Pith. sign in

REVIEW 3 major objections 4 minor 72 references

Vacuum Instability and False Vacuum Decay Induced by Domain Walls in the N2HDM

T0 review · 3 major / 4 minor · reviewed 2026-08-07 · deepseek-v4-flash

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

Pith's one-line read The paper's claim is that domain walls formed by the singlet field of the Next-to-Two-Higgs-Doublet model can erase the barrier between the electroweak vacuum and a deeper minimum, so the fields roll classically into the deeper vacuum and…

desk verdict A plausible new decay channel for long-lived N2HDM vacua, but the blanket exclusion is stronger than the evidence. read the letter →

arxiv 2506.14880 v1 pith:DIQS4SS2 submitted 2025-06-17 hep-ph

Mohamed Younes Sassi , Gudrid Moortgat-Pick This is my paper
classification hep-ph
keywords N2HDMdomainwallsvacuummetastabilityfalsedecayelectroweakbounceactionsingletscalarcosmologicalconstraints
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

The paper argues that the standard check for vacuum stability in the Next-to-Two-Higgs-Doublet model—compute the tunneling rate, and accept the point if the electroweak vacuum outlives the universe—is incomplete. The model contains a real singlet scalar with a discrete $\mathbb{Z}_2'$ symmetry, and when that symmetry breaks spontaneously, the early universe is divided into patches of opposite singlet values separated by domain walls, regions where the singlet field vanishes. Because the singlet couples to the two Higgs doublets, the effective doublet potential inside a wall is different from the potential outside it, and there the barrier between our electroweak minimum and a deeper minimum can disappear. The doublet fields then roll classically to the deeper vacuum, which nucleates inside the wall and expands outward, converting the entire universe to a vacuum with different particle masses. Parameter points previously classified as safe—some with lifetimes many orders of magnitude longer than the age of the universe—are therefore ruled out by this domain-wall channel.

What carries the argument

The central object is the singlet domain wall: a static kink profile $\phi_s(x)$ interpolating between the two degenerate minima $v_s$ and $-v_s$, with $\phi_s=0$ at its core. It acts as a position-dependent background for the doublet fields, shifting the effective doublet mass terms by $\frac{\lambda_7}{2}\phi_s^2(x)$ and $\frac{\lambda_8}{2}\phi_s^2(x)$; at the core these stabilizing shifts vanish. The paper solves the coupled field equations for the wall at $T=0$, with a damping term included to relax the configuration, and then follows the real-time evolution of the doublet fields; the rollover occurs because the electroweak point is not an extremum of the wall-core potential, so no tunneling is required. For the case of several minima in the wall-core potential, analytic conditions from the two-Higgs-doublet literature decide whether an intermediate minimum can coexist, and the eventual outcome is governed by the size of the friction term in the equation of motion.

What would settle it

Evolve the real-time equations for a constrained benchmark point such as P3, whose wall-core potential has an intermediate minimum, using a physically estimated plasma damping coefficient at the epoch just after electroweak symmetry breaking; if realistic friction of order $\hat d\approx1$ traps the fields in the intermediate minimum, then the claim that domain walls rule out all long-lived metastable parameter points is false. The complementary check is to compute the wall-network annihilation temperature and compare it with the time at which the rollover completes: if the walls vanish first, the excluded points survive.

Watch

Extended reading notes

Core claim

The central claim is that the presence of singlet domain walls opens a new, fully classical decay channel for the electroweak vacuum that is invisible to bounce-action calculations. Inside the wall, the singlet VEV crosses zero, and in the two-Higgs-doublet part of the potential evaluated at that background, the terms proportional to $\lambda_7$ and $\lambda_8$ that helped stabilize the electroweak minimum are absent; the point $(v_1, v_2, 0)$ is not a stationary point of the potential, so there is no barrier to tunnel through. The fields obeying the coupled equations of motion roll downhill to the global minimum in times of order $100\,m_h^{-1}$, and the true-vacuum region then expands outside the wall because the energy gain beats the wall tension. The authors demonstrate this for neutral, electric-charge-breaking, and CP-breaking global minima, and their benchmark point P1 has a bounce action $B\approx 95{,}368$—a lifetime vastly longer than the age of the universe—yet the wall triggers the decay. When the doublet potential inside the wall also has an intermediate minimum, the fate is dynamical: with a large damping term the fields can be trapped there, while with small damping they cross to the global minimum, so the paper's claim is not that every metastable point decays, but that bounce-only stability checks are insufficient and, for the small-friction scans performed, long-lived points whose global minimum has zero singlet VEV are excluded.

Load-bearing premise

The load-bearing premise is that the fields inside the wall roll downhill in the zero-temperature potential with negligible friction at the decay epoch; if plasma friction is actually of order one, the same simulations show the fields can get trapped in an intermediate minimum instead of reaching the global vacuum, so the blanket exclusion of long-lived parameter points would fail.

