98
Extending the Higgs sector by a singlet scalar seems to be the simplest choice, but it is difficult for such model to explain the observed $m_W$ under current limits [ref] .

Delta r and the W-boson mass in the Singlet Extension of the Standard Model · Introduction · 0.98

Cites as background 24 papers

For the Higgs precision measurements, the works [ref] have discussed them for the case of 2HDM systematically.

Type-I 2HDM under the Higgs and Electroweak Precision Measurements · SFOEWPT under Higgs, Z and W precision measurements · 0.88
For the Higgs precision measurements, the works [ref] have discussed them for the case of 2HDM systematically.

Learning from Higgs Physics at Future Higgs Factories · SFOEWPT under Higgs, Z and W precision measurements · 0.88
For the Higgs precision measurements, the works [ref] have discussed them for the case of 2HDM systematically.

Type-II 2HDM under the Precision Measurements at the $Z$-pole and a Higgs Factory · SFOEWPT under Higgs, Z and W precision measurements · 0.88

Discussion

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