Electroweak Baryogenesis: Advances in Sphaleron Rate Calculations and Implications of Thermal Phase Transitions

Yanda Wu

REVIEW 3 major objections 4 minor 297 references

Electroweak Baryogenesis: Advances in Sphaleron Rate Calculations and Implications of Thermal Phase Transitions

T0 review · 3 major / 4 minor · reviewed 2026-07-31 · deepseek-v4-flash

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

Pith's one-line read A gauge-invariant 3D EFT formalism for the sphaleron rate replaces the heuristic baryon-preservation criterion vc/Tc > 1 with a computable condition on x = λ₃/g₃², and constrains real-triplet extensions of the Standard Model.

desk verdict A serious thesis with a genuinely new 3D-EFT sphaleron-rate formalism and a plausible replacement for v/T, but the central first-order approximation is a fitted constant that needs independent confirmation before the x-criterion is trusted. read the letter →

arxiv 2607.24026 v1 pith:XGBD3C3T submitted 2026-07-27 hep-ph hep-th

Yanda Wu This is my paper · ORCID

classification hep-phhep-th

keywords electroweakbaryogenesissphaleronratethree-dimensionaleffectivefieldtheorydimensionalreductionbaryon-numberviolationfirst-orderphasetransitionprimordialblackholestopologicalconfigurations

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 thesis targets the washout problem in electroweak baryogenesis: after a first-order phase transition, sphaleron processes inside the broken-phase bubbles can erase the just-generated baryon asymmetry, and the usual practical criterion for stopping that — vc/Tc ≳ 1 — is both approximate and gauge-sensitive. The thesis develops a gauge-invariant formalism for the sphaleron rate in SU(2)+Higgs theory using three-dimensional thermal effective field theory, valid for first-order transitions and accurate to O(g⁴) in power counting, and shows that the baryon-preservation condition becomes a statement about the dimensionless ratio x = λ₃/g₃². A calibrated numerical approximation — the rescaled sphaleron action is essentially 29·v₃(x,y), with v₃ the gauge-invariant scalar minimum — turns the washout exponent into a computable quantity. Applying this to the real-triplet extension of the Standard Model yields large washout over much of the parameter space, strongly constraining the model; supplementary results extend sphaleron/monopole constructions to arbitrary SU(2) multiplets and link delayed phase transitions to primordial black hole production.

What carries the argument

The load-bearing object is the rescaled 3D sphaleron action S₃D = v₃(x,y)·C_sph(x,y), where v₃(x,y) is the minimizer of the leading-order scalar potential in the 3D EFT and x = λ₃/g₃², y = μ₃²/g₃⁴ are the two dimensionless parameters. Three ingredients carry the argument: soft-scale power counting (k ~ gT), which puts the sphaleron at a scale decoupled from bubble nucleation; kinetic dominance, the numerical result that C_sph(x,y) ≈ 29 is nearly constant across the (x,y) plane, so all parameter dependence enters through v₃(x,y); and normalization by g₃², which is positive-definite and gauge invariant, replacing the gauge-dependent v-normalization of earlier work. Gauge invariance to O(g⁴) re

What would settle it

A 3D lattice computation of the Chern–Simons diffusion rate in the first-order region (x ≲ 0.1, y > 0) would settle the claim: if the measured exponential suppression disagrees with exp(−29·v₃(x,y)) beyond the claimed O(g⁴) and prefactor uncertainties, kinetic dominance fails. A cheaper check is fully numerical — solve the full sphaleron equations with U(1) and A₀ modes included and verify that S₃D/v₃(x,y) stays within a few percent of 29 across the (x,y) region of interest; the thesis's own residual map shows where deviations already reach order one.

Watch

Extended reading notes

Core claim

The central claim is that the sphaleron rate during a first-order electroweak phase transition can be computed gauge-invariantly to O(g⁴) in the 3D EFT of SU(2)+Higgs theory, even though the barrier that sustains the transition comes from integrating out the spatial gauge fields. After rescaling by the gauge-invariant scalar minimum v₃(x,y), the sphaleron action is kinetic-dominated and well approximated by S₃D ≈ 29·v₃(x,y), with x = λ₃/g₃² and y = μ₃²/g₃⁴; the washout exponent is then integrated accurately, replacing vc/Tc ≳ 1 with a gauge-invariant condition on x. In the real-triplet extension, the resulting washout is large across most of the parameter space, strongly constraining such mo

Load-bearing premise

The computation treats the scalar potential as only a boundary-condition sector: the sphaleron action is approximated by its kinetic part, S₃D ≈ 29·v₃(x,y), on the numerical observation that 'the dominant contribution to the sphaleron action comes from the kinetic terms,' and the rate's dynamical prefactor is assumed (A_dyn ~ T) rather than computed — if kinetic dominance fails near the critical line or once U(1) and A₀ modes are added, the fitted constant and the x-criterion

Editorial extensions

If this is right

Baryon preservation after a first-order transition is decided by a gauge-invariant condition on x = λ₃/g₃², not by vc/Tc ≳ 1; washout exponents can be computed, so a model can overproduce the asymmetry via CP violation and then wash it down to the observed value.
The real-triplet extension of the Standard Model is strongly constrained: much of its parameter space exhibits large baryon washout, and consistent results require two-loop thermal matching of the 3D EFT parameters.
For a general SU(2) multiplet, nonzero hypercharge yields a sphaleron while zero hypercharge yields a monopole; the sphaleron one-form is representation-independent, and monopole masses can significantly exceed the SM sphaleron energy in two-step transitions, changing when baryon number can be violated.
A delayed first-order phase transition can produce primordial black holes with a relic abundance that is super-exponentially sensitive to phase-transition parameters (Eq. 7.22).
Collider searches for exotic Higgs decays at future lepton colliders can indirectly probe the strong first-order phase transition required by electroweak baryogenesis, covering a large portion of the relevant parameter space.

Reading between the lines

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

If kinetic dominance survives the inclusion of U(1) and A₀ modes, the S₃D ≈ 29·v₃(x,y) approximation is portable: any BSM model that maps onto the same SU(2)+Higgs 3D EFT gets a nearly parameter-free washout computation, reducing electroweak baryogenesis to a scan over x and the CP source.
A sharp, testable extension would be a 3D lattice measurement of the Chern-Simons diffusion rate in the first-order region (x ≲ 0.1, y > 0): agreement with exp(−29·v₃(x,y)) would substantiate the whole procedure, while the fit residuals the thesis itself reports near the critical line mark where the approximation is most exposed.
The monopole results suggest a concrete two-step chronology: an asymmetry generated during an intermediate monopole phase could be preserved by a heavy monopole mass, only to face full sphaleron washout in the second, Higgs-breaking step — a sequence the thesis's washout formalism makes computable for specific models.
Taking the thesis at its word, the baryon asymmetry becomes a computable function of 3D EFT parameters rather than a heuristic threshold; this implies EWBG model building can be inverted — fixing x and the CP-violating couplings from the observed asymmetry — a shift that would sharpen collider targets.

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

Here's the one thing to know about arXiv:2607.24026: it's a PhD thesis, and the real content is the gauge-invariant 3D-EFT formalism for sphaleron rates in first-order transitions, which replaces the old v_c/T_c > 1 rule with a criterion on x = lambda_3/g_3^2. The idea is sensible and the benchmark against lattice for the SM crossover looks reasonable. The general-J Wigner-D construction of the sphaleron matrix and the explicit representation-independence check of the one-form are new and solid, and the paper is unusually honest about its own gaps: it flags the superseded PBH analysis, corrects a sign error, and states where quantities are assumed rather than derived.

The soft spot is the first-order action itself. Sections 6.1–6.2 reduce the full sphaleron action to S3D ~ 29 v3(x,y), i.e. a calibrated constant times the cubic-potential minimum. The justification is that the kinetic terms dominate and the potential only sets boundary conditions. That is a numerical observation, not a controlled expansion; the sphaleron is a non-trivial gauge-field configuration, and the same spatial gauge fields being integrated out to generate the cubic term are retained in the kinetic action. There's no explicit small parameter. The residuals in Fig. 16 range over roughly -1.8 to +2.1 in Csph; a 7% action shift changes exp(-S3D/T) by a factor ~e^{-2}, and that can move the washout exponent and the x-criterion materially. The U(1) and A0 modes are also dropped. So the claim of O(g4) gauge invariance is credible for the crossover case, but for first-order transitions the accuracy of the end result is not established.

The second gap: Adyn ~ T is assumed on dimensional grounds, not computed. That's a known limitation and the thesis says so, but it means the absolute rate normalization retains an unknown O(1) factor.

The real-triplet extension in Sec. 6.6 inherits this S3D, so the strong washout constraint is directionally plausible but not a sharp bound at the claimed precision. No code or data is shipped, so the fits can't be independently checked from this text.

Who should read it: anyone working on electroweak baryogenesis washout, or on sphaleron rates for BSM scalar extensions. The pedagogical chapters are useful for students. It deserves a serious referee; my recommendation would be to engage with it, but require an independent numerical check of Csph and a clearer statement of the domain of validity of the 29 v3 approximation before the x-criterion is used for parameter scans.

Referee Report

3 major / 4 minor

Summary. This is a PhD-thesis-style manuscript addressing electroweak baryogenesis, focused on two claims: (i) a gauge-invariant 3D EFT formalism for the sphaleron rate in SU(2)+Higgs theory, claimed to be gauge invariant under power counting up to O(g^4); and (ii) a replacement of the traditional baryon-preservation criterion vc/Tc ≳ 1 by a new gauge-invariant criterion on x = λ3/g3^2 (Secs. 1.1, 6.1–6.2, 6.5.2). The central quantitative step is the calibrated fit S3D ≈ 29 v3(x,y) (Eq. 6.27), where v3 is the minimum of the effective cubic potential (6.12)/(6.15); the kinetic-dominance argument justifies using the potential only for boundary conditions, and the fit is validated numerically over the (x,y)-plane in Fig. 16. The dynamical prefactor Adyn is assumed to be ~T on dimensional grounds (Sec. 6.1). The formalism is benchmarked against the SM crossover lattice rate (Fig. 17) and applied to the real-triplet extension, yielding strong washout constraints (Sec. 6.6.2). Additional contributions include the general-SU(2)-multiplet sphaleron/monopole classification and construction (Sec. 3.4), monopole-catalyzed BNV (Sec. 4.3), PBH production from delayed transitions (Sec. 7.1), and CEPC collider probes (Sec. 7.2). A large fraction of the manuscript is pedagogical review.