Editorial extensions

If this is right

  • Vacuum-stability constraints in the N2HDM must be re-derived to include domain walls: a point with bounce action far above 440 (for example P1, with $B\approx 95{,}368$) can still be unstable, so the homogeneous-vacuum lifetime is not a sufficient criterion.
  • The mechanism works for every deep-vacuum type the model allows: neutral vacua with vanishing singlet VEV, electric-charge-breaking vacua, and CP-breaking vacua all nucleate inside the wall and expand.
  • In the 95 GeV Higgs-boson scenario, whole parameter regions can be excluded on this basis alone, most prominently for $m_{h3}\gtrsim 900$ GeV and $m_{12}^2\gtrsim 3\times10^4$ GeV$^2$; after collider, flavour, and electroweak precision constraints are imposed, the low-$m_{12}^2$ region below about $1.5\times10^4$ GeV$^2$ is swept out.
  • When the wall-core potential contains an intermediate minimum, the point's fate is not decided by the bounce action either: with a large damping term ($\hat d\approx1$) the fields become trapped and the vacuum survives, while with small damping ($\hat d\approx0.05$) they cross to the global minimum; all multi-minimum points in the paper's scans crossed over at small damping.
  • The constraint has three escape hatches: large explicit $\mathbb{Z}_2'$ breaking that eliminates the walls, parameter points where the electroweak vacuum itself has $v_s=0$, and regions with $\mathbb{Z}_2'$ symmetry non-restoration at high temperature, in which walls never form.

Reading between the lines

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

  • The same mechanism should operate in any model where a discrete-symmetry wall's core drives a coupled scalar sector to a field value at which the false vacuum's protecting barrier vanishes; the N2HDM here is the template, not the only possible home, for such a constraint.
  • If the physical plasma damping at the decay epoch is of order one rather than negligible, the P3 example shows that fields can be trapped in an intermediate minimum, so a quantitative estimate of friction—not just the Hubble term—would determine how large the excludable region really is.
  • Because the wall-seeded conversion happens on timescales of order $100\,m_h^{-1}$, far shorter than a Hubble time at that epoch, the transition is cosmologically instantaneous; the observable consequence is the absence of the predicted particle-mass-changing vacuum, not a direct signal from the rollover itself.
  • The annihilation temperature of the wall network is the main missing input: if the small bias making the two singlet vacua non-degenerate destroys the network before the rollover completes, the excluded points are rescued, so computing a full thermal history for benchmark points such as P1 would settle how robust the exclusion is.
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.

Referee Report

3 major / 4 minor

Summary. The paper studies vacuum decay induced by singlet domain walls in the Z2'-symmetric N2HDM. It argues that inside a domain wall, where the singlet VEV vanishes, the effective potential for the two doublets can lose the barrier separating the EW vacuum from deeper minima, allowing a classical rollover to nucleate the deeper vacuum inside the wall; the nucleated true vacuum then expands and destroys the EW vacuum everywhere. Using the codes ScannerS, EVADE, and a custom real-time solver for the classical field equations, the authors benchmark this mechanism for neutral, charge-breaking, and CP-breaking deeper vacua, and scan two phenomenological scenarios to identify regions where metastable EW vacua are ruled out by domain-wall-induced decay.

Significance. If the mechanism operates as claimed, it is an important new constraint: standard bounce-action stability checks would deem these points long-lived, and the DW rollover would rule them out. The paper's strengths are that the benchmark computations are explicit and reproducible in principle (the parameter inputs are tabulated), the classification into single-minimum vs multi-minimum cases inside the wall is clean, and the use of external codes (ScannerS, EVADE) and existing analytic conditions from [7,8] avoids circularity. The single-minimum case is argued convincingly. However, the blanket exclusion of multi-minima parameter points and the universal wording of the abstract are not supported by the demonstrated evidence, because the real-time dynamics depend on an unquantified friction coefficient.

