Two and three point functions in real singlet and complex doublet scalar model

Muhammad Saad; Tajdar Mufti

REVIEW 4 major objections 5 minor 32 references

Two and three point functions in real singlet and complex doublet scalar model

T0 review · 4 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗ Review JSON

Pith's one-line read This paper claims that a real scalar singlet coupled to an SU(2)-symmetric complex doublet through quartic and Yukawa interactions remains an interacting quantum field theory, escaping the triviality of pure phi^4 theory, as shown by…

desk verdict A genuinely new exploratory lattice scan of a scalar singlet plus SU(2) doublet model whose central nontriviality claim rests on single-cutoff, ML-extrapolated dressing functions; right to send back for major revision, not to desk-reject. read the letter →

arxiv 2506.23390 v2 pith:VQZF6RSJ submitted 2025-06-29 hep-lat hep-ph

Muhammad Saad , Tajdar Mufti This is my paper · ORCID

classification hep-lathep-ph PACS 11.15.Ha12.60.Fr

keywords scalarsingletSU(2)doubletlatticefieldtheorytrivialityYukawavertexpropagatorsmachinelearningcorrelationfunctions0+states

verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper tries to establish that a scalar field theory containing a real singlet and an SU(2) symmetric complex doublet, with all quartic couplings and a Yukawa coupling between them, is not trivial. Using lattice simulations at 192 points in parameter space and supervised machine learning to fit the correlation functions, the authors report scalar and Higgs propagators whose dressing functions rise significantly above 1, infrared enhancement relative to tree level, and a scalar-Yukawa vertex that depends weakly on field momenta across a wide range. Such behavior, if correct, means the triviality of the standalone $phi^{4}$ interaction is mitigated once the singlet is coupled to the doublet, making the model a viable nonperturbative window into Higgs-portal and dark-matter scalar sectors. The paper also maps a rich 0+ spectrum, from sub-eV to hundreds of TeV, with a relative scarcity of states near hundreds of GeV.

What carries the argument

The central objects are the renormalized scalar and Higgs propagators and the amputated scalar-Yukawa vertex. The propagators are written as tree-level forms plus polynomial corrections in the couplings, the momentum, and the scalar mass, while the vertex is written as the Yukawa coupling times a polynomial in the momentum invariants and the couplings. Supervised machine learning fits these polynomial forms to the lattice data; the fitted functions supply the deep-infrared behavior where the lattice itself cannot resolve it, and their outputs are what show dressing functions above 1 and a flat vertex. The paper's claim that the theory remains interacting stands on those fitted functions.

What would settle it

Run the same parameter points on a larger lattice, say $24^{4}$ or $32^{4}$, and check whether the propagator dressing functions computed directly at the lowest accessible momenta still rise significantly above 1 and whether the Yukawa vertex remains flat; if the enhancement shrinks or the vertex develops momentum dependence as the volume grows, the paper's central claim fails.

Watch

Extended reading notes

Core claim

The core discovery claimed is that the theory remains interacting in the presence of all allowed SU(2)-preserving scalar interactions. In the adopted renormalization scheme, the renormalized scalar and Higgs propagators are enhanced compared to their tree-level forms, with dressing functions rising markedly above 1, particularly for the lightest scalar masses. The variety of propagator shapes across the parameter space is interpreted as a strong sign of the absence of triviality, meaning the Yukawa and doublet interactions prevent the pure $phi^{4}$ sector from becoming free. The amputated scalar-Yukawa vertex, computed over the full two-dimensional momentum plane, is found to depend only weakly on the field momenta; combined with the propagator enhancement, this indicates a genuinely interacting scalar sector. In addition, the spectrum of 0+ operators ranges from ultralight masses to hundreds of TeV, with a notable scarcity around hundreds of GeV.

Load-bearing premise

The deep-infrared behavior of the propagators and the flatness of the Yukawa vertex come from the machine-learning fits of Eqs. (20)-(22), and the paper assumes those polynomial forms are faithful and that all deviations from the lattice data are numerical artifacts.