Significance. If the central claims hold, the manuscript supplies a formal, gauge-invariant replacement for the heuristic vc/Tc criterion and a concrete phenomenological output — the real-triplet exclusion from washout. The checkable strengths are real: the general-multiplet construction is verified for J ∈ {1,3/2,2,5/2,3}; the SM crossover benchmark agrees with lattice (Fig. 17); the calibrated fit (6.27) is validated over a stated parameter region; and the main approximations (Adyn, U(1)/A0 omission, the sign correction in footnote 37) are disclosed in the text rather than hidden. The contribution is conditional: the fitted-action residual (±6–7% if the Fig. 16 colorbar is in units of Csph ≈ 29) and the assumed prefactor both enter the washout exponent, and the manuscript does not yet translate them into an uncertainty on the x-criterion. Because the judgment 'this model is excluded by washout' depends on that translation, the quantitative significance is not yet fully established.

major comments (3)

[Sec. 6.2.2 (Eq. 6.27; Fig. 16)] The x-criterion of Sec. 6.5.2 and the real-triplet constraints of Sec. 6.6.2 inherit the calibrated approximation S3D ≈ 29 v3(x,y). The bottom row of Fig. 16 reports 'fit − exact' residuals spanning about −1.78 to 2.07 over the (x,y) plane, but the caption does not state the plotted units or the location of the critical line y_c(x). If these are units of Csph (≈29), the residual is ~±6–7% in the washout exponent; since the rate is exponential in S3D, this shifts the decoupling temperature and the derived x-criterion by an amount comparable to the criterion's discriminating power. Please state the units, report the residual in physical units of ΔS3D/T over the washout-relevant region (including near y_c(x), where the cubic term matters most), and propagate it into the baryon-preservation boundary (Fig. 18) and the triplet exclusion — or moderate the precision claim. The disclosed U(1)Y an
[Sec. 6.1 (Eq. 6.1)] The decomposition Γsph = Adyn × Astatic with Adyn ~ T assumed on dimensional grounds is disclosed explicitly, and I credit the disclosure. Nevertheless, the abstract and Sec. 1.1 present the washout computation as quantitative ('the washout can be computed precisely'). The prefactor enters the washout condition Γsph ≈ H only logarithmically (ln(Adyn/H) = S3D), so an O(1) coefficient error in Adyn shifts the required action by O(1) — smaller than, but comparable to, the Fig. 16 residual effect. Please quote the resulting uncertainty in the decoupling temperature and in the x-criterion, or state explicitly that the criterion controls only the exponential part of the rate.
[Sec. 1.1; Sec. 6.2.2] The Introduction's second bullet can be read as attributing O(g4) accuracy to the full first-order-transition sphaleron rate. The gauge-invariance-under-power-counting property is established for the 3D EFT matching (Sec. 5.3), not for the calibrated fit (6.27) or the assumed prefactor in Sec. 6.1. Please add a sentence distinguishing the power-counting property of the EFT from the numerical accuracy of the FOPT action fit, so that the 'new gauge-invariant criterion' is presented with an explicit accuracy statement rather than an implicit O(g4) one.

minor comments (4)

[Fig. 16] Label the colorbar units of the residual panel, and overlay the critical line y_c(x) so the washout-relevant region is identifiable.
[Sec. 5.3.1, footnote 37] The sign correction relative to Ref. [263] is welcome, but please show the corrected derivation or state explicitly that the matching result for λ3 in Eq. (5.34) is unchanged by the correction.
[Sec. 6.1 (Eq. 6.7)] Notation: the parameter x = λ3/g3^2 is also used for a spatial coordinate in Chs. 3–4, and y (mass parameter) clashes with hypercharge Y in Sec. 3.4. Please use a distinct font or symbol in the published version.
[Sec. 4.2.1 (Eq. 4.38)] The heuristic Γsph ~ T^4 exp(−Esph/T) is a pedagogical scaling estimate; please state explicitly that it is superseded by the 3D EFT computation of Sec. 6 and does not determine the prefactor.

Circularity Check

0 steps flagged · score 0.0 of 10

No circular reduction found; the sphaleron-rate derivation is internally computed and benchmarked against lattice results.

full rationale

The central chain is: 3D EFT action (6.2), dimensionless rescaling, numerical solution of the sphaleron equations (6.21)-(6.22), the numerically observed near-constancy of C_sph leading to the fit S_3D ≈ 29 v3(x,y) (6.27), and validation against the full numerical action (Fig. 16) and the lattice SM sphaleron rate (Fig. 17). The parameter x = λ3/g3^2 is an EFT input, not defined in terms of the washout result; the washout condition is obtained by exponentiating the computed action. Citations to Refs. [94] and [230] are disclosed reproductions of the author's own prior work, but the thesis reproduces the scaling derivation, equations of motion, numerical fits, and benchmarks rather than relying on an unverified self-citation as the sole support. The paper itself flags genuine limitations: 'we assume Adyn ∼ T on dimensional grounds' (Sec. 6.1) and questions whether it is legitimate to integrate out the spatial gauge fields (Sec. 6.1). These are correctness/robustness concerns, not circular reductions: they do not make the predicted washout equal to the input by construction. No step was found in which a quantity defined in terms of the target result is later presented as a prediction of that target.

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

Central claims rest on (i) numerical fits carrying the washout predictions (Eqs. 6.25-6.27); (ii) standard 3D-EFT matching assumptions, including gauge invariance to O(g4), integration of A0 as a heavy mode, and the assumed Adyn ~ T; (iii) an ansatz whose representation-independence is verified only up to J=3. No new particles, forces, or dimensions are introduced; the monopole/sphaleron configurations are standard topological objects extended to general SU(2) representations. The thesis's benchmark numbers (Bsph ~ 1.9, Bmon = 5.001145, Figs. 17-20) are reproduced from the author's own prior papers, so their independence from this manuscript is limited.

free parameters (4)

Csph fit constants (A, B, C, D) = A = 26.12, B = -2.145, C = 0.4237, D = 0.00717
Eqs. (6.25)-(6.26): four constants fitted to numerically computed sphaleron actions for the second-order (crossover) case; this fit supplies the action used in the SM-crossover benchmark and in washout estimates.
FOPT action proportionality constant (the '29' in S_3D ~ 29*v3) = 29
Eq. (6.27): the first-order-transition sphaleron action is approximated as 29*v3(x,y), calibrated to the numerical action over a scan in (x,y). This is load-bearing for all FOPT washout rates and the x-criterion.
Monopole BNV cross-section constant c = unspecified
Eq. (4.55): sigma_{DeltaB!=0} ~ v^{-1} c / E_f^2 inherits an undetermined constant from Ref. [434]; quoted, not fitted here, but it normalizes the monopole-catalyzed washout channel.
Dynamical rate prefactor Adyn = ~ T (assumed)
Sec. 6.1, Eq. (6.1): 'we assume Adyn ~ T on dimensional grounds, and focus on the static part Astatic.' This assumption sets the absolute normalization of every sphaleron rate in the framework.

assumptions (5)

standard math Standard homotopy results: pi_n(S^n) = Z, pi_n(S^m) = 0 for n < m, pi_2(G/H) = pi_1(H), pi_n(Maps_0(S^q -> S^m)) = pi_{n+q}(S^m)
Sec. 3.1 uses these to classify strings, monopoles, sphalerons, instantons; proofs are deferred ('The proof ... lies beyond the scope of this thesis', Refs. [385, 388]).
domain assumption Sphaleron dynamics is captured by the zero-Matsubara 3D EFT with O(g4)-matched couplings, and the temporal gauge field A0 is parametrically heavier than the sphaleron scale so it can be integrated out
Sec. 5.2 Table 2 and footnote 38: the whole rate computation lives in the 3D EFT; if the scale separation fails near the transition, the dimensional reduction and the computed rates are invalid.
domain assumption Static/dynamic factorization of the sphaleron rate with Adyn ~ T
Sec. 6.1, Eq. (6.1): the dynamical part is assumed on dimensional grounds; only the static part is computed.
domain assumption Kinetic terms dominate the sphaleron action, so the detailed scalar potential only sets boundary conditions through v3; this justifies integrating out spatial gauge fields in the first-order case
Sec. 6.1 (after Eq. 6.9) and Sec. 6.2.2: the author explicitly raises 'whether it is legitimate to integrate out the spatial gauge fields' and justifies it numerically; this is load-bearing for Eq. (6.27).
domain assumption The sphaleron ansatz with radial profiles (f, f3, f0, h) and representation-independent one-forms Fa
Eqs. (3.74)-(3.77), (3.92)-(3.95): standard Manton-Klinkhamer ansatz assumed; representation independence of Fa is explicitly checked only for J in {1, 3/2, 2, 5/2, 3}, not proven for all J.

how reviews work

0 comments

Cite this review

Pith. "Pith review of Electroweak Baryogenesis: Advances in Sphaleron Rate Calculations and Implications of Thermal Phase Transitions." pith.science (2026). https://pith.science/paper/XGBD3C3T

@misc{pith2026260724026,
  author       = {Pith},
  title        = {Pith review of: Electroweak Baryogenesis: Advances in Sphaleron Rate Calculations and Implications of Thermal Phase Transitions},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/XGBD3C3T}},
  note         = {Machine review of arXiv:2607.24026}
}

read the original abstract

This thesis reviews recent advances in calculating the sphaleron rate, with particular emphasis on electroweak baryogenesis. It also provides pedagogical introductions to sphaleron- and instanton-induced baryon-number violation, the vacuum structure of non-Abelian gauge theories, and other topological field configurations, and suggests "an zi" as a possible Chinese term for "sphaleron" (see p. 3). Broader implications of first-order phase transitions for collider searches and primordial black hole formation are also discussed.

Figures

Figures reproduced from arXiv: 2607.24026 by the authors.

**Figure 1.** Visualization of the homotopy group π1(S 1 ). The black circle represents the target space S 1 , and the pink curve represents a map from the domain S 1 to the target S 1 . The black dot at the bottom of the circle denotes the base point. Panel (a) is homotopic to the trivial map and therefore corresponds to the identity element 0 in π1(S 1 ). Panels (b) and (c) are homotopic to each other and correspond to the elem… view at source ↗

**Figure 2.** Visualization of the homotopy group π1(S 2 ). The blue sphere represents the target space S 2 , and the pink curve represents a map from S 1 to S 2 . The black dot on the sphere denotes the base point. All panels (a), (b), (c), and (d) are homotopic to each other, since each pink curve can be continuously deformed to the trivial map. They therefore all correspond to the same element 0 in the group π1(S 2 ). Hence, π… view at source ↗

**Figure 3.** Visualization of the homotopy group π1(Maps0 (S 1 → S 2 )). Here the target space is the space of maps from S 1 to S 2 , represented by the colored loops on the blue sphere. Although each individual loop is contractible to the base point, all loops together need not be simultaneously contractible. This configuration corresponds to the element 1 in the homotopy group π1(Maps0 (S 1 → S 2 )). provided that G is connect… view at source ↗

Figures from the paper (27 more)

**Figure 4.** Figure 4: Sphaleron radial-profile solutions for the pure Standard Model. The horizontal axis denotes the dimensionless radial coordinate ξ ≡ gΩr, with Ω = 246 GeV and g the SU(2) gauge coupling. This figure is reproduced from Ref. [94]. multiplet with the largest dimension sati…

**Figure 5.** Figure 5: Schematic illustration of the three scenarios for the electroweak phase transition. In each panel, the horizontal axis represents the Higgs field, while the vertical axis represents the septuplet field. Panel (a) represents the one-step phase transition from the symmet…