major comments (3)
  1. [Sec. 5.2 and Sec. 4.1] The statement in Sec. 5.2 that 'all these parameter points roll over to the global minimum' is based on evolving Eq. (4.1) with dhat ≈ 0, but Sec. 4.1 shows that for P3 with dhat = 1 the fields are trapped in the intermediate minimum (Fig. 7). The physical value of d is never estimated; the text states only that it 'depends heavily on the thermal evolution and the coupling between the scalars and fermions.' Since the exclusion of all multi-minima points is load-bearing for the paper's central claim, the abstract's universal conclusion that 'Such parameter points with a metastable EW minimum are ruled out' is stronger than the evidence. The authors should either estimate the physical damping rate or restrict the claim to the single-minimum case.
  2. [Sec. 4, paragraph after Fig. 2] The expansion of the nucleated vacuum 'outside of the wall everywhere in the universe' is asserted without a calculation. The 1D simulations in Figs. 2, 4, and 5 impose EW vacuum boundary conditions at x → ±∞ and show the wall region rolling over; they do not demonstrate that the true-vacuum region expands into the bulk, which requires a comparison of the energy gain with the wall tension or a higher-dimensional simulation. Footnote 5 acknowledges that thermal corrections would delay the expansion until the gain exceeds the tension, but no quantitative estimate is provided. The global-decay conclusion is therefore not established for any parameter point, although it is most plausible for the single-minimum benchmarks.
  3. [Sec. 5.1.1 and Sec. 6] The scan exclusions in Sec. 5.1.1 are conditional on the Z2' symmetry being restored at high temperatures; the paper itself notes that if symmetry non-restoration is real, the domain-wall network would not form and those parameter points would be rescued. This caveat is not carried through to the abstract or the summary's blanket 'ruled out,' so the phenomenological reach of the mass-plane exclusions is overstated relative to the demonstrated evidence.
minor comments (4)
  1. [Sec. 4, Figs. 4 and 5] The initial fluctuations v+(0) and ξ(0) for the CB and CP benchmarks are not specified; the outcome of the classical evolution in a symmetric potential may depend on their amplitude, and the paper should state whether these values represent generic thermal/quantum seeds or are chosen to make the rollover work.
  2. [Sec. 4.1, Eq. (4.3)] The symbol λ345 is used in Eqs. (4.3) and (4.4) without being defined in the text; it should be defined as λ3 + λ4 + λ5.
  3. [Sec. 4.1, third paragraph] There is a typo 'direclty' in the list of possible rollover outcomes, and the notation '(vint 1, vint 1, 0)' should presumably be '(vint 1, vint 2, 0)'.
  4. [Sec. 3, first paragraph] The scan size is written as '10 5' and should be '10^5'; the statistical significance of the finding that no trapped points were found in the scans is not discussed, so the statement 'we didn't find regions where the field configuration is trapped' is a statement about the sample, not a proof.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the domain-wall decay mechanism is a dynamical outcome of Eq. (4.1) with stated assumptions; the dhat≈0 choice is a transparent approximation, not a recycled prediction.

full rationale

The paper's central claim is that, inside the singlet domain wall, the 2HDM potential can lose the barrier protecting the electroweak vacuum, so the fields classically roll to a deeper vacuum that then expands. This claim is obtained by numerically solving the real-time field equation (4.1) for the N2HDM potential with specified boundary conditions, and by using external, independent tools and criteria: EVADE for bounce actions, ScannerS for scans, and the two-minima conditions of Refs. [7,8]. No fitted parameter is later renamed as a prediction. The only self-citation, Ref. [33], appears in a general list of domain-wall/baryogenesis references and is not load-bearing for any step of the argument. The closest candidate for circularity is the treatment of the friction term d in Section 4.1 and Section 5.2: the paper shows that P3 is trapped in an intermediate minimum for dhat=1 and rolls over for dhat=0.05, and later computes all multi-minima scan points with 'dhat approximately 0', finding that all roll to the global minimum. This is an explicit modeling assumption, not a hidden input-output identification: the rollover is a dynamical result of Eq. (4.1) for that parameter choice, not identical to the assumption by construction. The paper also qualifies its own extrapolation, stating 'One cannot, however, conclude that any parameter point with multiple minima will necessarily experience vacuum decay via domain walls', and explicitly notes that the plasma contribution to d 'depends heavily on the thermal evolution and the coupling between the scalars and fermions' and leaves its evaluation to future work. These caveats limit the strength of the blanket abstract wording, but they are limitations of evidence or undetermined assumptions, not circular derivations. No self-definitional step, no fitted-input-called-prediction step, and no load-bearing self-citation chain is exhibited, so the appropriate circularity score is 0.

Assumptions & free parameters 4 free parameters · 6 assumptions · 0 invented entities

The central result does not introduce new particles or forces. It depends on five domain assumptions about the early universe (symmetry restoration, small bias, zero-T potential, expansion, small friction) and on free numerical parameters in the solver (friction, initial seed, grid). The single-minimum rollover for benchmark P1 is more robust; the blanket exclusion of multi-minimum points depends on the unquantified dhat assumption.

