Making the small oblique parameters large

Ling-Fong Li; L. Lavoura

REVIEW

Making the small oblique parameters large

L. Lavoura, Ling-Fong Li

High Energy Physics - Phenomenology · Submitted 14 Sep 1993 · 8 references

Pith's verdict: A correct one-loop calculation with a real punchline — the S/T hierarchy is not general — but the unqualified J³ claim outruns the one-loop regime it's derived in.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 13, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

T0 AI review An AI read the paper and answered a fixed list of questions.
T1 Audit Automatic checks that the references and files the paper relies on exist and match.
T2 Compute The paper's code or calculations re-run with the same results.
T3 Formal statement The claims written out in a formal math language a computer can read.
T4 Proof Those claims proved, and the proof checked by computer.

How Pith checks papers →

· 2 major objections · 7 minor · Ask about this paper · The compiled record · Read the full review →

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-ph/9309262 (version 1)

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

CitationLing-Fong Li, L. Lavoura. "Making the small oblique parameters large." arXiv:hep-ph/9309262 (1993). https://pith.science/paper/KKVAHGTV

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

The short version: this is a clean, correct one-loop paper with a useful punchline — the oblique-parameter hierarchy is not general. Lavoura and Li compute S, T, U, V, W, X for one complex scalar multiplet of arbitrary isospin J and hypercharge Y, and show that holding the extreme masses fixed while J grows gives U, V, W, X scaling like J³ and T only like J. The J=1,3,5 figures back it up, and the decoupling check in Eqs. 29–31 is done properly, which a lot of this literature doesn't bother with. What's new is the general-multiplet computation of V, W, X — the definitions are the Montreal group's and are reproduced in Eqs. 1–6, so there's no ambiguity about what's being computed — plus the scaling observation itself. The ξ and ρ functions are written out explicitly, so anyone can reproduce the numbers without guessing at conventions. Soft spots, in order of weight. The abstract's 'increase like J³' is stated without qualification, but the same SU(2) coupling that produces the J³ also makes the one-loop expansion parameter grow like g²J²/16π². For J=5 that's fine; by J around 20 the one-loop term is no longer leading, and the paper never says so. That doesn't touch the J=1,3,5 plots, but it does bound the asymptotic claim, and a referee should ask for one sentence acknowledging it. Second, the claim on p. 6 that a general hypercharge admits only two quartic couplings fails at Y=±1/2, where (ΔH)² is also allowed — and the paper's own example is Y=−1/2, so Eq. 33 is a special case with the third coupling switched off. Minor, since the scaling only needs equal spacing, but worth flagging. Third, the remark that M1, M2 > MZ/4 is 'not excluded by experiment' is asserted, not shown; it reads as a side comment and should be treated as one. The authors are upfront that they know of no theoretical motivation for large multiplets near mZ, which is the right way to frame it. Who should read it: anyone doing electroweak precision work on extended scalar sectors, or fitting oblique parameters and tempted to assume S and T dominate. Worth a serious referee — the calculation is solid and the caveats are fixable in revision.

Referee report

Significance

The result is a clean, explicitly checkable one-loop calculation, and the observation that the standard S–T hierarchy is not generic is a useful caution for global fits. The paper is careful in several respects: the V, W, X definitions are reproduced rather than merely cited, the decoupling theorem is checked explicitly, and the physical explanation of why T scales differently (quadratic rather than logarithmic mass dependence, with a 1/J suppression per mass splitting) is transparent. The degenerate-limit formulas in Eqs. 40–44 are particularly valuable because they do not depend on the equal-spacing ansatz, so the J³ scaling of U, V, W, X is robust for a degenerate multiplet. The claim is falsifiable in the sense that it predicts a definite pattern of oblique parameters for a specified spectrum, and the figures make that pattern concrete for J=1, 3, 5.