**Figure 6.** Figure 6: Radial profile functions when only the septuplet obtains a vev during a two-step EWPT, for v = 0 GeV, vϕ = 500 GeV, λ13 = 0.05, and λs = 0.005. At this stage, the Higgs profile does not appear because its vev vanishes, and the monopole-mass value is Bmon = 5.001145. Th…

**Figure 7.** Figure 7: Monopole mass Bmon when only the septuplet obtains a vev during a two-step EWPT. The horizontal axis is the septuplet vev vϕ in GeV, and the vertical axis is Bmon. The viable monopole-mass region is the part of the orange band to the right of the dashed vertical line a…

**Figure 8.** Figure 8: Illustration of the spacetime structure as a cylinder. Each horizontal slice represents a spatial slice at fixed time, while the vertical direction corresponds to imaginary time. The spatial boundary at infinity (|x| = R with R → ∞), together with the imaginarytime di…

**Figure 9.** Figure 9: Comparison of the instanton and sphaleron mechanisms for baryon-number violation. (a) Instanton mechanism: quantum tunneling from the vacuum with Chern-Simons number j = 1 to the vacuum with Chern-Simons number j = 2. (b) Sphaleron mechanism: thermal transition over t…

**Figure 10.** Figure 10: Finite-temperature barrier crossing in one-dimensional quantum mechanics with a double-well potential. According to the WKB approximation in quantum mechanics, the tunneling amplitude is dominated by the exponential of the Euclidean action. Therefore, the leading-orde…

**Figure 11.** Figure 11: Schematic stages of electroweak baryogenesis: (i) a first-order phase transition proceeds through bubble nucleation from the false vacuum to the true vacuum; (ii) CPviolating interactions with the expanding wall generate a nonzero left-handed fermion density; (iii) i…

**Figure 12.** Figure 12: One-loop diagrams for the two-point Green’s function of the scalar field that contribute to scalar wave-function renormalization. The dashed, wavy, and solid lines denote the scalar, gauge, and fermion fields, respectively. The first two diagrams arise from the non-ze…

**Figure 13.** Figure 13: Hierarchy of thermal scales together with the corresponding sphaleron and bubblenucleation processes. [264, 268], where x = λ3/g 2 3 . This ultrasoft scale is also the characteristic scale of a firstorder phase transition. Note that the static spatial gauge fields a…

**Figure 14.** Figure 14: Phase diagram in the x-y plane, with x and y defined in Eq. (6.7). The blue line denotes the critical-temperature line, which is very close to the nucleation-temperature line when the phase transition does not involve significant supercooling. As the temperature decre…

**Figure 15.** Figure 15: Rescaled sphaleron action Csph as a function of x. The black points show the exact numerical values of Csph, while the red curve shows the fit in Eq. (6.25). The agreement is so good that the two are nearly indistinguishable. The dashed curves indicate the separate c…

**Figure 16.** Figure 16: Top row: v3-rescaled sphaleron action for the cubic potential. Left: Csph as a function of x at fixed y = 0.008. The red curve shows the total action, the magenta curve shows the combined Yang–Mills and covariant-derivative contributions, and the orange curve shows th…

**Figure 17.** Figure 17: Sphaleron rate for the Standard Model crossover. The blue curve shows the LO sphaleron rate in Eq. (6.52), while the red curve shows the NLO sphaleron rate in Eq. (6.53), including the zero-mode contribution. The black curve is the lattice result from Ref. [250], and …

**Figure 18.** Figure 18: Phase-transition diagram and sphaleron-decoupling line in the (x, y) plane. The solid blue and dashed red curves denote the critical- and nucleation-temperature lines, respectively. The black dash-dotted curve marks sphaleron decoupling, defined by ΓB = H. As the Uni…

**Figure 19.** Figure 19: Phase structure and baryon-number preservation condition in the (a2, MΣ) plane from the one-loop result for λ3 in the ΣSM. The solid black line denotes µ 2 Σ = 0. Below this line, µ 2 Σ > 0, where our EFT is valid; the white region corresponds to µ 2 Σ < 0, where our …

**Figure 20.** Figure 20: Phase structure and baryon-number preservation condition in the (a2, MΣ) plane from the two-loop result for λ3 in the ΣSM. The meaning of the different color regions is the same as in the one-loop result shown in [PITH_FULL_IMAGE:figures/full_fig_p122_20.png]

**Figure 21.** Figure 21: Illustration of PBH production from a delayed first-order phase transition. The blue (green) background represents the false (true) vacuum, as shown in the left panel of the effective potential. The true-vacuum regions arise from bubble nucleation, as indicated by the…

**Figure 22.** Figure 22: fpbh as a function of µ3 for the benchmark points listed in [PITH_FULL_IMAGE:figures/full_fig_p131_22.png]

**Figure 23.** Figure 23: Feynman diagram for e +e − → Zh2, followed by Z → ℓ +ℓ − (ℓ = e, µ), h2 → h1h1, and h1 → b ¯b, giving the final state ℓ +ℓ −b ¯bb¯b . and SM-Higgs-like mass eigenstates, respectively. This implies that we take m2 ≈ 125 GeV. We also take cos θ = 0.01 as our benchmark c…

**Figure 24.** Figure 24: The vertical axis shows the scaled branching ratio Br(h2 → h1h1), and the horizontal axis shows the mass of the singlet-like scalar eigenstate h1. The black dotted curve gives the expected BDT sensitivity, with the 1σ and 2σ uncertainty bands shown in yellow and green…

**Figure 25.** Figure 25: Triangle diagrams for π 0 → γγ. The dashed, solid, and wavy lines denote the pion, proton, and photon fields, respectively. Panels (a1) and (a2) contribute to T µν in Eq. (A.6), while panels (b1)–(b4) contribute to T ρµν in Eq. (A.9). The crossed vertex denotes the in…

**Figure 26.** Figure 26: Triangle diagram (b1) of [PITH_FULL_IMAGE:figures/full_fig_p151_26.png]

**Figure 27.** Figure 27: Three example potentials, with the minima normalized to V = 0. (a) A quadratic potential centered at x = 0. (b) A double-well potential with minima at x = ±a. (c) A periodic potential with multiple minima at x = na for integer n. 155 [PITH_FULL_IMAGE:figures/full_fig…

**Figure 28.** Figure 28: Instanton-like trajectory interpolating from x = −a to x = a in imaginary time (blue solid curve). The red dashed curve shows the anti-instanton trajectory interpolating from x = a to x = −a. (ii) For the double-well potential in [PITH_FULL_IMAGE:figures/full_fig_p15…

**Figure 29.** Figure 29: Two example instanton/anti-instanton configurations contributing to the amplitude ⟨jf = 2|e −Hτ |ji = 0⟩ in the periodic potential, where the initial minimum is at ji = 0 (green point) and the final minimum is at jf = 2 (orange point). (a) Two instantons, 2n. (b) Thr…

**Figure 30.** Figure 30: Instanton-induced baryon number violation in the Standard Model. The JB and JL denote the baryon and lepton sources, respectively. For each quark and lepton, the upper index r denotes the QCD color, and the lower index L and R denote the chirality. Each baryonic sourc…

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

297 extracted references · 21 canonical work pages

[1]

A Saddle Point Solution in the Weinberg-Salam Theory

F. R. Klinkhamer and N. S. Manton. “A Saddle Point Solution in the Weinberg-Salam Theory”. In: Phys. Rev. D 30 (1984), p. 2212. doi: 10.1103/PhysRevD.30.2212

doi:10.1103/physrevd.30.2212 1984
[2]

Topology in the Weinberg-Salam Theory

N. S. Manton. “Topology in the Weinberg-Salam Theory”. In: Phys. Rev. D 28 (1983), p. 2019. doi: 10.1103/PhysRevD.28.2019

doi:10.1103/physrevd.28.2019 1983
[3]

Recent progress in baryogenesis

A. Riotto and M. Trodden. “Recent progress in baryogenesis”. In: Ann. Rev. Nucl. Part. Sci. 49 (1999), pp. 35–75. doi: 10 . 1146 / annurev . nucl . 49 . 1 . 35. arXiv: hep-ph/9901362

arXiv 1999
[4]

The Origin of the matter - antimatter asymmetry

M. Dine and A. Kusenko. “The Origin of the matter - antimatter asymmetry”. In: Rev. Mod. Phys. 76 (2003), p. 1. doi: 10.1103/RevModPhys.76.1. arXiv: hep-ph/0303065

arXiv 2003
[5]

Baryogenesis from the weak scale to the grand unifi- cation scale

D. Bodeker and W. Buchmuller. “Baryogenesis from the weak scale to the grand unifi- cation scale”. In: Rev. Mod. Phys. 93.3 (2021), p. 035004. doi: 10.1103/RevModPhys. 93.035004. arXiv: 2009.07294 [hep-ph]

arXiv 2021
[6]

Planck 2018 results. VI. Cosmological parameters

N. Aghanim et al. “Planck 2018 results. VI. Cosmological parameters”. In: Astron. Astrophys. 641 (2020). [Erratum: Astron.Astrophys. 652, C4 (2021)], A6. doi: 10 . 1051/0004-6361/201833910. arXiv: 1807.06209 [astro-ph.CO]

arXiv 2018
[7]

Big-Bang Nucleosynthesis after Planck

B. D. Fields, K. A. Olive, T.-H. Yeh, and C. Young. “Big-Bang Nucleosynthesis after Planck”. In: JCAP 03 (2020). [Erratum: JCAP 11, E02 (2020)], p. 010. doi: 10.1088/ 1475-7516/2020/03/010. arXiv: 1912.01132 [astro-ph.CO]

arXiv 2020
[8]

A Matter - antimatter universe?