free parameters (4)
  • Friction coefficient d (dimensionless dhat=d/m_h) = dhat in {1, 0.05, approximately 0}
    Introduced by hand in Eq. (4.1) to relax fields; for P3, dhat=1 traps in the intermediate minimum while dhat=0.05 rolls over to the global minimum. Actual plasma and Hubble friction are not computed.
  • Initial charged-field fluctuation v+(0) = small, value not given
    Seeds the charge-breaking rollover in Figure 4; without it the initial field may sit at a symmetric extremum.
  • Domain-wall initial profile width delta = not specified
    Initial tanh(delta x) profile chosen in Section 4; the physical width should follow from the potential, and no convergence test for delta is reported.
  • Euler solver grid spacing and timestep = not stated
    The numerical real-time evolution used a three-point central difference and Euler method; no resolution or convergence checks are given.
assumptions (6)
  • domain assumption The Z2 prime soft-breaking terms are small enough to avoid the cosmological domain-wall problem but do not affect vacuum structure or phenomenology.
    Invoked in Section 2 and used to keep degenerate walls; if bias is large, walls annihilate or the vacuum landscape changes.
  • domain assumption Z2 prime and electroweak symmetries are restored at high temperature so that singlet domain walls actually form.
    Section A.1.4 uses Arnold-Espinosa resummation conditions; the paper notes other resummation schemes can disagree and includes symmetry non-restoration cases.
  • domain assumption The zero-temperature potential is adequate for the wall dynamics that cause the decay.
    Section 4 justifies T=0 by arguing DWs do not annihilate before EWSB and thermal corrections are small at O(GeV), but no finite-T check of the barrier disappearance is made.
  • domain assumption The conditions (4.5)-(4.6) from [7,8] correctly classify when the 2HDM potential inside the wall has multiple stationary points.
    Used in Section 4.1 to decide when a real-time simulation is needed; the paper relies on these published conditions.
  • domain assumption The nucleated deeper vacuum expands outside the domain wall because the potential energy gain exceeds the wall tension.
    Stated in Section 4; no calculation of the expansion rate, wall tension, or critical radius is provided.
  • ad hoc to paper At the epoch of decay the friction term is small enough (dhat approximately 0) that fields roll to the global minimum rather than being trapped.
    Used in Section 5.2 for points with multiple minima; the paper itself shows P3 is trapped for dhat=1 and notes plasma friction could be sizable.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Vacuum Instability and False Vacuum Decay Induced by Domain Walls in the N2HDM." pith.science (2026). https://pith.science/paper/DIQS4SS2

@misc{pith2026250614880,
  author       = {Pith},
  title        = {Pith review of: Vacuum Instability and False Vacuum Decay Induced by Domain Walls in the N2HDM},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/DIQS4SS2}},
  note         = {Machine review of arXiv:2506.14880}
}
abstract

The Next-to-Two-Higgs-Doublet model (N2HDM) has a rich vacuum structure where multiple electroweak (EW) breaking minima, as well as CP and electric-charge breaking minima, can coexist. These minima can be deeper than the electroweak vacuum $v_{ew} \approx 246\text{ GeV}$ of our universe, making our vacuum metastable. In such a case, one needs to calculate the tunneling rate from the EW vacuum to the deeper minimum. If the lifetime of the EW vacuum is longer than the universe's age, our vacuum is deemed long-lived, and the parameter point is, in principle, allowed. If the decay rate is smaller than the universe's age, then our vacuum is unstable and the parameter point is ruled out. However, domain walls (DW) in the N2HDM can substantially alter this picture. We show in this work that inside the DW, the barrier between our electroweak minimum and the deeper minimum can disappear, leading the scalar fields to classically roll over to the deeper minimum that nucleates inside the DW and then expands outside of it everywhere in the universe. We show that such behavior can happen to parameter points where the lifetime of our minimum is even several orders of magnitude larger than the age of the universe. Such parameter points with a metastable EW minimum are ruled out.

Discussion (0). Sign in to comment.

Reference graph

Works this paper leans on

72 extracted references · 9 canonical work pages

  1. [1]

    Hiller, T

    G. Hiller, T. H¨ ohne, D.F. Litim and T. Steudtner, Vacuum stability in the Standard Model and beyond, Phys. Rev. D 110 (2024) 115017 [ 2401.08811]

    arXiv 2024

  2. [2]

    Bednyakov, B.A

    A.V. Bednyakov, B.A. Kniehl, A.F. Pikelner and O.L. Veretin, Stability of the Electroweak Vacuum: Gauge Independence and Advanced Precision , Phys. Rev. Lett. 115 (2015) 201802 [1507.08833]

    arXiv 2015

  3. [3]

    CMS collaboration, Measurement of t¯t normalised multi-differential cross sections in pp collisions at √s = 13 TeV, and simultaneous determination of the strong coupling strength, top quark pole mass, and parton distribution functions , Eur. Phys. J. C 80 (2020) 658 [1904.05237]

    arXiv 2020

  4. [4]