Major objections (2)

[Abstract (s1) and the paragraph following Eq. 44] The abstract states without qualification that U and the three new parameters 'increase like J³' as J increases, and the text after Eq. 44 repeats that all oblique parameters except T grow like J(J+1)(2J+1). This is a one-loop statement, but the same SU(2) vertices that produce the J² factor (the √((J+I)(J−I+1)) couplings in Eq. 10) also make the one-loop expansion parameter grow like g²J²/(16π²). For J=5 this is about 0.07 and the figures are safe, but the asymptotic claim is uncontrolled beyond J ~ 4π/g ~ 20, where the one-loop result ceases to be the leading term and higher orders or partial-wave unitarity bounds become relevant. The paper should state this limitation explicitly, either in the abstract or immediately after Eqs. 40–44, so that the J³ statement is not read as holding for arbitrarily large J. This does not affect the J=1, 3, 5 results, but it does bound the scope of the central asymptotic claim.
[p. 6, sentence beginning 'For a general hypercharge of ∆, there are only two quartic couplings'] This statement is not correct for Y=±1/2. When the multiplet hypercharge is −1/2 (the value used in all the figures) or +1/2, the gauge-invariant contraction (ΔH)² is also allowed in addition to the two couplings written, and it can contribute to the mass matrix in a way not captured by Eq. 33. The paper's own numerical examples use Y=−1/2, so Eq. 33 should be presented as a special case in which the (ΔH)² coupling is set to zero, not as the general consequence of having only two quartic couplings. The J³ scaling in Eqs. 40–44 survives this because it holds in the degenerate limit independently of Eq. 33, but the generality claim attached to the spectrum should be corrected.

Minor objections (7)

[p. 2, discussion of the fit in ref. [6]] The quantitative statements that the precision on five oblique parameters is of order ±1 while W is poorly known rest on refs. [4] and [6], both listed as unpublished McGill reports. Since the paper's own results do not depend on these numbers, this is not a blocking issue, but the reader cannot check them and the text should make clear that they are quoted from unpublished work.
[Abstract (s1)] The abstract's statement that all three new parameters increase like J³ is slightly imprecise for X: the Y² term in Eq. 44 grows only like (2J+1), as the text itself notes after Eq. 44. The abstract should either add the qualifier or refer to the leading J(J+1)(2J+1) behavior.
[Eq. 39] The coefficients t_{2n} are described only as 'the functions of J which are found by performing the relevant summations' and are never written explicitly. The argument that the maximum power of I is I^n and the sum over I gives J^{n+1}, divided by J^n, yields linear growth in J is sound, but giving at least the first few t_{2n} would let the reader verify the claim directly.
[Eqs. 35, 36, 39] The expansions in powers of (M₂−M₁)/(M₂+M₁) converge only for |M₂−M₁| < M₂+M₁, i.e., for positive M₁. The paper should state this condition, since the figures keep m₁ fixed and positive but the text does not say the expansion is restricted to that regime.
[p. 6, sentence about M₁ and M₂ being higher than M_Z/4] The assertion that the scenario is 'not excluded by experiment' provided both M₁ and M₂ exceed M_Z/4 is not justified. A brief indication of which experimental constraint is being applied, or a softening of the claim, would be appropriate.
[Figures 2 and 3 captions] The captions give no axis ranges or units, and the curves are identified only by line style. Adding the plotted ranges of m₂ and the values of the fixed parameters (m₁, Y, and the renormalization scale if relevant) would make the figures self-contained.
[Eq. 33 and surrounding text] The paper should emphasize that the J³ scaling of U, V, W, X in Eqs. 40–44 is derived in the degenerate limit and therefore does not rely on the equal-spacing ansatz of Eq. 33. As written, a reader may incorrectly conclude that the headline result depends on the linear-in-I spectrum, when in fact only the S′, U′, and T scalings use it.

How Pith checks papers → · Full audit of this paper →

The paper

The paper claims

For large scalar multiplets, the oblique parameters U and V can outgrow S and T, which are usually assumed to dominate electroweak precision physics.