A. G. Cohen, A. De Rujula, and S. L. Glashow. “A Matter - antimatter universe?” In: Astrophys. J. 495 (1998), pp. 539–549. doi: 10 . 1086 / 305328. arXiv: astro - ph/9707087

arXiv 1998

Show all 297 references

[9]

Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe

A. D. Sakharov. “Violation of CP Invariance, C asymmetry, and baryon asymmetry of the universe”. In: Pisma Zh. Eksp. Teor. Fiz. 5 (1967), pp. 32–35. doi: 10.1070/ PU1991v034n05ABEH002497. 192

1967
[10]

On the Anomalous Elec- troweak Baryon Number Nonconservation in the Early Universe

V. A. Kuzmin, V. A. Rubakov, and M. E. Shaposhnikov. “On the Anomalous Elec- troweak Baryon Number Nonconservation in the Early Universe”. In: Phys. Lett. B 155 (1985), p. 36. doi: 10.1016/0370-2693(85)91028-7

1985 doi
[11]

Baryogenesis Without Grand Unification

M. Fukugita and T. Yanagida. “Baryogenesis Without Grand Unification”. In: Phys. Lett. B 174 (1986), pp. 45–47. doi: 10.1016/0370-2693(86)91126-3

1986 doi
[12]

A New mechanism for baryogenesis in low- energy supersymmetry breaking models

R. H. Brandenberger and A. Riotto. “A New mechanism for baryogenesis in low- energy supersymmetry breaking models”. In: Phys. Lett. B 445 (1999), pp. 323–330. doi: 10.1016/S0370-2693(98)01448-8. arXiv: hep-ph/9801448

1999 arXiv
[13]

Thermodynamic Generation of the Baryon Asymme- try

A. G. Cohen and D. B. Kaplan. “Thermodynamic Generation of the Baryon Asymme- try”. In: Phys. Lett. B 199 (1987), pp. 251–258. doi: 10.1016/0370-2693(87)91369- 4

1987 doi
[14]

SPONTANEOUS BARYOGENESIS

A. G. Cohen and D. B. Kaplan. “SPONTANEOUS BARYOGENESIS”. In: Nucl. Phys. B 308 (1988), pp. 913–928. doi: 10.1016/0550-3213(88)90134-4

1988 doi
[15]

Grav- itational baryogenesis

H. Davoudiasl, R. Kitano, G. D. Kribs, H. Murayama, and P. J. Steinhardt. “Grav- itational baryogenesis”. In: Phys. Rev. Lett. 93 (2004), p. 201301. doi: 10 . 1103 / PhysRevLett.93.201301. arXiv: hep-ph/0403019

2004 arXiv
[16]

A New Mechanism for Baryogenesis

I. Affleck and M. Dine. “A New Mechanism for Baryogenesis”. In: Nucl. Phys. B 249 (1985), pp. 361–380. doi: 10.1016/0550-3213(85)90021-5

1985 doi
[17]

E. W. Kolb and M. S. Turner. The Early Universe . Vol. 69. Taylor and Francis, May
[18]

Resonant leptogenesis

A. Pilaftsis and T. E. J. Underwood. “Resonant leptogenesis”. In: Nucl. Phys. B 692 (2004), pp. 303–345. doi: 10. 1016 / j . nuclphysb . 2004 . 05. 029. arXiv: hep- ph/0309342

2004
[19]

Axiogenesis

R. T. Co and K. Harigaya. “Axiogenesis”. In: Phys. Rev. Lett. 124.11 (2020), p. 111602. doi: 10.1103/PhysRevLett.124.111602. arXiv: 1910.02080 [hep-ph]

2020 arXiv
[20]

Baryogenesis from Hawking Radiation

A. Hook. “Baryogenesis from Hawking Radiation”. In: Phys. Rev. D 90.8 (2014), p. 083535. doi: 10.1103/PhysRevD.90.083535. arXiv: 1404.0113 [hep-ph] . 193

2014 arXiv
[21]

Baryogenesis and Dark Matter from B Mesons

G. Elor, M. Escudero, and A. Nelson. “Baryogenesis and Dark Matter from B Mesons”. In: Phys. Rev. D 99.3 (2019), p. 035031. doi: 10.1103/PhysRevD.99.035031. arXiv: 1810.00880 [hep-ph]

2019 arXiv
[22]

Peccei-Quinn Genesis

E. J. Chun, H. M. Lee, and J.-H. Song. “Peccei-Quinn Genesis”. In: (Dec. 2025). arXiv: 2512.12637 [hep-ph]

2025
[23]

New Ideas in Baryogenesis: A Snowmass White Paper

G. Elor et al. “New Ideas in Baryogenesis: A Snowmass White Paper”. In: Snowmass
[24]

Electroweak baryogenesis

D. E. Morrissey and M. J. Ramsey-Musolf. “Electroweak baryogenesis”. In: New J. Phys. 14 (2012), p. 125003. doi: 10.1088/1367-2630/14/12/125003 . arXiv: 1206. 2942 [hep-ph]

2012 doi
[25]

Progress in electroweak baryogenesis

A. G. Cohen, D. B. Kaplan, and A. E. Nelson. “Progress in electroweak baryogenesis”. In: Ann. Rev. Nucl. Part. Sci. 43 (1993), pp. 27–70. doi: 10.1146/annurev.ns.43. 120193.000331. arXiv: hep-ph/9302210

1993
[26]

Baryogenesis

J. M. Cline. “Baryogenesis”. In: Les Houches Summer School - Session 86: Particle Physics and Cosmology: The Fabric of Spacetime . Sept. 2006. arXiv: hep-ph/0609145

2006 arXiv
[27]

Quantum Transport and Electroweak Baryogenesis

T. Konstandin. “Quantum Transport and Electroweak Baryogenesis”. In: Phys. Usp. 56 (2013), pp. 747–771. doi: 10.3367/UFNe.0183.201308a.0785 . arXiv: 1302.6713 [hep-ph]

2013
[28]

Why is there more matter than antimatter? Calculational methods for leptogenesis and electroweak baryogenesis

B. Garbrecht. “Why is there more matter than antimatter? Calculational methods for leptogenesis and electroweak baryogenesis”. In: Prog. Part. Nucl. Phys. 110 (2020), p. 103727. doi: 10.1016/j.ppnp.2019.103727. arXiv: 1812.02651 [hep-ph]

2020
[29]

A Pedagogical Introduction to Electroweak Baryogenesis

G. A. White. “A Pedagogical Introduction to Electroweak Baryogenesis”. In: (Nov. 2016). doi: 10.1088/978-1-6817-4457-5

2016 doi
[30]

Bubble Trouble: a Review on Electroweak Baryogenesis

J. van de Vis, J. de Vries, and M. Postma. “Bubble Trouble: a Review on Electroweak Baryogenesis”. In: (Aug. 2025). arXiv: 2508.09989 [hep-ph]

2025 arXiv
[31]

Electroweak Baryogenesis with BARYONET: a self-contained review of the WKB approach

G. Barni. “Electroweak Baryogenesis with BARYONET: a self-contained review of the WKB approach”. In: (Oct. 2025). arXiv: 2510.21915 [hep-ph] . 194

2025
[32]

Electroweak baryogenesis with electroweak strings

R. H. Brandenberger and A.-C. Davis. “Electroweak baryogenesis with electroweak strings”. In: Phys. Lett. B 308 (1993), pp. 79–84. doi: 10.1016/0370-2693(93)90604- G. arXiv: astro-ph/9206001

1993 arXiv
[33]

Cosmic strings and electroweak baryogenesis

R. H. Brandenberger, A.-C. Davis, and M. Trodden. “Cosmic strings and electroweak baryogenesis”. In: Phys. Lett. B 335 (1994), pp. 123–130. doi: 10 . 1016 / 0370 - 2693(94)91402-8. arXiv: hep-ph/9403215

1994 arXiv
[34]

Particle physics models, topo- logical defects and electroweak baryogenesis

M. Trodden, A.-C. Davis, and R. H. Brandenberger. “Particle physics models, topo- logical defects and electroweak baryogenesis”. In: Phys. Lett. B 349 (1995), pp. 131–

1995
[35]

Local and nonlocal defect mediated electroweak baryogenesis

R. H. Brandenberger, A.-C. Davis, T. Prokopec, and M. Trodden. “Local and nonlocal defect mediated electroweak baryogenesis”. In: Phys. Rev. D 53 (1996), pp. 4257–4266. doi: 10.1103/PhysRevD.53.4257. arXiv: hep-ph/9409281

1996 arXiv
[36]

Baryogenesis from domain walls in the next-to-minimal supersymmetric standard model

S. A. Abel and P. L. White. “Baryogenesis from domain walls in the next-to-minimal supersymmetric standard model”. In: Phys. Rev. D 52 (1995), pp. 4371–4379. doi: 10.1103/PhysRevD.52.4371. arXiv: hep-ph/9505241

1995 arXiv
[37]

Baryogenesis from cosmic strings at the electroweak scale

I. Dasgupta. “Baryogenesis from cosmic strings at the electroweak scale”. In: Phys. Rev. D 55 (1997), pp. 3318–3329. doi: 10.1103/PhysRevD.55 .3318 . arXiv: hep- ph/9604356

1997
[38]

Electroweak baryogenesis with embedded domain walls

R. H. Brandenberger, W. Kelly, and M. Yamaguchi. “Electroweak baryogenesis with embedded domain walls”. In: Prog. Theor. Phys. 117 (2007), pp. 823–834. doi: 10. 1143/PTP.117.823. arXiv: hep-ph/0503211

2007 arXiv
[39]

Domain Walls Seeding the Electroweak Phase Transition

S. Blasi and A. Mariotti. “Domain Walls Seeding the Electroweak Phase Transition”. In: Phys. Rev. Lett. 129.26 (2022), p. 261303. doi: 10 . 1103 / PhysRevLett . 129 . 261303. arXiv: 2203.16450 [hep-ph]

2022 arXiv
[40]

Domain walls in the Two-Higgs-Doublet Model and their charge and CP-violating interactions with Standard Model fermions

M. Y. Sassi and G. Moortgat-Pick. “Domain walls in the Two-Higgs-Doublet Model and their charge and CP-violating interactions with Standard Model fermions”. In: JHEP 04 (2024), p. 101. doi: 10 . 1007 / JHEP04(2024 ) 101. arXiv: 2309 . 12398 [hep-ph]. 195

2024
[41]

Electroweak symmetry restoration in the N2HDM via domain walls

M. Y. Sassi and G. Moortgat-Pick. “Electroweak symmetry restoration in the N2HDM via domain walls”. In: JHEP 06 (2025), p. 072. doi: 10 . 1007 / JHEP06(2025 ) 072. arXiv: 2407.14468 [hep-ph]

2025 arXiv
[42]

Embedded domain walls and electroweak baryo- genesis

T. Schröder and R. Brandenberger. “Embedded domain walls and electroweak baryo- genesis”. In: Phys. Rev. D 110.4 (2024), p. 043516. doi: 10.1103/PhysRevD.110. 043516. arXiv: 2404.13035 [hep-ph]

2024 arXiv
[43]

Cosmological first-order phase transitions without bubbles

D. Wei, H. Chen, Q. Fan, and Y. Jiang. “Cosmological first-order phase transitions without bubbles”. In: (Jan. 2024). arXiv: 2401.08801 [hep-ph]

2024 arXiv
[44]

Minimal electroweak baryogenesis via domain walls

J. Azzola, O. Matsedonskyi, and A. Weiler. “Minimal electroweak baryogenesis via domain walls”. In: JHEP 04 (2025), p. 103. doi: 10.1007/JHEP04(2025)103 . arXiv: 2412.10495 [hep-ph]

2025 arXiv
[45]

Inverse Electroweak Baryogenesis

J. Azzola, O. Matsedonskyi, and A. Weiler. “Inverse Electroweak Baryogenesis”. In: (Mar. 2026). arXiv: 2603.20414 [hep-ph]

2026 arXiv
[46]

Baryon Asymmetry from Electroweak- Symmetric Domain Walls

J. Azzola, O. Matsedonskyi, and A. Weiler. “Baryon Asymmetry from Electroweak- Symmetric Domain Walls”. In: (Apr. 2026). arXiv: 2604.16603 [hep-ph]

2026 arXiv
[47]