    Ferreira, M

    P.M. Ferreira, M. M¨ uhlleitner, R. Santos, G. Weiglein and J. Wittbrodt, Vacuum Instabilities in the N2HDM , JHEP 09 (2019) 006 [ 1905.10234]

    arXiv 2019

  5. [5]

    Lahiri and G

    J. Lahiri and G. Moortgat-Pick, Vacuum (in)stability in 2HDMS vs N2HDM , 2408.13592

    arXiv

  6. [6]

    Barroso, P.M

    A. Barroso, P.M. Ferreira and R. Santos, Charge and CP symmetry breaking in two Higgs doublet models, Phys. Lett. B 632 (2006) 684 [ hep-ph/0507224]

    arXiv 2006

  7. [7]

    Barroso, P.M

    A. Barroso, P.M. Ferreira, I.P. Ivanov, R. Santos and J.P. Silva, Evading death by vacuum , Eur. Phys. J. C 73 (2013) 2537 [ 1211.6119]

    arXiv 2013

  8. [8]

    Barroso, P.M

    A. Barroso, P.M. Ferreira, I.P. Ivanov and R. Santos, Metastability bounds on the two Higgs doublet model, JHEP 06 (2013) 045 [ 1303.5098]

    arXiv 2013

Show all 72 references
  1. [9]

    Ivanov, Minkowski space structure of the Higgs potential in 2HDM , Phys

    I.P. Ivanov, Minkowski space structure of the Higgs potential in 2HDM , Phys. Rev. D 75 (2007) 035001 [ hep-ph/0609018]

    2007 arXiv

  2. [10]

    Branchina, F

    V. Branchina, F. Contino and P.M. Ferreira, Electroweak vacuum lifetime in two Higgs doublet models, JHEP 11 (2018) 107 [ 1807.10802]

    2018 arXiv

  3. [11]

    Ivanov, Minkowski space structure of the Higgs potential in 2HDM

    I.P. Ivanov, Minkowski space structure of the Higgs potential in 2HDM. II. Minima, symmetries, and topology , Phys. Rev. D 77 (2008) 015017 [ 0710.3490]

    2008 arXiv

  4. [12]

    Biek¨ otter, S

    T. Biek¨ otter, S. Heinemeyer, J.M. No, M.O. Olea and G. Weiglein, Fate of electroweak symmetry in the early Universe: Non-restoration and trapped vacua in the N2HDM , JCAP 06 (2021) 018 [ 2103.12707]

    2021 arXiv

  5. [13]

    Glaus, M

    S. Glaus, M. M¨ uhlleitner, J. M¨ uller, S. Patel and R. Santos,Electroweak corrections to dark matter direct detection in the dark singlet phase of the N2HDM , Phys. Lett. B 833 (2022) 137342 [2204.13145]

    2022 arXiv

  6. [14]

    Engeln, P

    I. Engeln, P. Ferreira, M.M. M¨ uhlleitner, R. Santos and J. Wittbrodt, The Dark Phases of the N2HDM , JHEP 08 (2020) 085 [ 2004.05382]

    2020 arXiv

  7. [15]

    Biek¨ otter, M

    T. Biek¨ otter, M. Chakraborti and S. Heinemeyer, A 96 GeV Higgs boson in the N2HDM , Eur. Phys. J. C 80 (2020) 2 [ 1903.11661]

    2020 arXiv

  8. [16]

    Biek¨ otter, S

    T. Biek¨ otter, S. Heinemeyer and G. Weiglein,Mounting evidence for a 95 GeV Higgs boson , JHEP 08 (2022) 201 [ 2203.13180]

    2022 arXiv

  9. [17]

    Heinemeyer, C

    S. Heinemeyer, C. Li, F. Lika, G. Moortgat-Pick and S. Paasch, Phenomenology of a 96 GeV Higgs boson in the 2HDM with an additional singlet , Phys. Rev. D 106 (2022) 075003 [2112.11958]. – 35 –

    2022 arXiv

  10. [18]

    ATLAS collaboration, Search for resonances in the 65 to 110 GeV diphoton invariant mass range using 80 fb −1 of pp collisions collected at √s = 13 TeV with the ATLAS detector ,

  11. [19]

    ATLAS collaboration, ATLAS searches for additional scalars and exotic Higgs boson decays with the LHC Run 2 dataset , 2405.04914

    arXiv

  12. [20]

    CMS collaboration, Search for a standard model-like Higgs boson in the mass range between 70 and 110 GeV in the diphoton final state in proton-proton collisions at √s = 8 and 13 TeV, Phys. Lett. B 793 (2019) 320 [ 1811.08459]

    2019 arXiv

  13. [21]

    CMS collaboration, Search for a standard model-like Higgs boson in the mass range between 70 and 110 GeV in the diphoton final state in proton-proton collisions at √s = 13 TeV , 2405.18149

    arXiv

  14. [22]