Editorial extensions

If this is right

If the claim holds, a scalar singlet coupled to a doublet provides a nonperturbative counterexample to the expectation that scalar-only theories are trivial, opening a path to interacting Higgs-portal models beyond perturbation theory.
The machine-learned propagator and vertex functions give a parameter-space map that can be used as input to nonperturbative bound-state calculations, since they reduce the need for arbitrary ansatze.
The reported 0+ spectrum, spanning from ultra-light to hundreds of TeV with a gap near hundreds of GeV, would give specific, testable predictions for scalar extensions of the Standard Model and for ultralight dark matter searches.
The observed classification of field expectation values into distinct trajectories, with no conclusive phase transition, implies that the model has structural changes in parameter space that future larger-lattice studies can pin down.

Reading between the lines

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

Editorial inference: the polynomial machine-learning fits are only as trustworthy as their extrapolation into the deep infrared, so a direct test on a larger lattice that resolves those momenta without fitting would either confirm the infrared enhancement or expose it as a fitting artifact.
Editorial inference: the flatness of the Yukawa vertex could be a consequence of the renormalization condition at the chosen scale, and checking the vertex at several renormalization points or against a perturbative comparison would show whether the flatness is physical or scheme-induced.
Editorial inference: the reported scarcity of 0+ states near hundreds of GeV may depend on the choice of the Higgs-ball operator and the smallest nonzero lattice mass for setting the scale, so an independent scale-setting operator would test whether the gap is a genuine spectral feature.

Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Desk Editor's Note

read the letter

Short version: this is a new lattice parameter scan for a scalar singlet plus SU(2) doublet model, and it is worth reading as an exploratory study. But the abstract's nontriviality claim — that the model evades scalar triviality — is not backed by the data shown. The reader's skeptic is right; the stress-test note holds up on reading.

What is actually new: nobody has run this particular scalar-only model with all quartic plus singlet-doublet Yukawa interactions, so the 192-point scan of propagators, the vertex, and the 0+ operators is a new dataset. The paper is transparent about the action, the update algorithm, and the scale-setting choice, and the ML fit coefficients are tabulated in appendices, which is a reproducible artifact even without raw data. The sign-of-action discussion is honest and checked.

The soft spot is load-bearing. Section 3.4 concludes absence of triviality from dressing functions that are 'significantly above 1,' but at the lowest directly accessed momenta they are typically 1.05–1.2, and the deep-infrared enhancement comes from the polynomial ansatze in Eqs. 20–21. Those fits are trained on the same lattice data and then deviations are assigned to 'numerical (lattice) artifacts' without an independent test. There are no statistical errors, one lattice size (18^4), no continuum extrapolation, and no independent regulator variation; a finite-cutoff scalar theory is interacting even if its continuum limit is trivial. So 'variety of scalar propagators' cannot carry the nontriviality conclusion. The same problem affects the flat Yukawa vertex and the claimed continuum-like scaling window in Fig. 3, which is only ln a against ln(Λ ms). The 0+ masses from meV to TeV are dominated by the scale-setting convention that fixes the lowest Higgs-ball mass to 125.09 GeV; I would not quote those as physical predictions.

None of this is a takedown of the numerical work. The paper has real exploratory value: the model is new, the scan is broad, and the ML parametrizations could feed DSE studies if labeled as parametrizations, not measurements. I agree with the reader that it should be reframed as a pilot study and sent back for major revision: add error bars, at least one second lattice size or a genuine a→0 statement, an independent scale observable, and validation of the ML fits on held-out momenta or parameter points.

Who this is for: lattice scalar practitioners and BSM model-builders who want an existing dataset and ansatze for a two-scalar model. I would not cite the triviality claim, but I would send it to a serious referee rather than desk-reject: the model scan is not available elsewhere, and a revision could be valuable.