Electroweak Baryogenesis from Collapsing Domain Walls

Y. Bai, K.-F. Lyu, and Y. Zhao. “Electroweak Baryogenesis from Collapsing Domain Walls”. In: (Apr. 2026). arXiv: 2604.27376 [hep-ph]

2026 arXiv
[48]

Catalyzed baryogenesis

Y. Bai, J. Berger, M. Korwar, and N. Orlofsky. “Catalyzed baryogenesis”. In: JHEP 10 (2021), p. 147. doi: 10.1007/JHEP10(2021)147. arXiv: 2106.12589 [hep-ph]

2021 arXiv
[49]

Baryogenesis from Exploding Primordial Black Holes

A. P. Klipfel, M. Vanvlasselaer, S. Trifinopoulos, and D. I. Kaiser. “Baryogenesis from Exploding Primordial Black Holes”. In: (Mar. 2026). arXiv: 2603.29024 [hep-ph]

2026
[50]

Sphalerons, baryogenesis, and helical magne- togenesis in the electroweak transition of the minimal standard model

D. Kharzeev, E. Shuryak, and I. Zahed. “Sphalerons, baryogenesis, and helical magne- togenesis in the electroweak transition of the minimal standard model”. In: Phys. Rev. D 102.7 (2020), p. 073003. doi: 10.1103/PhysRevD.102.073003. arXiv: 1906.04080 [hep-ph]

2020 arXiv
[51]

Baryogenesis from sphaleron decoupling

M. Hong, K. Kamada, and J. Yokoyama. “Baryogenesis from sphaleron decoupling”. In: Phys. Rev. D 108.6 (2023), p. 063502. doi: 10 . 1103 / PhysRevD . 108 . 063502. arXiv: 2304.13999 [hep-ph] . 196

2023 arXiv
[52]

Sphalerogenesis

M. Tanaka. “Sphalerogenesis”. In: (May 2025). arXiv: 2505.09984 [hep-ph]

2025 arXiv
[53]

Baryogenesis in SU (2)L multiplet models

K. Ogawa and M. Tanaka. “Baryogenesis in SU (2)L multiplet models”. In: (Apr. 2026). arXiv: 2604.00649 [hep-ph]

2026 arXiv
[54]

The Electroweak phase transition: A Nonperturbative analysis

K. Kajantie, M. Laine, K. Rummukainen, and M. E. Shaposhnikov. “The Electroweak phase transition: A Nonperturbative analysis”. In: Nucl. Phys. B 466 (1996), pp. 189–

1996
[55]

Is there a hot electroweak phase transition at mH ≳mW ?

K. Kajantie, M. Laine, K. Rummukainen, and M. E. Shaposhnikov. “Is there a hot electroweak phase transition at mH ≳mW ?” In: Phys. Rev. Lett. 77 (1996), pp. 2887–

1996
[56]

A Nonpertur- bative analysis of the finite T phase transition in SU(2) x U(1) electroweak theory

K. Kajantie, M. Laine, K. Rummukainen, and M. E. Shaposhnikov. “A Nonpertur- bative analysis of the finite T phase transition in SU(2) x U(1) electroweak theory”. In: Nucl. Phys. B 493 (1997), pp. 413–438. doi: 10.1016/S0550-3213(97)00164-8 . arXiv: hep-lat/9612006

1997 arXiv
[57]

The Strength of the electroweak phase transition at m(H) approximately = 80-GeV

F. Csikor, Z. Fodor, and J. Heitger. “The Strength of the electroweak phase transition at m(H) approximately = 80-GeV”. In: Phys. Lett. B 441 (1998), pp. 354–362. doi: 10.1016/S0370-2693(98)01127-7. arXiv: hep-lat/9807021

1998 arXiv
[58]

The Endpoint of the first order phase transition of the SU(2) gauge Higgs model on a four-dimensional isotropic lattice

Y. Aoki, F. Csikor, Z. Fodor, and A. Ukawa. “The Endpoint of the first order phase transition of the SU(2) gauge Higgs model on a four-dimensional isotropic lattice”. In: Phys. Rev. D 60 (1999), p. 013001. doi: 10.1103/PhysRevD.60.013001 . arXiv: hep-lat/9901021

1999 arXiv
[59]

Standard model CP violation and baryon asymmetry

M. B. Gavela, P. Hernandez, J. Orloff, and O. Pene. “Standard model CP violation and baryon asymmetry”. In: Mod. Phys. Lett. A 9 (1994), pp. 795–810. doi: 10.1142/ S0217732394000629. arXiv: hep-ph/9312215

1994 arXiv
[60]

Standard model CP violation and baryon asymmetry. Part 2: Finite temperature

M. B. Gavela, P. Hernandez, J. Orloff, O. Pene, and C. Quimbay. “Standard model CP violation and baryon asymmetry. Part 2: Finite temperature”. In: Nucl. Phys. B 430 (1994), pp. 382–426. doi: 10.1016/0550-3213(94)00410-2. arXiv: hep-ph/9406289. 197

1994 arXiv
[61]

Electroweak baryogenesis and standard model CP violation

P. Huet and E. Sather. “Electroweak baryogenesis and standard model CP violation”. In: Phys. Rev. D 51 (1995), pp. 379–394. doi: 10.1103/PhysRevD.51.379 . arXiv: hep-ph/9404302

1995 arXiv
[62]

Singlet Higgs phenomenol- ogy and the electroweak phase transition

S. Profumo, M. J. Ramsey-Musolf, and G. Shaughnessy. “Singlet Higgs phenomenol- ogy and the electroweak phase transition”. In: JHEP 08 (2007), p. 010. doi: 10.1088/ 1126-6708/2007/08/010. arXiv: 0705.2425 [hep-ph]

2007 arXiv
[63]

The Electroweak phase transition with a singlet

J. R. Espinosa and M. Quiros. “The Electroweak phase transition with a singlet”. In: Phys. Lett. B 305 (1993), pp. 98–105. doi: 10.1016/0370-2693(93)91111-Y . arXiv: hep-ph/9301285

1993 arXiv
[64]

LHC Phenomenology of an Extended Standard Model with a Real Scalar Singlet

V. Barger, P. Langacker, M. McCaskey, M. J. Ramsey-Musolf, and G. Shaughnessy. “LHC Phenomenology of an Extended Standard Model with a Real Scalar Singlet”. In: Phys. Rev. D 77 (2008), p. 035005. doi: 10.1103/PhysRevD.77.035005 . arXiv: 0706.4311 [hep-ph]

2008 arXiv
[65]

Effective Field Theory and Electroweak Baryogenesis in the Singlet-Extended Standard Model

P. H. Damgaard, A. Haarr, D. O’Connell, and A. Tranberg. “Effective Field Theory and Electroweak Baryogenesis in the Singlet-Extended Standard Model”. In: JHEP 02 (2016), p. 107. doi: 10.1007/JHEP02(2016)107. arXiv: 1512.01963 [hep-ph]

2016 arXiv
[66]

Singlet-catalyzed electroweak phase transitions in the 100 TeV frontier

A. V. Kotwal, M. J. Ramsey-Musolf, J. M. No, and P. Winslow. “Singlet-catalyzed electroweak phase transitions in the 100 TeV frontier”. In: Phys. Rev. D 94.3 (2016), p. 035022. doi: 10.1103/PhysRevD.94.035022. arXiv: 1605.06123 [hep-ph]

2016 arXiv
[67]

Dimen- sional reduction of the Standard Model coupled to a new singlet scalar field

T. Brauner, T. V. I. Tenkanen, A. Tranberg, A. Vuorinen, and D. J. Weir. “Dimen- sional reduction of the Standard Model coupled to a new singlet scalar field”. In: JHEP 03 (2017), p. 007. doi: 10.1007/JHEP03(2017)007. arXiv: 1609.06230 [hep-ph]

2017 arXiv
[68]

Electroweak baryogenesis from a dark sector

J. M. Cline, K. Kainulainen, and D. Tucker-Smith. “Electroweak baryogenesis from a dark sector”. In: Phys. Rev. D 95.11 (2017), p. 115006. doi: 10.1103/PhysRevD.95. 115006. arXiv: 1702.08909 [hep-ph]

2017 arXiv
[69]

Nonperturbative analysis of the gravitational waves from a first-order 198 electroweak phase transition

O. Gould, J. Kozaczuk, L. Niemi, M. J. Ramsey-Musolf, T. V. I. Tenkanen, and D. J. Weir. “Nonperturbative analysis of the gravitational waves from a first-order 198 electroweak phase transition”. In: Phys. Rev. D 100.11 (2019), p. 115024. doi: 10. 1103/PhysRevD.100.115024. arX...

2019 arXiv
[70]

Electroweak phase transition with spontaneous Z2-breaking

M. Carena, Z. Liu, and Y. Wang. “Electroweak phase transition with spontaneous Z2-breaking”. In: JHEP 08 (2020), p. 107. doi: 10.1007/JHEP08(2020)107 . arXiv: 1911.10206 [hep-ph]

2020 arXiv
[71]

Singlet-assisted electroweak phase tran- sition at two loops

L. Niemi, P. Schicho, and T. V. I. Tenkanen. “Singlet-assisted electroweak phase tran- sition at two loops”. In: Phys. Rev. D 103.11 (2021). [Erratum: Phys.Rev.D 109, 039902 (2024)], p. 115035. doi: 10.1103/PhysRevD.103.115035. arXiv: 2103.07467 [hep-ph]

2021 arXiv
[72]

Study of Electroweak Phase Transition in Exotic Higgs Decays at the CEPC

Z. Wang, X. Zhu, E. E. Khoda, S.-C. Hsu, N. Konstantinidis, K. Li, S. Li, M. J. Ramsey-Musolf, Y. Wu, and Y. E. Zhang. “Study of Electroweak Phase Transition in Exotic Higgs Decays at the CEPC”. In: Snowmass 2021. Mar. 2022. arXiv: 2203.10184 [hep-ex]

2021 arXiv
[73]

Nonperturbative study of the elec- troweak phase transition in the real scalar singlet extended standard model

L. Niemi, M. J. Ramsey-Musolf, and G. Xia. “Nonperturbative study of the elec- troweak phase transition in the real scalar singlet extended standard model”. In: Phys. Rev. D 110.11 (2024), p. 115016. doi: 10.1103/PhysRevD.110.115016. arXiv: 2405.01191 [hep-ph]

2024 arXiv
[74]

The scalar singlet exten- sion of the Standard Model: gravitational waves versus baryogenesis

J. Ellis, M. Lewicki, M. Merchand, J. M. No, and M. Zych. “The scalar singlet exten- sion of the Standard Model: gravitational waves versus baryogenesis”. In: JHEP 01 (2023), p. 093. doi: 10.1007/JHEP01(2023)093. arXiv: 2210.16305 [hep-ph]

2023 arXiv
[75]

Enhancing electroweak baryogenesis: The role of dimension-six oper- ators in the real singlet extension of the Standard Model

A. Giovanakis. “Enhancing electroweak baryogenesis: The role of dimension-six oper- ators in the real singlet extension of the Standard Model”. In: Phys. Dark Univ. 46 (2024), p. 101682. doi: 10.1016/j.dark.2024.101682. arXiv: 2410.04428 [hep-ph]

2024
[76]

A Comprehensive Framework for Electroweak Phase Tran- sitions: Thermal History and Dynamics from Bubble Nucleation to Percolation

H. Chen and Y. Jiang. “A Comprehensive Framework for Electroweak Phase Tran- sitions: Thermal History and Dynamics from Bubble Nucleation to Percolation”. In: (Mar. 2025). arXiv: 2503.00421 [hep-ph] . 199

2025 arXiv
[77]

What is the criterion for a strong first order electroweak phase transition in singlet models?