The reading

Electroweak precision measurements are summarized by a handful of 'oblique parameters' that record how new heavy particles bend the W, Z and photon propagators. The working folklore is that $S$ and $T$ dominate: $T$ because it grows quadratically with the masses of new particles, and $S$ because each chiral fermion doublet contributes a mass-independent piece. Lavoura and Li compute all six parameters, including the three newer ones $V$, $W$ and $X$ that measure the curvature of the vacuum-polarization functions, for a single complex scalar multiplet of arbitrary weak isospin $J$ and hypercharge $Y$, with no vacuum expectation value and no mixing among components. They then hold the heaviest and lightest component masses fixed while $J$ grows, so the spacing between neighbouring masses shrinks like $1/J$. In that limit $U$, $V$, $W$ and $X$ grow like $J^3$, $S$ like $J^2$, and $T$ only like $J$, so for large multiplets whose masses are not far above $m_Z$, $U$ and $V$ can be much larger than the parameters usually assumed to rule.

What carries the argument

The engine is the one-loop vacuum-polarization function $F(M_1,M_2,P)$ for a scalar pair, together with the angular-momentum weights that appear in the couplings: the photon couples with strength proportional to $I+Y$, the $Z$ with $Ic_w^2 - Ys_w^2$, and the $W$ with $e/(c_w s_w)$ times $F(M_I,M_{I-1},P)$ weighted by $(J^2-I^2+J+I)$. Summing these weights over $I=-J$ to $J$ converts powers of $I$ into polynomials in $J$ of one degree higher, which is where the $J^3$ growth comes from: one factor of $J$ from the number of graphs in the loop, and two more from the squared isospin at the two SU(2) vertices. The behaviour of $T$ is controlled separately by the function $theta_+(M_1,M_2)$, whose expansion in powers of $(M_2-M_1)/(M_2+M_1)$ carries a compensating $1/J^n$, leaving only linear growth. The paper also verifies the decoupling theorem: as the common mass $M$ goes to infinity with splittings fixed, all six parameters fall off like $1/M$.

Extended reading notes

Core claim

The paper's claim is a reversal of the usual hierarchy among oblique parameters. For one complex scalar multiplet of weak isospin $J$ and hypercharge $Y$, with the squared masses of its components taken to be equally spaced, $M_I = M + I(M_2-M_1)/J$, and with the extreme masses $M_1$ and $M_2$ held fixed as $J$ increases, the parameter $U$ and the three newer parameters $V$, $W$ and $X$ grow with the cube of $J$, while $T$ grows only linearly and $S$ quadratically. The reason $T$ is the exception is that it depends quadratically rather than logarithmically on mass differences, so each power of the shrinking mass splitting $(M_2-M_1)/J$ costs a factor $1/J$. The paper closes with plots for $J=1,3,5$ showing that, at low $m_2$ with $m_1=150$ GeV, $U'$ and $V$ become the largest of the six, though a partial cancellation between the two pieces of $S$ keeps $S$ from growing as fast as its $J^2$ scaling alone would suggest.

Load-bearing premise

The scaling result rests on assuming that the squared masses of the multiplet's components are exactly equally spaced, $M_I = M + I(M_2-M_1)/J$, as produced by a single quartic coupling to one Higgs doublet with no mixing and no vacuum expectation value; if additional couplings or radiative corrections distorted that spacing, the sums over isospin that generate the $J^3$ growth would not go through as stated, and the paper does not examine how natural or stable that spectrum is at large $J$.

Editorial extensions

If this is right

Fits to precision electroweak data should not assume that $S$ and $T$ are the only parameters that can be large; $V$ and $X$ enter the $Z$-pole and low-energy observables and must be included when new scalars sit near the $Z$ mass.
A large scalar multiplet with masses of order $m_Z$ would show up most strongly through $U$ and $V$, which affect $m_W$ and the $W$ width, rather than through the $S$–$T$ plane alone.
Decoupling survives: when the common multiplet mass is taken to infinity with the splittings held fixed, all six oblique parameters vanish like $1/M$, so the effect is confined to new physics near the electroweak scale.
The growth with $J$ is generic to any scalar sector of large weak isospin, since it follows from the isospin weights at the two gauge vertices rather than from details of the potential.