Referee Report

4 major / 5 minor

Summary. The paper studies a Euclidean lattice model containing a real scalar singlet and an SU(2)-preserving complex doublet, with quartic and Yukawa interactions, on a single 18^4 lattice at 192 parameter points. Using multi-hit Metropolis and smeared operators, the authors compute Higgs-ball and scalar-ball masses, 0+ operator masses, field expectations, propagators, and the amputated Yukawa vertex. They fit degree-5 polynomial 'machine learning' functions to the lattice spacing, the scalar and Higgs propagators, and the vertex. The central claims are that the propagator dressing functions are infrared-enhanced, the Yukawa vertex depends only weakly on momenta, and this indicates absence of triviality and a 'continuum-like scaling window' in the parameter space.

Significance. If the central claims were established, the paper would be a significant non-perturbative indication that adding an SU(2) doublet and Yukawa couplings to a scalar singlet evades the triviality of pure φ^4 theory. The paper does provide a broad parameter scan, explicit ML coefficient tables in Appendices A–D that could serve as inputs to Dyson–Schwinger studies, and a careful sign-stability check of the action over a billion histories. However, the main physics conclusion is not backed by the presented evidence: the data are all at one lattice spacing per point with no continuum extrapolation, no statistical errors are reported, and the ML fits are fitted to the same data from which the physics is inferred. The claimed deep-infrared behavior is an extrapolation of polynomial ansatze rather than a measured lattice signal.

major comments (4)

[Section 3.4, Eqs. (20)–(21), Figs. 14–17] The claim that 'the variety of scalar propagators in the parameter space is a strong sign of absence of triviality' is not supported by the data presented. All simulations are on a single lattice volume L=18^4, with one lattice spacing per parameter point, and no L→∞ or a→0 extrapolation is performed. A lattice scalar theory with finite bare couplings is interacting at any finite cutoff even if its continuum limit is trivial, so dressing functions rising above 1 at a single cutoff cannot discriminate between trivial and non-trivial continuum limits. The abstract's 'continuum-like scaling window' likewise has no scaling analysis: Figure 3 merely plots ln a versus ln Λms and contains no demonstration of a scaling regime.
[Section 3.4, after Fig. 17, and Eqs. (20)–(22)] The machine-learning procedure is circular for the main conclusions. The functions in Eqs. (20) and (21) are fitted to the same lattice data points from which the infrared enhancement and weak momentum dependence of the vertex are inferred; no train/test split, cross-validation, or independent data set is described. The statement that 'the observed deviations stem from numerical (lattice) artifacts with a likely small contribution from the limitations of the representative functions' is an assumption, not a test. In particular, the claimed infrared enhancement below the lowest directly accessed momenta is an extrapolation of a degree-5 polynomial, and the flatness of the Yukawa vertex in Figs. 18–21 is largely a property of the fitted ansatz rather than of the raw lattice data.
[Section 3.1, Eqs. (6)–(7)] The scale-setting procedure relies on the unjustified identification of the lowest non-zero mass from the three-exponential fit of the Higgs-ball operator with the physical Higgs mass M_h = 125.09 GeV. The paper offers no evidence that this fitted mass indeed corresponds to the physical Higgs state rather than a lattice artifact or a different operator state. The subsequent conversion of lattice masses to physical units produces values spanning from μeV to hundreds of TeV (Figs. 5–11), which the paper attributes to 'extraordinary rise ... due to the low values of lattice spacing.' Without an independent scale-setting check or a continuum extrapolation, these mass assignments are not reliable.
[Section 2, Table 1, and Section 3.5] No statistical errors are reported for any quantity. The Yukawa vertex is described as 'one of the noisiest quantities,' and the differences between lattice and ML vertex values in Figs. 18–21 are of comparable magnitude to the claimed weak momentum dependence. Without error bars, the classification of expectation values in Figs. 12–13 and the conclusion that the vertex is 'weakly depending upon the field momenta' cannot be assessed. The paper should report at least jackknife or bootstrap errors for the underlying correlation functions and propagated errors for the dressing functions and vertex.

minor comments (5)