    Janot, The infamous 95 GeV b b excess at LEP: two b or not two b? , JHEP 10 (2024) 223 [2407.10948]

    P. Janot, The infamous 95 GeV b b excess at LEP: two b or not two b? , JHEP 10 (2024) 223 [2407.10948]

    2024 arXiv

  15. [23]

    LEP Working Group for Higgs boson searches, ALEPH, DELPHI, L3, OPAL collaboration, Search for the standard model Higgs boson at LEP , Phys. Lett. B 565 (2003) 61 [hep-ex/0306033]

    2003 arXiv

  16. [24]

    Branco, P.M

    G.C. Branco, P.M. Ferreira, L. Lavoura, M.N. Rebelo, M. Sher and J.P. Silva, Theory and phenomenology of two-Higgs-doublet models , Phys. Rept. 516 (2012) 1 [ 1106.0034]

    2012 arXiv

  17. [25]

    Kibble, Topology of Cosmic Domains and Strings , J

    T.W.B. Kibble, Topology of Cosmic Domains and Strings , J. Phys. A 9 (1976) 1387

    1976

  18. [26]

    Zeldovich, I.Y

    Y.B. Zeldovich, I.Y. Kobzarev and L.B. Okun, Cosmological Consequences of the Spontaneous Breakdown of Discrete Symmetry , Zh. Eksp. Teor. Fiz. 67 (1974) 3

    1974

  19. [27]

    Vilenkin, Cosmic strings and domain walls , Physics Reports 121 (1985) 263

    A. Vilenkin, Cosmic strings and domain walls , Physics Reports 121 (1985) 263

    1985

  20. [28]

    Vachaspati, Kinks and Domain Walls: An Introduction to Classical and Quantum Solitons, Cambridge University Press (2023), 10.1017/9781009290456

    T. Vachaspati, Kinks and Domain Walls: An Introduction to Classical and Quantum Solitons, Cambridge University Press (2023), 10.1017/9781009290456

    2023 doi

  21. [29]

    Dvali and G

    G.R. Dvali and G. Senjanovic, Is there a domain wall problem? , Phys. Rev. Lett. 74 (1995) 5178 [hep-ph/9501387]

    1995 arXiv

  22. [30]

    NANOGrav collaboration, The NANOGrav 15 yr Data Set: Evidence for a Gravitational-wave Background, Astrophys. J. Lett. 951 (2023) L8 [ 2306.16213]

    2023 arXiv

  23. [31]

    Gouttenoire and E

    Y. Gouttenoire and E. Vitagliano, Domain wall interpretation of the PTA signal confronting black hole overproduction , Phys. Rev. D 110 (2024) L061306 [ 2306.17841]

    2024 arXiv

  24. [32]

    Brandenberger, A.-C

    R.H. Brandenberger, A.-C. Davis, T. Prokopec and M. Trodden, Local and nonlocal defect mediated electroweak baryogenesis, Phys. Rev. D 53 (1996) 4257 [ hep-ph/9409281]

    1996 arXiv

  25. [33]

    Sassi and G

    M.Y. Sassi and G. Moortgat-Pick, Electroweak Symmetry Restoration in the N2HDM via Domain Walls , 2407.14468

    arXiv

  26. [34]

    Schr¨ oder and R

    T. Schr¨ oder and R. Brandenberger,Embedded Domain Walls and Electroweak Baryogenesis , 2404.13035

    arXiv

  27. [35]

    Azzola, O

    J. Azzola, O. Matsedonskyi and A. Weiler, Minimal Electroweak Baryogenesis via Domain Walls, 2412.10495

    arXiv

  28. [36]

    Vanvlasselaer, DW-genesis:generating the baryon number from domain walls , PoS DISCRETE2024 (2025) 012 [ 2501.00491]

    M. Vanvlasselaer, DW-genesis:generating the baryon number from domain walls , PoS DISCRETE2024 (2025) 012 [ 2501.00491]

    2025 arXiv

  29. [37]

    Blasi and A

    S. Blasi and A. Mariotti, Domain Walls Seeding the Electroweak Phase Transition , Phys. Rev. Lett. 129 (2022) 261303 [ 2203.16450]. – 36 –

    2022 arXiv

  30. [38]

    Agrawal, S

    P. Agrawal, S. Blasi, A. Mariotti and M. Nee, Electroweak phase transition with a double well done doubly well , JHEP 06 (2024) 089 [ 2312.06749]

    2024 arXiv

  31. [39]

    Fichet and P

    S. Fichet and P. Saraswat, Approximate Symmetries and Gravity , JHEP 01 (2020) 088 [1909.02002]

    2020 arXiv

  32. [40]