Reading between the lines

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

The $J^3$ result is really a statement about summing a tower with equally spaced masses; one could ask whether an analogous tower sum applies to higher-spin or fermionic multiplets, where the isospin weights differ.
Because the fits quoted in the paper bound $V$ and $X$ at roughly $\pm 1$, the region where $U$ and $V$ dominate is likely already in tension with data unless cancellations occur; checking whether the partial $S'$–$S''$ cancellation the authors note for small $m_2$ extends to $V$ would sharpen this.
If such multiplets exist, the leading experimental handle would be a shift in the $W$ mass or width rather than a $Z$-pole asymmetry, since $U$ and $W$ are the parameters that enter there.

Original abstract

We compute the oblique parameters, including the three new parameters $ V $, $ W $ and $ X $ introduced recently by the Montreal group, for the case of one scalar multiplet of arbitrary weak isospin $ J $ and weak hypercharge $ Y $. We show that, when the masses of the heaviest and lightest components of the multiplet remain constant, but $ J $ increases, the oblique parameter $ U $ and the three new oblique parameters increase like $ J^3 $, while $ T $ only increases like $ J $. For large multiplets with masses not much higher than $ m_Z $, the oblique parameters $ U $ and $ V $ may become much larger than $ T $ and $ S $.

The compiled record

The paper's own sentences, arranged, kept beside the review and separate from it. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 3,131 input tokens, $0.0001 reported.

What the abstract itself states, as probabilities: claims first 0.05 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.06 · randomized assignment 0.01 · states quantitative result 0.75 · compares with prior results 0.24 · 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.

We compute the oblique parameters, including the three new parameters $ V $, $ W $ and $ X $ introduced recently by the Montreal group, for the case of one scalar multiplet of arbitrary weak isospin $ J $ and weak hypercharge $ Y $. We show that, when the masses of the heaviest and lightest components of the multiplet remain constant, but $ J $ increases, the oblique parameter $ U $ and the three new oblique parameters increase like $ J^3 $, while $ T $ only increases like $ J $. For large multiplets with masses not much higher than $ m_Z $, the oblique parameters $ U $ and $ V $ may become much larger than $ T $ and $ S $.

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 compute the oblique parameters, including the three new parameters $ V $, $ W $ and $ X $ introduced recently by the Montreal group, for the case of one scalar multiplet of arbitrary weak isospin $ J $ and weak hypercharge $ Y $.	contribution 0.98	0.94	0.04	asserted 0.89
s1	We show that, when the masses of the heaviest and lightest components of the multiplet remain constant, but $ J $ increases, the oblique parameter $ U $ and the three new oblique parameters increase like $ J^3 $, while $ T $ only increases like $ J $.	result 1.00	0.94	0.62	asserted 1.00
s2	For large multiplets with masses not much higher than $ m_Z $, the oblique parameters $ U $ and $ V $ may become much larger than $ T $ and $ S $.	result 0.82	0.86	0.59	hedged possibility 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 0.71.

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.** Feynman diagrams relevant for the computation of the va

Figures reproduced from arXiv:hep-ph/9309262 by the authors.

References

Works cited (8)

[1]

M. B. Einhorn, D. R. T. Jones and M. Veltman, Nucl. Phys. B191, 146 (1981)

View on Pith 1981
[2]

M. E. Peskin and T. Takeuchi, Phys. Rev. Lett. 65, 964 (1990); Phys. Rev. D 46, 381 (1992). 8

View on Pith 1990
[3]

D. C. Kennedy and B. W. Lynn, Nucl. Phys. B322, 1 (1989); W. J. Marciano and J. L. Rosner, Phys. Rev. Lett. 65, 2963 (1990); D. C. Kennedy and P. Langacker, Phys. Rev. Lett. 65, 2967 (1990); 66, 395(E); Phys. Rev. D 44, 1591 (1991); G. Altarelli and R. Barbieri, Phys. Lett. B 253, 161 (1991)