[Eq. (22)] The vertex function FΓ is written with β among its variables even though β is held fixed throughout the study; the notation should be clarified so that the reader knows which parameters are actually varied.
[Eqs. (14)–(15)] The renormalization conditions do not state the numerical value of the renormalization point µ used in the fits; the scheme is not fully reproducible without this information.
[Figs. 5–11] The legends such as '1,1' and the axis labels like 'mass [GeV]+0' are ambiguous; the meaning of the plotted curves and the notation for parameter tuples should be defined explicitly.
[Section 2] The sentence 'The simulations and calculations are performed in C++ environment, and ROOT CERN is used to produce the diagrams' is an implementation detail that would be better placed in a footnote than in the main text.
[Throughout] There are several typographical and grammatical errors, including 'the theory remain interactive' in Section 3.4 (should be 'remains interactive') and inconsistent use of ligatures in words such as 'eﬀects'; a careful proofread is needed.

Circularity Check

1 steps flagged · score 4.0 of 10

One definitional circularity: the non-vanishing Yukawa vertex is fixed by the renormalization condition, while the propagator-based non-triviality claim is independent.

self definitional [Section 3.5 (Eq. 18) and Section 4 (Conclusion)]
"The renormalized form of the vertex differs by a multiplicative constant which is calculated by the renormalization condition Γ( µ, ν, −µ − ν) = λ ... The scalar Yukawa coupling, despite its relatively distinct symmetry, does have a role in the parameter space of the model. It does not vanish which support this conclusion."

Equation 18 defines the renormalized vertex so that Γ(μ,ν)=λ at the renormalization point, and λ is nonzero for every studied point (the region λ=0 is excluded). Therefore the statement that the vertex 'does not vanish' is guaranteed by the chosen normalization, not by the lattice measurement. The paper uses this non-vanishing as evidence that the Yukawa coupling has a role, so the support is circular: the conclusion is a restatement of the input renormalization condition rather than an independent result. The momentum dependence of the vertex is independent content, but the non-null claim reduces by construction to the definition.

full rationale

The central non-triviality claim is based on the directly measured renormalized propagators and dressing functions in Figures 14-17, whose values rise above 1 in the lattice data themselves. The ML functions (Eqs. 19-22) are descriptive fits to those same data, and the paper does not present them as independent predictions; the lack of a train/test split and the attribution of ML-vs-lattice residuals to artifacts are methodological/correctness concerns, not circular reductions. The renormalization scheme is cited from the authors' prior work [12], but that scheme does not force the dressing functions to deviate from tree level, so it is not load-bearing circularity. The one genuine circular step is the conclusion that the Yukawa vertex does not vanish: Eq. 18 normalizes Γ(μ,ν) to λ≠0, making the non-null result true by construction, and the paper then cites that non-vanishing as evidence for the Yukawa coupling's role. Because this affects a secondary supporting claim while the propagator-based interacting conclusion remains independent, the overall circularity is limited rather than central.

Assumptions & free parameters 5 free parameters · 4 assumptions · 0 invented entities

The central claims depend on the ML fits, the scale-setting identification, and the positivity of the lattice action. The ML coefficients are fitted numbers; the scale-setting and polynomial ansatz are paper-specific assumptions.

free parameters (5)

ML coefficients for lattice spacing fit (Eq. 19, Appendix A) = 129 coefficients (listed in Appendix A)
Fitted to the computed lattice spacings over the 192 parameter points.
ML coefficients for scalar propagator fit (Eq. 20, Appendix B) = Coefficients c_ijklt (Appendix B)
Fitted to the renormalized scalar propagator, then used to infer infrared behavior.
ML coefficients for Higgs propagator fit (Eq. 21, Appendix C) = Coefficients c_ijklt (Appendix C)
Fitted to the renormalized Higgs propagator.
ML coefficients for Yukawa vertex fit (Eq. 22, Appendix D) = Coefficients c_ijklmn (Appendix D)
Fitted to the amputated vertex; used to conclude weak momentum dependence.
renormalization scale mu = not specified
Used in Eqs. 14-15 to fix z and delta m^2; the paper never states the numerical value, so results cannot be reproduced.