    Muhlleitner, M.O.P

    M. Muhlleitner, M.O.P. Sampaio, R. Santos and J. Wittbrodt, The N2HDM under Theoretical and Experimental Scrutiny , JHEP 03 (2017) 094 [ 1612.01309]

    2017 arXiv

  33. [41]

    M¨ uhlleitner, M.O.P

    M. M¨ uhlleitner, M.O.P. Sampaio, R. Santos and J. Wittbrodt, Phenomenological Comparison of Models with Extended Higgs Sectors , JHEP 08 (2017) 132 [ 1703.07750]

    2017 arXiv

  34. [42]

    C.-Y. Chen, M. Freid and M. Sher, Next-to-minimal two Higgs doublet model , Phys. Rev. D 89 (2014) 075009 [ 1312.3949]

    2014 arXiv

  35. [43]

    Gouttenoire, S.F

    Y. Gouttenoire, S.F. King, R. Roshan, X. Wang, G. White and M. Yamazaki, Cosmological Consequences of Domain Walls Biased by Quantum Gravity , 2501.16414

  36. [44]

    Roussy et al., An improved bound on the electron ’s electric dipole moment, Science 381 (2023) adg4084 [ 2212.11841]

    T.S. Roussy et al., An improved bound on the electron ’s electric dipole moment, Science 381 (2023) adg4084 [ 2212.11841]

    2023 arXiv

  37. [45]

    Chupp, P

    T. Chupp, P. Fierlinger, M. Ramsey-Musolf and J. Singh, Electric dipole moments of atoms, molecules, nuclei, and particles , Rev. Mod. Phys. 91 (2019) 015001 [ 1710.02504]

    2019 arXiv

  38. [46]

    Hollik, G

    W.G. Hollik, G. Weiglein and J. Wittbrodt, Impact of Vacuum Stability Constraints on the Phenomenology of Supersymmetric Models , JHEP 03 (2019) 109 [ 1812.04644]

    2019 arXiv

  39. [47]

    M¨ uhlleitner, M.O.P

    M. M¨ uhlleitner, M.O.P. Sampaio, R. Santos and J. Wittbrodt, ScannerS: parameter scans in extended scalar sectors, Eur. Phys. J. C 82 (2022) 198 [ 2007.02985]

    2022 arXiv

  40. [48]

    Basler, L

    P. Basler, L. Biermann, M. M¨ uhlleitner, J. M¨ uller, R. Santos and J.a. Viana,BSMPT v3 A Tool for Phase Transitions and Primordial Gravitational Waves in Extended Higgs Sectors , 2404.19037

    arXiv

  41. [49]

    Kolb and M.S

    E.W. Kolb and M.S. Turner, The Early Universe , vol. 69, Taylor and Francis (5, 2019), 10.1201/9780429492860

    2019 doi

  42. [50]

    Bittar, S

    P. Bittar, S. Roy and C.E.M. Wagner, Self Consistent Thermal Resummation: A Case Study of the Phase Transition in 2HDM , 2504.02024

  43. [51]

    Bechtle, D

    P. Bechtle, D. Dercks, S. Heinemeyer, T. Klingl, T. Stefaniak, G. Weiglein et al., HiggsBounds-5: Testing Higgs Sectors in the LHC 13 TeV Era , Eur. Phys. J. C 80 (2020) 1211 [2006.06007]

    2020 arXiv

  44. [52]

    Bechtle, S

    P. Bechtle, S. Heinemeyer, T. Klingl, T. Stefaniak, G. Weiglein and J. Wittbrodt, HiggsSignals-2: Probing new physics with precision Higgs measurements in the LHC 13 TeV era, Eur. Phys. J. C 81 (2021) 145 [ 2012.09197]

    2021 arXiv

  45. [53]

    Bechtle, S

    P. Bechtle, S. Heinemeyer, O. Stal, T. Stefaniak and G. Weiglein, Applying Exclusion Likelihoods from LHC Searches to Extended Higgs Sectors , Eur. Phys. J. C 75 (2015) 421 [1507.06706]

    2015 arXiv

  46. [54]

    Hunter, Matplotlib: A 2d graphics environment , Computing in Science & Engineering 9 (2007) 90

    J.D. Hunter, Matplotlib: A 2d graphics environment , Computing in Science & Engineering 9 (2007) 90

    2007

  47. [55]

    Harris, K.J

    C.R. Harris, K.J. Millman, S.J. van der Walt, R. Gommers, P. Virtanen, D. Cournapeau et al., Array programming with NumPy, Nature 585 (2020) 357–362

    2020

  48. [56]

    Schwartz, Quantum Field Theory and the Standard Model , Cambridge University Press (2013)

    M.D. Schwartz, Quantum Field Theory and the Standard Model , Cambridge University Press (2013). – 37 –

    2013

  49. [57]