View on Pith 1989
[4]

I. Maksymyk, C. P. Burgess and D. London, McGill Report No. Mc Gill-93/13, 1993 (un- published)

View on Pith 1993
[5]

B. Grinstein and M. B. Wise, Phys. Lett. B 265, 326 (1991)

View on Pith 1991
[6]

C. P. Burgess, S. Godfrey, H. K¨ onig, D. London and I. Maksym yk, McGill Report No. McGill-93/24, 1993 (unpublished)

View on Pith 1993
[7]

L.-F. Li, Carnegie-Mellon Report No. CMU-HEP92-18, 1992 (unpu blished)

View on Pith 1992
[8]

T. Appelquist and J. Carrazone, Phys. Rev. D 11, 2856 (1975). FIGURE CAPTIONS Figure 1: Feynman diagrams relevant for the computation of the va cuum polarizations. Figure 2: Plot of S′ (full line), T (dotted line) and U ′ (dashed line) against m2, with m1 = 150 GeV kept ﬁxed. All ﬁgures are for a scalar multiplet with hyperc harge −1/2. Figure 2a is for a...

View on Pith 1975

Forward citations

Cited by 16 Pith papers

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

Precision Electroweak Constraints on Neutrinophilic Scalars
hep-ph 2026-06 unverdicted novelty 7.0 of 10

Electroweak precision data constrain neutrinophilic scalar couplings to neutrinos via charged-current corrections, with the result holding in a UV-complete model for wide parameter ranges.
Electroweak corrections to the SM-like Higgs boson decays and the Higgs trilinear coupling in the real Higgs triplet model
hep-ph 2026-11 conditional novelty 6.0 of 10

One-loop electroweak corrections in the real Higgs triplet model produce sizable deviations in SM-like Higgs decay rates and the trilinear coupling that can distinguish the model from other extended Higgs sectors.
Electroweak Thermal Histories in the Minimal Type-II Seesaw Model with a Renormalization Group-Improved Effective Potential
hep-ph 2026-11 accept novelty 6.0 of 10

In the minimal type-II seesaw model, RG-improved finite-temperature effective potential calculations show only weak, fast first-order phase transitions with gravitational wave signals far below planned detector sensitivities.
Radiative Neutrino Mass in a Nonholomorphic $T'$ Modular Invariant Model
hep-ph 2026-06 unverdicted novelty 6.0 of 10

A nonholomorphic T' modular model realizes the T4-2-i one-loop topology for radiative Majorana neutrino masses, forbids tree-level seesaws via modular assignments, stabilizes DM with residual Z2, and fits oscillation ...
The last Complex WIMPs standing
hep-ph 2022-05 conditional novelty 6.0 of 10

Complex hypercharged WIMP multiplets up to the perturbative unitarity limit are classified and their thermal masses computed, and only the hypercharge-1/2 doublet escapes all planned direct detection experiments, leav...

Show 11 more citing papers

Perturbativity and mass scales of Left-Right Higgs bosons
hep-ph 2016-03 accept novelty 6.0 of 10

The minimal Left-Right model's scalar potential remains perturbative up to a right-handed scale near 3 TeV, and oblique parameters plus the Higgs diphoton rate push the triplet scalars above the reach of a 3 TeV W_R.
Accidental matter at the LHC
hep-ph 2015-04 conditional novelty 6.0 of 10

Requiring new weak-scale matter to preserve the Standard Model's accidental symmetries, stay perturbative to 10^15 GeV, and not spoil Big Bang nucleosynthesis leaves a finite list of long-lived charged or colored stat...
W-boson mass in the triplet seesaw model
hep-ph 2022-04 conditional novelty 5.0 of 10

A type-II seesaw scalar triplet with order-one quartic coupling and a few-hundred-GeV mass can account for the CDF W-mass shift, predicting a doubly-charged scalar in the 100-200 GeV window that LHC data should confir...
Scalar phenomenology in type-II seesaw model
hep-ph 2019-03 conditional novelty 5.0 of 10