assumptions (4)

domain assumption The lattice action has a positive-definite measure; no negative actions were observed in over a billion histories.
Section 2, Eq. 3 and following paragraph.
ad hoc to paper The lowest non-zero mass from the three-exponential fit of the Higgs ball operator is the physical Higgs mass (125.09 GeV) and determines the lattice spacing via a = m_i / M_h.
Section 2, Eqs. 5-7.
ad hoc to paper The degree-5 polynomial ML ansatze (Eqs. 19-22) are flexible enough to represent the true momentum and parameter dependence of the propagators and vertex; deviations from lattice data are assigned to lattice artifacts.
Section 3.4, after Eq. 20 and before Eq. 21.
ad hoc to paper Operator eigenvalues fitted to one exponential (Eq. 9) give the ground-state masses for the 0+ operators.
Section 3.2, Eq. 9 and the associated fitting procedure.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Two and three point functions in real singlet and complex doublet scalar model." pith.science (2026). https://pith.science/paper/VQZF6RSJ

@misc{pith2026250623390,
  author       = {Pith},
  title        = {Pith review of: Two and three point functions in real singlet and complex doublet scalar model},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/VQZF6RSJ}},
  note         = {Machine review of arXiv:2506.23390}
}

abstract

We study dynamics of an interacting theory of a real singlet scalar and an $SU(2)$ symmetry preserving complex doublet scalar fields using lattice simulations over a broad region of the parameter space. The model contains all $SU(2)$-preserving quartic and a real singlet-$SU(2)$ invariant doublet field Yukawa interactions. The field propagators and the Yukawa vertex are the central structures for the study. We complement the study by implementing machine learning routines to the correlation functions in order to probe the underlying physics. The model reveals the role of nonperturbative effects in terms of infrared enhanced field propagators with a stable amputated Yukawa vertex, and a continuum-like scaling window in the parameter space with large regulator. The ultraviolet effects are visible in terms of an scaling structure appearing in a composite operator of mixed scalar interactions and the singlet expectation value.

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

32 extracted references · 32 canonical work pages

[1]

Georges Aad et al. Search for a new heavy scalar particle d ecaying into a Higgs boson and a new scalar singlet in ﬁnal states with one o r two light leptons and a pair of τ-leptons with the ATLAS detector. JHEP, 10:009, 2023

work page 2023
[2]

Ramsey-Musolf

Vincenzo Cirigliano and Michael J. Ramsey-Musolf. Low E nergy Probes of Physics Beyond the Standard Model. Prog. Part. Nucl. Phys. , 71:2– 20, 2013

work page 2013
[3]

Lewis, and Matthew Sullivan

Shekhar Adhikari, Ian M. Lewis, and Matthew Sullivan. Be yond the Standard Model eﬀective ﬁeld theory: The singlet extended St andard Model. Phys. Rev. D , 103(7):075027, 2021

work page 2021
[4]

The Real singlet scalar dar k matter model

Wan-Lei Guo and Yue-Liang Wu. The Real singlet scalar dar k matter model. JHEP, 10:083, 2010

work page 2010
[5]

Schwartz

Matthew D. Schwartz. Quantum Field Theory and the Standard Model . Cambridge University Press, 2014

work page 2014
[6]

M. Kaku. Quantum ﬁeld theory: A Modern introduction . 1993

work page 1993
[7]

Roberts and Anthony G

Craig D. Roberts and Anthony G. Williams. Dyson-Schwing er equa- tions and their application to hadronic physics. Prog. Part. Nucl. Phys. , 33:477–575, 1994

work page 1994
[8]

Heinz J. Rothe. Lattice Gauge Theories, An Introduction . World Sci- entiﬁc, London, 1996. London, UK: world Scientiﬁc (1996) 38 1 p. 42

work page 1996

Show all 32 references

[9]