    Gunion, H.E

    J.F. Gunion, H.E. Haber, G.L. Kane and S. Dawson, The Higgs Hunter’s Guide , vol. 80 (2000), 10.1201/9780429496448

    2000 doi

  50. [58]

    Coleman, Fate of the false vacuum: Semiclassical theory , Phys

    S. Coleman, Fate of the false vacuum: Semiclassical theory , Phys. Rev. D 15 (1977) 2929

    1977

  51. [59]

    Arnold and O

    P.B. Arnold and O. Espinosa, The Effective potential and first order phase transitions: Beyond leading-order, Phys. Rev. D 47 (1993) 3546 [ hep-ph/9212235]

    1993 arXiv

  52. [60]

    Coimbra, M.O.P

    R. Coimbra, M.O.P. Sampaio and R. Santos, ScannerS: Constraining the phase diagram of a complex scalar singlet at the LHC , Eur. Phys. J. C 73 (2013) 2428 [ 1301.2599]

    2013 arXiv

  53. [61]

    Ferreira, R

    P.M. Ferreira, R. Guedes, M.O.P. Sampaio and R. Santos, Wrong sign and symmetric limits and non-decoupling in 2HDMs , JHEP 12 (2014) 067 [ 1409.6723]

    2014 arXiv

  54. [62]

    Costa, M

    R. Costa, M. M¨ uhlleitner, M.O.P. Sampaio and R. Santos, Singlet Extensions of the Standard Model at LHC Run 2: Benchmarks and Comparison with the NMSSM , JHEP 06 (2016) 034 [ 1512.05355]

    2016 arXiv

  55. [63]

    Bechtle, O

    P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein and K.E. Williams, HiggsBounds: Confronting Arbitrary Higgs Sectors with Exclusion Bounds from LEP and the Tevatron , Comput. Phys. Commun. 181 (2010) 138 [ 0811.4169]

    2010 arXiv

  56. [64]

    Bechtle, O

    P. Bechtle, O. Brein, S. Heinemeyer, G. Weiglein and K.E. Williams, HiggsBounds 2.0.0: Confronting Neutral and Charged Higgs Sector Predictions with Exclusion Bounds from LEP and the Tevatron, Comput. Phys. Commun. 182 (2011) 2605 [ 1102.1898]

    2011 arXiv

  57. [65]

    Bechtle, O

    P. Bechtle, O. Brein, S. Heinemeyer, O. Stal, T. Stefaniak, G. Weiglein et al., Recent Developments in HiggsBounds and a Preview of HiggsSignals , PoS CHARGED2012 (2012) 024 [1301.2345]

    2012 arXiv

  58. [66]

    Bechtle, O

    P. Bechtle, O. Brein, S. Heinemeyer, O. St ˚ al, T. Stefaniak, G. Weiglein et al., HiggsBounds − 4: Improved Tests of Extended Higgs Sectors against Exclusion Bounds from LEP, the Tevatron and the LHC , Eur. Phys. J. C 74 (2014) 2693 [ 1311.0055]

    2014 arXiv

  59. [67]

    Bechtle, S

    P. Bechtle, S. Heinemeyer, O. St ˚ al, T. Stefaniak and G. Weiglein,HiggsSignals : Confronting arbitrary Higgs sectors with measurements at the Tevatron and the LHC , Eur. Phys. J. C 74 (2014) 2711 [ 1305.1933]

    2014 arXiv

  60. [68]

    St ˚ al and T

    O. St ˚ al and T. Stefaniak,Constraining extended Higgs sectors with HiggsSignals , PoS EPS-HEP2013 (2013) 314 [ 1310.4039]

    2013 arXiv

  61. [69]

    Bechtle, S

    P. Bechtle, S. Heinemeyer, O. St ˚ al, T. Stefaniak and G. Weiglein,Probing the Standard Model with Higgs signal rates from the Tevatron, the LHC and a future ILC , JHEP 11 (2014) 039 [ 1403.1582]

    2014 arXiv

  62. [70]

    Haller, A

    J. Haller, A. Hoecker, R. Kogler, K. M¨ onig, T. Peiffer and J. Stelzer, Update of the global electroweak fit and constraints on two-Higgs-doublet models , Eur. Phys. J. C 78 (2018) 675 [1803.01853]

    2018 arXiv

  63. [71]

    Particle Data Group Collaborationcollaboration, Review of particle physics , Phys. Rev. D 110 (2024) 030001

    2024

  64. [72]

    Grimus, L

    W. Grimus, L. Lavoura, O.M. Ogreid and P. Osland, A Precision constraint on multi-Higgs-doublet models, J. Phys. G 35 (2008) 075001 [ 0711.4022]. – 38 –

    2008 arXiv

Pith tools

Reviewed August 7, 2026 · model on record in the stance chip above.