The type-II seesaw scalar sector is constrained across its full parameter space by combining electroweak precision, Higgs data, lepton flavor violation, and a recast CMS multilepton search that reaches the previously ...
New Scalar Contributions to $h\to Z\gamma$
hep-ph 2013-01 conditional novelty 5.0 of 10

Recalculating the scalar-loop contribution to h to Z gamma corrects prior formulas and yields the conditional bound 0.76 < R_Zgamma < 2.05 from the observed 1.5 to 2.0 diphoton excess.
125 GeV Higgs Boson and the Type-II Seesaw Model
hep-ph 2013-01 conditional novelty 5.0 of 10

In the type-II seesaw model, a 125 GeV Higgs can coexist with a stable vacuum up to the Planck scale for a wide range of triplet couplings, and any diphoton enhancement implies an upper bound on the seesaw scale.
Vacuum Stability, Perturbativity, EWPD and Higgs-to-diphoton rate in Type II Seesaw Models
hep-ph 2012-09 conditional novelty 5.0 of 10

Joint vacuum-stability, perturbativity and electroweak-precision constraints in the type II seesaw model leave a narrow coupling window in which the Higgs-to-diphoton rate can rise by up to 100% for a 100 GeV doubly c...
Quirks at the Tevatron and Beyond
hep-ph 2011-06 conditional novelty 5.0 of 10

Scalar quirks (squirks) carrying QCD color, weak isospin, and a new infracolor charge can produce the CDF Wjj excess through beta-decay and subsequent annihilation into gluon jets.
The SM extension with color-octet scalars: diphoton enhancement and global fit of LHC Higgs data
hep-ph 2013-03 conditional novelty 4.0 of 10

A fit of the Manohar-Wise color-octet scalar model to 2013 ATLAS and CMS Higgs data yields lower chi-squared than the Standard Model, with the gluon-fusion coupling sign flipped to accommodate the ATLAS diphoton excess.
Electroweak Precision Fit and New Physics in light of $W$ Boson Mass
hep-ph 2022-04 conditional novelty 3.0 of 10

A global electroweak fit using the CDF 2022 W mass yields S = 0.06 ± 0.10, T = 0.11 ± 0.12, U = 0.14 ± 0.09, and a two-Higgs-doublet model can fit these values if the charged Higgs mass lies outside the range spanned ...
Towards deconstructing the simplest seesaw mechanism
hep-ph 2022-03 conditional novelty 3.0 of 10

The triplet seesaw's doubly-charged scalar decays into lepton pairs whose pattern encodes the neutrino mass ordering, so future colliders could read off neutrino properties from four-lepton events, while non-standard ...

How the literature uses it

37 arXiv papers cite this in 55 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 · 31 sentences without a confident label

Contests it 1 paper

Since there was a typo in the $U$ parameter in Ref. [ref] , we re-drive the expressions using the result in Ref. [ref] which computed the oblique parameters for generic scalar multiplets assuming their VEVs are negligibly small.

Towards deconstructing the simplest seesaw mechanism · Calculation of the oblique parameters $S$, $T$ and $U$ parameters · contest 0.87

Builds on it 1 paper

Following the notations used in [ref] , [equation] where $s = sinθ_W$, and $c=√(1-s^2)$.

Precision Electroweak Constraints on Neutrinophilic Scalars · Contribution to Electroweak Oblique Parameters · 0.88

Uses its method or tool 8 papers

Using the full expressions for the oblique parameters [ref] and neglecting the tree-level contribution from Eq. [ref] by making $v_Δ≪v$, we find the required values in the $λ_4$–$m_H$ plane that resolve the $m_W$ anomaly in Fig. [ref] (top).

W-boson mass in the triplet seesaw model · Introduction · 0.95
We use the general expressions presented in [ref] .

Consistency of New CDF-II W Boson Mass with 123-Model · Bounds from the Electroweak Precision tests · 0.97
At one loop level, we obtain the oblique parameters by choosing the weak isospin $J=1$ and hypercharge $Y=1$ in Ref. [ref] [equation] where the functions are defined as [equation] We find that the above functions are symmetric under the exchange of $x$ and $y$.