Quantum Chromodynamics on the Lattice

Christof Gattringer and Christian B Lang. Quantum Chromodynamics on the Lattice . Springer, Berlin, 2010. Heidelberg, Germany: Springer (2010) 343 p

2010
[10]

Spectroscopic analysis of t he phase dia- gram of Yang-Mills-Higgs theory

Axel Maas and Tajdar Mufti. Spectroscopic analysis of t he phase dia- gram of Yang-Mills-Higgs theory. Phys. Rev. , D91(11):113011, 2015

2015
[11]

Φ 4 theory is trivial

Renata Jora. Φ 4 theory is trivial. Rom. J. Phys. , 61(3-4):314, 2016

2016
[12]

Two- and three-point functi ons in Landau gauge Yang-Mills-Higgs theory

Axel Maas and Tajdar Mufti. Two- and three-point functi ons in Landau gauge Yang-Mills-Higgs theory. JHEP, 04:006, 2014

2014
[13]

The Higgs portal to cosmology

Oleg Lebedev. The Higgs portal to cosmology. Prog. Part. Nucl. Phys. , 120:103881, 2021

2021
[14]

The Higgs- portal for dark matter: eﬀective ﬁeld theories versus concre te realiza- tions

Giorgio Arcadi, Abdelhak Djouadi, and Marumi Kado. The Higgs- portal for dark matter: eﬀective ﬁeld theories versus concre te realiza- tions. Eur. Phys. J. C , 81(7):653, 2021

2021
[15]

Latti ce scalar ﬁeld theory at complex coupling

Scott Lawrence, Hyunwoo Oh, and Yukari Yamauchi. Latti ce scalar ﬁeld theory at complex coupling. Phys. Rev. D , 106(11):114503, 2022

2022
[16]

Asit K. De, A. Harindranath, Jyotirmoy Maiti, and Tilak Sinha. In- vestigations in 1+1 dimensional lattice phi**4 theory. Phys. Rev. D , 72:094503, 2005

2005
[17]

The phase transition of the two Higgs extension of the standard model

Vasilios Zarikas. The phase transition of the two Higgs extension of the standard model. Phys. Lett. B , 384:180–184, 1996

1996
[18]

Posi tivity bounds on Higgs-Portal dark matter

Seong-Sik Kim, Hyun Min Lee, and Kimiko Yamashita. Posi tivity bounds on Higgs-Portal dark matter. JHEP, 06:124, 2023

2023
[19]

Ruderman, and Oren Slone

Cristina Mondino, Maxim Pospelov, Joshua T. Ruderman, and Oren Slone. Dark Higgs Dark Matter. Phys. Rev. D , 103(3):035027, 2021

2021
[20]

Higgs boson induced reheating and ultraviolet frozen-in dark matter

Aqeel Ahmed, Bohdan Grzadkowski, and Anna Socha. Higgs boson induced reheating and ultraviolet frozen-in dark matter. JHEP, 02:196, 2023

2023
[21]

Higgs Boson- Induced Reheating and Dark Matter Production

Aqeel Ahmed, Bohdan Grzadkowski, and Anna Socha. Higgs Boson- Induced Reheating and Dark Matter Production. Symmetry, 14(2):306, 2022

2022
[22]

Scalar dark matter candidates revisited

C´ eline Boehm, Xiaoyong Chu, Jui-Lin Kuo, and Josef Pra dler. Scalar dark matter candidates revisited. Phys. Rev. D , 103(7):075005, 2021

2021
[23]

Teixei ra

Carsten van de Bruck, Gaspard Poulot, and Elsa M. Teixei ra. Scalar ﬁeld dark matter and dark energy: a hybrid model for the dark s ector. JCAP, 07:019, 2023. 43

2023
[24]

Machine Learning - An Algorithmic Perspective

Stephen Marsland. Machine Learning - An Algorithmic Perspective. Chapman and Hall / CRC machine learning and pattern recognit ion series. CRC Press, 2009

2009
[25]