A. Ahriche. “What is the criterion for a strong first order electroweak phase transition in singlet models?” In: Phys. Rev. D 75 (2007), p. 083522. doi: 10.1103/PhysRevD. 75.083522. arXiv: hep-ph/0701192

2007 arXiv
[78]

Strong Electroweak Phase Transitions in the Standard Model with a Singlet

J. R. Espinosa, T. Konstandin, and F. Riva. “Strong Electroweak Phase Transitions in the Standard Model with a Singlet”. In: Nucl. Phys. B 854 (2012), pp. 592–630. doi: 10.1016/j.nuclphysb.2011.09.010. arXiv: 1107.5441 [hep-ph]

2012 arXiv
[79]

Testing Electroweak Baryogenesis with Future Colliders

D. Curtin, P. Meade, and C.-T. Yu. “Testing Electroweak Baryogenesis with Future Colliders”. In: JHEP 11 (2014), p. 127. doi: 10 . 1007 / JHEP11(2014 ) 127. arXiv: 1409.0005 [hep-ph]

2014 arXiv
[80]

Singlet- catalyzed electroweak phase transitions and precision Higgs boson studies

S. Profumo, M. J. Ramsey-Musolf, C. L. Wainwright, and P. Winslow. “Singlet- catalyzed electroweak phase transitions and precision Higgs boson studies”. In: Phys. Rev. D 91.3 (2015), p. 035018. doi: 10.1103/PhysRevD.91.035018. arXiv: 1407.5342 [hep-ph]

2015 arXiv
[81]

Electroweak baryogenesis and gravitational waves from a real scalar singlet

V. Vaskonen. “Electroweak baryogenesis and gravitational waves from a real scalar singlet”. In: Phys. Rev. D 95.12 (2017), p. 123515. doi: 10 . 1103 / PhysRevD . 95 . 123515. arXiv: 1611.02073 [hep-ph]

2017 arXiv
[82]

Gravitational wave, collider and dark matter signals from a scalar singlet electroweak baryogenesis

A. Beniwal, M. Lewicki, J. D. Wells, M. White, and A. G. Williams. “Gravitational wave, collider and dark matter signals from a scalar singlet electroweak baryogenesis”. In: JHEP 08 (2017), p. 108. doi: 10.1007/JHEP08(2017)108 . arXiv: 1702.06124 [hep-ph]

2017 arXiv
[83]

Dynamics of Electroweak Phase Transition In Singlet- Scalar Extension of the Standard Model

G. Kurup and M. Perelstein. “Dynamics of Electroweak Phase Transition In Singlet- Scalar Extension of the Standard Model”. In: Phys. Rev. D 96.1 (2017), p. 015036. doi: 10.1103/PhysRevD.96.015036. arXiv: 1704.03381 [hep-ph]

2017 arXiv
[84]

Collider and Gravitational Wave Complementarity in Exploring the Singlet Extension of the Standard Model

A. Alves, T. Ghosh, H.-K. Guo, K. Sinha, and D. Vagie. “Collider and Gravitational Wave Complementarity in Exploring the Singlet Extension of the Standard Model”. In: JHEP 04 (2019), p. 052. doi: 10.1007/JHEP04(2019)052 . arXiv: 1812.09333 [hep-ph]. 200

2019 arXiv
[85]

Exotic Higgs boson decays and the electroweak phase transition

J. Kozaczuk, M. J. Ramsey-Musolf, and J. Shelton. “Exotic Higgs boson decays and the electroweak phase transition”. In: Phys. Rev. D 101.11 (2020), p. 115035. doi: 10.1103/PhysRevD.101.115035. arXiv: 1911.10210 [hep-ph]

2020 arXiv
[86]

First-Order Electroweak Phase Transition and Baryo- genesis from a Naturally Light Singlet Scalar

K. Harigaya and I. R. Wang. “First-Order Electroweak Phase Transition and Baryo- genesis from a Naturally Light Singlet Scalar”. In: (July 2022). arXiv: 2207.02867 [hep-ph]

2022 arXiv
[87]

Constraining the real scalar singlet extension of the SM

M. Bosse, G. Hiller, D. Litim, F. Maltoni, M. J. Ramsey-Musolf, S. Tentori, and G. Xia. “Constraining the real scalar singlet extension of the SM”. In: (June 2026). arXiv: 2606.12533 [hep-ph]

2026 arXiv
[88]

Triplet Scalars and Dark Matter at the LHC

P. Fileviez Perez, H. H. Patel, M. J. Ramsey-Musolf, and K. Wang. “Triplet Scalars and Dark Matter at the LHC”. In: Phys. Rev. D 79 (2009), p. 055024. doi: 10.1103/ PhysRevD.79.055024. arXiv: 0811.3957 [hep-ph]

2009 arXiv
[89]

Dark Matter as the Trigger of Strong Electroweak Phase Transition

T. A. Chowdhury, M. Nemevsek, G. Senjanovic, and Y. Zhang. “Dark Matter as the Trigger of Strong Electroweak Phase Transition”. In: JCAP 02 (2012), p. 029. doi: 10.1088/1475-7516/2012/02/029. arXiv: 1110.5334 [hep-ph]

2012 arXiv
[90]

Stepping Into Electroweak Symmetry Break- ing: Phase Transitions and Higgs Phenomenology

H. H. Patel and M. J. Ramsey-Musolf. “Stepping Into Electroweak Symmetry Break- ing: Phase Transitions and Higgs Phenomenology”. In: Phys. Rev. D 88 (2013), p. 035013. doi: 10.1103/PhysRevD.88.035013. arXiv: 1212.5652 [hep-ph]

2013 arXiv
[91]

Electroweak phase transition in the real triplet extension of the SM: Dimensional reduction

L. Niemi, H. H. Patel, M. J. Ramsey-Musolf, T. V. I. Tenkanen, and D. J. Weir. “Electroweak phase transition in the real triplet extension of the SM: Dimensional reduction”. In: Phys. Rev. D 100.3 (2019), p. 035002. doi: 10.1103/PhysRevD.100. 035002. arXiv: 1802.10500 [hep-ph]

2019 arXiv
[92]

Scalar Electroweak Multiplet Dark Matter

W. Chao, G.-J. Ding, X.-G. He, and M. Ramsey-Musolf. “Scalar Electroweak Multiplet Dark Matter”. In: JHEP 08 (2019), p. 058. doi: 10.1007/JHEP08(2019)058 . arXiv: 1812.07829 [hep-ph]

2019 arXiv
[93]

Thermodynamics of a Two-Step Electroweak Phase Transition

L. Niemi, M. J. Ramsey-Musolf, T. V. I. Tenkanen, and D. J. Weir. “Thermodynamics of a Two-Step Electroweak Phase Transition”. In: Phys. Rev. Lett. 126.17 (2021), p. 171802. doi: 10.1103/PhysRevLett.126.171802. arXiv: 2005.11332 [hep-ph] . 201

2021 arXiv
[94]

Phase transitions, anomalous baryon number violation, and electroweak multiplet dark matter

Y. Wu, W. Zhang, and M. J. Ramsey-Musolf. “Phase transitions, anomalous baryon number violation, and electroweak multiplet dark matter”. In: Phys. Rev. D 112.5 (2025), p. 053003. doi: 10.1103/lz6d-kn77. arXiv: 2307.02187 [hep-ph]

2025
[95]

Two-Step Electroweak Baryoge- nesis

S. Inoue, G. Ovanesyan, and M. J. Ramsey-Musolf. “Two-Step Electroweak Baryoge- nesis”. In: Phys. Rev. D 93 (2016), p. 015013. doi: 10.1103/PhysRevD.93.015013 . arXiv: 1508.05404 [hep-ph]

2016 arXiv
[96]

Gravitational wave and collider probes of a triplet Higgs sector with a low cutoff

M. Chala, M. Ramos, and M. Spannowsky. “Gravitational wave and collider probes of a triplet Higgs sector with a low cutoff”. In: Eur. Phys. J. C 79.2 (2019), p. 156. doi: 10.1140/epjc/s10052-019-6655-1 . arXiv: 1812.01901 [hep-ph]

2019 arXiv
[97]

Electroweak phase transition and gravitational waves in the type-II seesaw model

R. Zhou, L. Bian, and Y. Du. “Electroweak phase transition and gravitational waves in the type-II seesaw model”. In: JHEP 08 (2022), p. 205. doi: 10.1007/JHEP08(2022)

2022 doi
[98]

Baryon asymmetry from a two stage electroweak phase transition?

A. Hammerschmitt, J. Kripfganz, and M. G. Schmidt. “Baryon asymmetry from a two stage electroweak phase transition?” In: Z. Phys. C 64 (1994), pp. 105–110. doi: 10.1007/BF01557241. arXiv: hep-ph/9404272

1994 arXiv
[99]

Phase transitions in the two doublet model

N. Turok and J. Zadrozny. “Phase transitions in the two doublet model”. In: Nucl. Phys. B 369 (1992), pp. 729–742. doi: 10.1016/0550-3213(92)90284-I

1992 doi
[100]

Baryogenesis con- straints on two Higgs doublet models

A. T. Davies, C. D. froggatt, G. Jenkins, and R. G. Moorhouse. “Baryogenesis con- straints on two Higgs doublet models”. In: Phys. Lett. B 336 (1994), pp. 464–470. doi: 10.1016/0370-2693(94)90559-2

1994 doi
[101]

Electroweak phase transition in two Higgs doublet models

J. M. Cline and P.-A. Lemieux. “Electroweak phase transition in two Higgs doublet models”. In: Phys. Rev. D 55 (1997), pp. 3873–3881. doi: 10.1103/PhysRevD.55

1997 doi
[102]

A strong electroweak phase transition in the 2HDM after LHC8

G. C. Dorsch, S. J. Huber, and J. M. No. “A strong electroweak phase transition in the 2HDM after LHC8”. In: JHEP 10 (2013), p. 029. doi: 10.1007/JHEP10(2013)029 . arXiv: 1305.6610 [hep-ph] . 202

2013 arXiv
[103]

A new insight into the phase transition in the early Universe with two Higgs doublets

J. Bernon, L. Bian, and Y. Jiang. “A new insight into the phase transition in the early Universe with two Higgs doublets”. In: JHEP 05 (2018), p. 151. doi: 10.1007/ JHEP05(2018)151. arXiv: 1712.08430 [hep-ph]