Electroweak precision tests for triplet scalars · $Y=1$ triplet scalar · 0.88

Compares with it 3 papers

Thus, the contribution of a scalar multiplet $Φ_JY$ to $S$ can be written as [equation] Note that the expressions of $S_Φ_JY$ and $T_Φ_JY$ are consistent with those given in Ref. [ref] .

$W$-Boson Mass Anomaly from a General $SU(2)_{L}$ Scalar Multiplet · Calculation Details for the Scalar Multiplet Contributions to $T$ and $S$ · 0.99
We reproduced the oblique parameters computed in [ref] and note that our results of $S$ and $T$ are consistent with a similar calculation in [ref] .

GUT origins of general electroweak multiplets and their oblique parameters · $Π_IJ(q^2)$ for the general scalar electroweak multiplets · 1.00
Our result for $_S$ is consistent with the result in Ref. [ref] , first computed in [ref] .

The last Complex WIMPs standing · Electroweak precision observables · 0.99

Cites it as background 6 papers

It is well known that the triplet can affect the values of the oblique parameters, in particular the $S$ and $T$ parameters [ref] .

Scalar phenomenology in type-II seesaw model · Introduction · 0.80
The new triplet Higgs bosons contribute to the electroweak precision observables, namely, the S,T, U parameters [ref] .

Revisiting the high-scale validity of Type-II seesaw model with novel LHC signature · Theoretical and Experimental constraints · 0.86
In this section we analyze the impact of constraints arising from electroweak precision measurements, especially the oblique parameters [ref] on our model.

Revisiting Generalized Two Higgs Doublet Model in the Light of Muon Anomaly and Lepton Flavor Violating Decays at HL-LHC · Electroweak constraints · 0.91

Discussion

Disagree with the review, or know something it missed? Leave a comment, highlight any passage above to comment on it, or challenge this review formally.

[1] [1]

M. B. Einhorn, D. R. T. Jones and M. Veltman, Nucl. Phys. B191, 146 (1981)

View on Pith 1981

[2] [2]

M. E. Peskin and T. Takeuchi, Phys. Rev. Lett. 65, 964 (1990); Phys. Rev. D 46, 381 (1992). 8

View on Pith 1990

[3] [3]

D. C. Kennedy and B. W. Lynn, Nucl. Phys. B322, 1 (1989); W. J. Marciano and J. L. Rosner, Phys. Rev. Lett. 65, 2963 (1990); D. C. Kennedy and P. Langacker, Phys. Rev. Lett. 65, 2967 (1990); 66, 395(E); Phys. Rev. D 44, 1591 (1991); G. Altarelli and R. Barbieri, Phys. Lett. B 253, 161 (1991)

View on Pith 1989

[4] [4]

I. Maksymyk, C. P. Burgess and D. London, McGill Report No. Mc Gill-93/13, 1993 (un- published)

View on Pith 1993

[5] [5]

B. Grinstein and M. B. Wise, Phys. Lett. B 265, 326 (1991)

View on Pith 1991

[6] [6]

C. P. Burgess, S. Godfrey, H. K¨ onig, D. London and I. Maksym yk, McGill Report No. McGill-93/24, 1993 (unpublished)

View on Pith 1993

[7] [7]

L.-F. Li, Carnegie-Mellon Report No. CMU-HEP92-18, 1992 (unpu blished)

View on Pith 1992

[8] [8]

T. Appelquist and J. Carrazone, Phys. Rev. D 11, 2856 (1975). FIGURE CAPTIONS Figure 1: Feynman diagrams relevant for the computation of the va cuum polarizations. Figure 2: Plot of S′ (full line), T (dotted line) and U ′ (dashed line) against m2, with m1 = 150 GeV kept ﬁxed. All ﬁgures are for a scalar multiplet with hyperc harge −1/2. Figure 2a is for a...

View on Pith 1975