Higgs portal for real scalar singlet

Tajdar Mufti. Higgs portal for real scalar singlet. unpublished
[26]

Artiﬁcial intelligence in higgs-scalar singlet model

Tajdar Mufti. Artiﬁcial intelligence in higgs-scalar singlet model. un- published
[27]

Ostriker, Scott Tremaine, and Edwa rd Wit- ten

Lam Hui, Jeremiah P. Ostriker, Scott Tremaine, and Edwa rd Wit- ten. Ultralight scalars as cosmological dark matter. Phys. Rev. D , 95(4):043541, 2017

2017
[28]

D. C. Curtis, M. R. Pennington, and D. Walsh. Dynamical m ass gener- ation in QED in three-dimensions and the 1/N expansion. Phys. Lett. B, 295:313–319, 1992

1992
[29]

Dynamical generation of the baryon asymmetry from a sc ale hierarchy

Jae Hyeok Chang, Kwang Sik Jeong, Chang Hyeon Lee, and Ch ang Sub Shin. Dynamical generation of the baryon asymmetry from a sc ale hierarchy. Phys. Rev. D , 110(5):055038, 2024

2024
[30]

Dy- namical origin of neutrino masses and dark matter from a new c onﬁning sector

Maximilian Berbig, Juan Herrero-Garcia, and Giacomo L andini. Dy- namical origin of neutrino masses and dark matter from a new c onﬁning sector. Phys. Rev. D , 110(3):035011, 2024

2024
[31]

Dynamical mass gener- ation in qed $ 3$: A non-perturbative approach

G B de Gracia, B M Pimentel, and L Rabanal. Dynamical mass gener- ation in qed $ 3$: A non-perturbative approach. Progress of Theoretical and Experimental Physics , 2019(7):073B05, 07 2019

2019
[32]

Dynamical mass gener ation of spin- 2 ﬁelds in de Sitter space for an O(N) symmetric model at large N

Nahomi Kan and Kiyoshi Shiraishi. Dynamical mass gener ation of spin- 2 ﬁelds in de Sitter space for an O(N) symmetric model at large N. Phys. Rev. D , 108(10):105022, 2023. 44

2023

Pith tools

Reviewed August 6, 2026 · model on record in the stance chip above.

[1] [1]

Georges Aad et al. Search for a new heavy scalar particle d ecaying into a Higgs boson and a new scalar singlet in ﬁnal states with one o r two light leptons and a pair of τ-leptons with the ATLAS detector. JHEP, 10:009, 2023

work page 2023

[2] [2]

Ramsey-Musolf

Vincenzo Cirigliano and Michael J. Ramsey-Musolf. Low E nergy Probes of Physics Beyond the Standard Model. Prog. Part. Nucl. Phys. , 71:2– 20, 2013

work page 2013

[3] [3]

Lewis, and Matthew Sullivan

Shekhar Adhikari, Ian M. Lewis, and Matthew Sullivan. Be yond the Standard Model eﬀective ﬁeld theory: The singlet extended St andard Model. Phys. Rev. D , 103(7):075027, 2021

work page 2021

[4] [4]

The Real singlet scalar dar k matter model

Wan-Lei Guo and Yue-Liang Wu. The Real singlet scalar dar k matter model. JHEP, 10:083, 2010

work page 2010

[5] [5]

Schwartz

Matthew D. Schwartz. Quantum Field Theory and the Standard Model . Cambridge University Press, 2014

work page 2014

[6] [6]

M. Kaku. Quantum ﬁeld theory: A Modern introduction . 1993

work page 1993

[7] [7]

Roberts and Anthony G

Craig D. Roberts and Anthony G. Williams. Dyson-Schwing er equa- tions and their application to hadronic physics. Prog. Part. Nucl. Phys. , 33:477–575, 1994

work page 1994

[8] [8]

Heinz J. Rothe. Lattice Gauge Theories, An Introduction . World Sci- entiﬁc, London, 1996. London, UK: world Scientiﬁc (1996) 38 1 p. 42

work page 1996