2018 arXiv
[104]

On the validity of perturbative studies of the electroweak phase transi- tion in the Two Higgs Doublet model

K. Kainulainen, V. Keus, L. Niemi, K. Rummukainen, T. V. I. Tenkanen, and V. Vaskonen. “On the validity of perturbative studies of the electroweak phase transi- tion in the Two Higgs Doublet model”. In: JHEP 06 (2019), p. 075. doi: 10.1007/ JHEP06(2019)075. arXiv: 1904.01329 [hep-ph]

2019 arXiv
[105]

Benchmarking a fading window: electroweak baryogenesis in the C2HDM, LHC constraints after Run 2 and prospects for LISA

T. Biekötter and M. O. Olea-Romacho. “Benchmarking a fading window: electroweak baryogenesis in the C2HDM, LHC constraints after Run 2 and prospects for LISA”. In: JHEP 12 (2025), p. 040. doi: 10.1007/JHEP12(2025)040 . arXiv: 2505.09670 [hep-ph]

2025
[106]

Electroweak baryogenesis in 2HDM without EDM cancellation

M. Aiko, M. Endo, S. Kanemura, and Y. Mura. “Electroweak baryogenesis in 2HDM without EDM cancellation”. In: JHEP 07 (2025), p. 236. doi: 10.1007/JHEP07(2025)

2025 doi
[107]

Multistep strong first-order elec- troweak phase transitions in the inverted type-I 2HDM: Parameter space, gravitational waves, and collider phenomenology

S. Lee, D. Kim, J.-H. Cho, J. Kim, and J. Song. “Multistep strong first-order elec- troweak phase transitions in the inverted type-I 2HDM: Parameter space, gravitational waves, and collider phenomenology”. In: Phys. Rev. D 112.5 (2025), p. 055035. doi: 10.1103/cbgr-w9cb. arXiv...

2025 arXiv
[108]

Baryogenesis and EDMs in the 2HDM+CS

B. Garbrecht and E. Wang. “Baryogenesis and EDMs in the 2HDM+CS”. In: (Dec. 2025). arXiv: 2512.17695 [hep-ph]

2025
[109]

Towards precise baryogenesis in the 2HDM+a

T. Gent, S. Huber, K. Mimasu, and J. M. No. “Towards precise baryogenesis in the 2HDM+a”. In: (Dec. 2025). arXiv: 2512.22081 [hep-ph]

2025
[110]

Baryogenesis in the two-Higgs doublet model

L. Fromme, S. J. Huber, and M. Seniuch. “Baryogenesis in the two-Higgs doublet model”. In: JHEP 11 (2006), p. 038. doi: 10.1088/1126-6708/2006/11/038 . arXiv: hep-ph/0605242

2006 arXiv
[111]

The Evolution of vacuum states and phase transitions in 2HDM during cooling of Universe

I. F. Ginzburg, I. P. Ivanov, and K. A. Kanishev. “The Evolution of vacuum states and phase transitions in 2HDM during cooling of Universe”. In: Phys. Rev. D 81 (2010), p. 085031. doi: 10.1103/PhysRevD.81.085031. arXiv: 0911.2383 [hep-ph] . 203

2010 arXiv
[112]

Electroweak Baryogenesis in Two Higgs Doublet Models and B meson anomalies

J. M. Cline, K. Kainulainen, and M. Trott. “Electroweak Baryogenesis in Two Higgs Doublet Models and B meson anomalies”. In: JHEP 11 (2011), p. 089. doi: 10.1007/ JHEP11(2011)089. arXiv: 1107.3559 [hep-ph]

2011 arXiv
[113]

Cold Electroweak Baryogenesis in the Two Higgs-Doublet Model

A. Tranberg and B. Wu. “Cold Electroweak Baryogenesis in the Two Higgs-Doublet Model”. In: JHEP 07 (2012), p. 087. doi: 10.1007/JHEP07(2012)087 . arXiv: 1203. 5012 [hep-ph]

2012 doi
[114]

Echoes of the Electroweak Phase Transition: Discovering a second Higgs doublet through A0 →ZH0

G. C. Dorsch, S. J. Huber, K. Mimasu, and J. M. No. “Echoes of the Electroweak Phase Transition: Discovering a second Higgs doublet through A0 →ZH0”. In: Phys. Rev. Lett. 113.21 (2014), p. 211802. doi: 10.1103/PhysRevLett.113.211802. arXiv: 1405.5537 [hep-ph]

2014 arXiv
[115]

Strong First Or- der Electroweak Phase Transition in the CP-Conserving 2HDM Revisited

P. Basler, M. Krause, M. Muhlleitner, J. Wittbrodt, and A. Wlotzka. “Strong First Or- der Electroweak Phase Transition in the CP-Conserving 2HDM Revisited”. In: JHEP 02 (2017), p. 121. doi: 10.1007/JHEP02(2017)121. arXiv: 1612.04086 [hep-ph]

2017 arXiv
[116]

A Second Higgs Doublet in the Early Universe: Baryogenesis and Gravitational Waves

G. C. Dorsch, S. J. Huber, T. Konstandin, and J. M. No. “A Second Higgs Doublet in the Early Universe: Baryogenesis and Gravitational Waves”. In: JCAP 05 (2017), p. 052. doi: 10.1088/1475-7516/2017/05/052. arXiv: 1611.05874 [hep-ph]

2017 arXiv
[117]

Strong first order electroweak phase transition in 2HDM confronting future Z & Higgs factories

W. Su, A. G. Williams, and M. Zhang. “Strong first order electroweak phase transition in 2HDM confronting future Z & Higgs factories”. In: JHEP 04 (2021), p. 219. doi: 10.1007/JHEP04(2021)219. arXiv: 2011.04540 [hep-ph]

2021 arXiv
[118]

Dark matter and nature of electroweak phase transition with an inert doublet

S. Fabian, F. Goertz, and Y. Jiang. “Dark matter and nature of electroweak phase transition with an inert doublet”. In: JCAP 09 (2021), p. 011. doi: 10.1088/1475- 7516/2021/09/011. arXiv: 2012.12847 [hep-ph]

2021 arXiv
[119]

Gravitational wave and electroweak baryogenesis with two Higgs doublet models

R. Zhou and L. Bian. “Gravitational wave and electroweak baryogenesis with two Higgs doublet models”. In: Phys. Lett. B 829 (2022), p. 137105. doi: 10.1016/j. physletb.2022.137105. arXiv: 2001.01237 [hep-ph]

2022
[120]

Possibility of a multi-step electroweak phase transition in the two-Higgs doublet models

M. Aoki, T. Komatsu, and H. Shibuya. “Possibility of a multi-step electroweak phase transition in the two-Higgs doublet models”. In: PTEP 2022.6 (2022), 063B05. doi: 10.1093/ptep/ptac068. arXiv: 2106.03439 [hep-ph] . 204

2022 arXiv
[121]

Electroweak phase transition in the 2HDM: Collider and gravitational wave complementarity

D. Gonçalves, A. Kaladharan, and Y. Wu. “Electroweak phase transition in the 2HDM: Collider and gravitational wave complementarity”. In: Phys. Rev. D 105.9 (2022), p. 095041. doi: 10.1103/PhysRevD.105.095041. arXiv: 2108.05356 [hep-ph]

2022 arXiv
[122]

Fate of elec- troweak symmetry in the early Universe: Non-restoration and trapped vacua in the N2HDM

T. Biekötter, S. Heinemeyer, J. M. No, M. O. Olea, and G. Weiglein. “Fate of elec- troweak symmetry in the early Universe: Non-restoration and trapped vacua in the N2HDM”. In: JCAP 06 (2021), p. 018. doi: 10 . 1088 / 1475 - 7516 / 2021 / 06 / 018. arXiv: 2103.12707 [hep-ph]

2021 arXiv
[123]

Electroweak baryogenesis in the CP-violating two-Higgs doublet model

P. Basler, L. Biermann, M. Mühlleitner, and J. Müller. “Electroweak baryogenesis in the CP-violating two-Higgs doublet model”. In: Eur. Phys. J. C 83.1 (2023), p. 57. doi: 10.1140/epjc/s10052-023-11192-9 . arXiv: 2108.03580 [hep-ph]

2023 arXiv
[124]

Two-Higgs-doublet models in light of current experiments: a brief review

L. Wang, J. M. Yang, and Y. Zhang. “Two-Higgs-doublet models in light of current experiments: a brief review”. In: Commun. Theor. Phys. 74.9 (2022), p. 097202. doi: 10.1088/1572-9494/ac7fe9. arXiv: 2203.07244 [hep-ph]

2022 arXiv
[125]

The trap in the early Universe: impact on the interplay between gravitational waves and LHC physics in the 2HDM

T. Biekötter, S. Heinemeyer, J. M. No, M. O. Olea-Romacho, and G. Weiglein. “The trap in the early Universe: impact on the interplay between gravitational waves and LHC physics in the 2HDM”. In: JCAP 03 (2023), p. 031. doi: 10 . 1088 / 1475 - 7516/2023/03/031. arXiv: 2208.1446...

2023 arXiv
[126]

Electroweak phase transition in the standard model with a dimension-six Higgs operator at one-loop level

S. W. Ham and S. K. Oh. “Electroweak phase transition in the standard model with a dimension-six Higgs operator at one-loop level”. In: Phys. Rev. D 70 (2004), p. 093007. doi: 10.1103/PhysRevD.70.093007. arXiv: hep-ph/0408324

2004 arXiv
[127]

The Baryon asymmetry in the standard model with a low cut-off

D. Bodeker, L. Fromme, S. J. Huber, and M. Seniuch. “The Baryon asymmetry in the standard model with a low cut-off”. In: JHEP 02 (2005), p. 026. doi: 10.1088/1126- 6708/2005/02/026. arXiv: hep-ph/0412366

2005 arXiv
[128]

First-order electroweak phase transition in the standard model with a low cutoff

C. Grojean, G. Servant, and J. D. Wells. “First-order electroweak phase transition in the standard model with a low cutoff”. In: Phys. Rev. D 71 (2005), p. 036001. doi: 10.1103/PhysRevD.71.036001. arXiv: hep-ph/0407019. 205

2005 arXiv
[129]

Dynamics of Non-renormalizable Elec- troweak Symmetry Breaking

C. Delaunay, C. Grojean, and J. D. Wells. “Dynamics of Non-renormalizable Elec- troweak Symmetry Breaking”. In: JHEP 04 (2008), p. 029. doi: 10 . 1088 / 1126 - 6708/2008/04/029. arXiv: 0711.2511 [hep-ph]

2008 arXiv
[130]

The gravitational waves from the first-order phase transition with a dimension-six operator

R.-G. Cai, M. Sasaki, and S.-J. Wang. “The gravitational waves from the first-order phase transition with a dimension-six operator”. In: JCAP 08 (2017), p. 004. doi: 10.1088/1475-7516/2017/08/004. arXiv: 1707.03001 [astro-ph.CO]

2017 arXiv
[131]

Signals of the electroweak phase transition at colliders and gravitational wave observatories

M. Chala, C. Krause, and G. Nardini. “Signals of the electroweak phase transition at colliders and gravitational wave observatories”. In: JHEP 07 (2018), p. 062. doi: 10.1007/JHEP07(2018)062. arXiv: 1802.02168 [hep-ph]

2018 arXiv
[132]

On the Maximal Strength of a First-Order Elec- troweak Phase Transition and its Gravitational Wave Signal

J. Ellis, M. Lewicki, and J. M. No. “On the Maximal Strength of a First-Order Elec- troweak Phase Transition and its Gravitational Wave Signal”. In: JCAP 04 (2019), p. 003. doi: 10.1088/1475-7516/2019/04/003. arXiv: 1809.08242 [hep-ph]

2019 arXiv
[133]

Sphaleron in the first- order electroweak phase transition with the dimension-six Higgs field operator

V. Q. Phong, P. H. Khiem, N. P. D. Loc, and H. N. Long. “Sphaleron in the first- order electroweak phase transition with the dimension-six Higgs field operator”. In: Phys. Rev. D 101.11 (2020), p. 116010. doi: 10.1103/PhysRevD.101.116010. arXiv: 2003.09625 [hep-ph]

2020 arXiv
[134]

A new perspective on the elec- troweak phase transition in the Standard Model Effective Field Theory

J. E. Camargo-Molina, R. Enberg, and J. Löfgren. “A new perspective on the elec- troweak phase transition in the Standard Model Effective Field Theory”. In: JHEP 10 (2021), p. 127. doi: 10.1007/JHEP10(2021)127. arXiv: 2103.14022 [hep-ph]

2021 arXiv
[135]

Gravitational waves from patterns of electroweak symmetry breaking: an effective perspective

R.-G. Cai, K. Hashino, S.-J. Wang, and J.-H. Yu. “Gravitational waves from patterns of electroweak symmetry breaking: an effective perspective”. In: Commun. Theor. Phys. 77.5 (2025), p. 055204. doi: 10.1088/1572-9494/ad9c3d . arXiv: 2202.08295 [hep-ph]

2025 arXiv
[136]

arXiv: hep-ph/9412266

doi: 10.1016/0370-2693(95)00214-6. arXiv: hep-ph/9412266

arXiv
[137]

First-order electroweak phase transition at finite density

R. Qin and L. Bian. “First-order electroweak phase transition at finite density”. In: JHEP 08 (2024), p. 157. doi: 10 . 1007 / JHEP08(2024 ) 157. arXiv: 2407 . 01981 [hep-ph]

2024
[138]

Higher-order-operator corrections to phase-transition parameters in dimensional reduction

M. Chala, J. C. Criado, L. Gil, and J. L. Miras. “Higher-order-operator corrections to phase-transition parameters in dimensional reduction”. In: JHEP 10 (2024), p. 025. doi: 10.1007/JHEP10(2024)025. arXiv: 2406.02667 [hep-ph]

2024 arXiv
[139]

Electroweak phase transition in singlet ex- tensions of the standard model with dimension-six operators

V. K. Oikonomou and A. Giovanakis. “Electroweak phase transition in singlet ex- tensions of the standard model with dimension-six operators”. In: Phys. Rev. D 109.5 (2024), p. 055044. doi: 10.1103/PhysRevD.109.055044. arXiv: 2403.01591 [hep-ph]

2024 arXiv
[140]

Opening the window for electroweak baryogenesis

M. Carena, M. Quiros, and C. E. M. Wagner. “Opening the window for electroweak baryogenesis”. In: Phys. Lett. B 380 (1996), pp. 81–91. doi: 10.1016/0370-2693(96) 00475-3. arXiv: hep-ph/9603420

1996 arXiv
[141]

A Light stop and electroweak baryogenesis

D. Delepine, J. M. Gerard, R. Gonzalez Felipe, and J. Weyers. “A Light stop and electroweak baryogenesis”. In: Phys. Lett. B 386 (1996), pp. 183–188. doi: 10.1016/ 0370-2693(96)00921-5. arXiv: hep-ph/9604440

1996 arXiv
[142]

Supersymmetric electroweak phase transition: Be- yond perturbation theory

J. M. Cline and K. Kainulainen. “Supersymmetric electroweak phase transition: Be- yond perturbation theory”. In: Nucl. Phys. B 482 (1996), pp. 73–91. doi: 10.1016/ S0550-3213(96)00519-6. arXiv: hep-ph/9605235

1996 arXiv
[143]

Phase transitions in the NMSSM

K. Funakubo, S. Tao, and F. Toyoda. “Phase transitions in the NMSSM”. In: Prog. Theor. Phys. 114 (2005), pp. 369–389. doi: 10 . 1143 / PTP . 114 . 369. arXiv: hep - ph/0501052

2005
[144]

Electroweak phase transition in the nearly aligned Higgs effective field theory

S. Kanemura, R. Nagai, and M. Tanaka. “Electroweak phase transition in the nearly aligned Higgs effective field theory”. In: JHEP 06 (2022), p. 027. doi: 10 . 1007 / JHEP06(2022)027. arXiv: 2202.12774 [hep-ph] . 206

2022 arXiv
[145]

Stop-Catalyzed Baryogenesis Beyond the MSSM

A. Katz, M. Perelstein, M. J. Ramsey-Musolf, and P. Winslow. “Stop-Catalyzed Baryogenesis Beyond the MSSM”. In: Phys. Rev. D 92.9 (2015), p. 095019. doi: 10.1103/PhysRevD.92.095019. arXiv: 1509.02934 [hep-ph] . 207

2015 arXiv
[146]

New insights in the electroweak phase transition in the NMSSM

W. Huang, Z. Kang, J. Shu, P. Wu, and J. M. Yang. “New insights in the electroweak phase transition in the NMSSM”. In: Phys. Rev. D 91.2 (2015), p. 025006. doi: 10. 1103/PhysRevD.91.025006. arXiv: 1405.1152 [hep-ph]

2015 arXiv
[147]

Electroweak phase transition in the Z 3-invariant NMSSM: Implications of LHC and Dark matter searches and prospects of detecting the gravitational waves

A. Chatterjee, A. Datta, and S. Roy. “Electroweak phase transition in the Z 3-invariant NMSSM: Implications of LHC and Dark matter searches and prospects of detecting the gravitational waves”. In: JHEP 06 (2022), p. 108. doi: 10.1007/JHEP06(2022)108 . arXiv: 2202.12476 [hep-ph]

2022 arXiv
[148]

Revisiting the electron EDM in the NMSSM

K. Ning and M. J. Ramsey-Musolf. “Revisiting the electron EDM in the NMSSM”. In: Phys. Lett. B 869 (2025), p. 139867. doi: 10.1016/j.physletb.2025.139867 . arXiv: 2507.06320 [hep-ph]

2025
[149]

Electroweak baryogenesis in supersymmetric models

P. Huet and A. E. Nelson. “Electroweak baryogenesis in supersymmetric models”. In: Phys. Rev. D 53 (1996), pp. 4578–4597. doi: 10.1103/PhysRevD.53.4578 . arXiv: hep-ph/9506477

1996 arXiv
[150]

Supersymmetric baryogenesis at the electroweak phase transition

M. P. Worah. “Supersymmetric baryogenesis at the electroweak phase transition”. In: Phys. Rev. D 56 (1997), pp. 2010–2018. doi: 10.1103/PhysRevD.56.2010 . arXiv: hep-ph/9702423

1997 arXiv
[151]

Supersymmetric electroweak phase transition: Baryoge- nesis versus experimental constraints

J. M. Cline and G. D. Moore. “Supersymmetric electroweak phase transition: Baryoge- nesis versus experimental constraints”. In: Phys. Rev. Lett. 81 (1998), pp. 3315–3318. doi: 10.1103/PhysRevLett.81.3315. arXiv: hep-ph/9806354

1998 arXiv
[152]

Excluding Electroweak Baryogenesis in the MSSM

D. Curtin, P. Jaiswal, and P. Meade. “Excluding Electroweak Baryogenesis in the MSSM”. In: JHEP 08 (2012), p. 005. doi: 10.1007/JHEP08(2012)005. arXiv: 1203. 2932 [hep-ph]

2012 doi
[153]

Electroweak phase transition in a nonminimal supersymmetric model

S. W. Ham, S. K. OH, C. M. Kim, E. J. Yoo, and D. Son. “Electroweak phase transition in a nonminimal supersymmetric model”. In: Phys. Rev. D 70 (2004), p. 075001. doi: 10.1103/PhysRevD.70.075001. arXiv: hep-ph/0406062

2004 arXiv
[154]

Electroweak Phase Transition and Baryogenesis in the nMSSM

S. J. Huber, T. Konstandin, T. Prokopec, and M. G. Schmidt. “Electroweak Phase Transition and Baryogenesis in the nMSSM”. In: Nucl. Phys. B 757 (2006), pp. 172–

2006
[155]

Electroweak phase transition, critical bubbles and sphaleron decoupling condition in the MSSM

K. Funakubo and E. Senaha. “Electroweak phase transition, critical bubbles and sphaleron decoupling condition in the MSSM”. In: Phys. Rev. D 79 (2009), p. 115024. doi: 10.1103/PhysRevD.79.115024. arXiv: 0905.2022 [hep-ph]

2009 arXiv
[156]

Light Dark Matter and the Electroweak Phase Transition in the NMSSM

M. Carena, N. R. Shah, and C. E. M. Wagner. “Light Dark Matter and the Electroweak Phase Transition in the NMSSM”. In: Phys. Rev. D 85 (2012), p. 036003. doi: 10. 1103/PhysRevD.85.036003. arXiv: 1110.4378 [hep-ph]

2012 arXiv
[157]

Interpretation of the Galactic Center excess and electroweak phase transition in the NMSSM

X.-J. Bi, L. Bian, W. Huang, J. Shu, and P.-F. Yin. “Interpretation of the Galactic Center excess and electroweak phase transition in the NMSSM”. In: Phys. Rev. D 92 (2015), p. 023507. doi: 10.1103/PhysRevD.92.023507. arXiv: 1503.03749 [hep-ph]

2015 arXiv
[158]

Nucleation is more than critical: A case study of the electroweak phase transition in the NMSSM

S. Baum, M. Carena, N. R. Shah, C. E. M. Wagner, and Y. Wang. “Nucleation is more than critical: A case study of the electroweak phase transition in the NMSSM”. In: JHEP 03 (2021), p. 055. doi: 10.1007/JHEP03(2021)055 . arXiv: 2009.10743 [hep-ph]

2021 arXiv
[159]

Electroweak Baryogenesis and Higgs Physics

C. E. M. Wagner. “Electroweak Baryogenesis and Higgs Physics”. In: LHEP 2023 (2023), p. 466. doi: 10.31526/lhep.2023.466. arXiv: 2311.06949 [hep-ph]

2023 arXiv
[160]

Supersymmetric electroweak baryogen- esis

J. M. Cline, M. Joyce, and K. Kainulainen. “Supersymmetric electroweak baryogen- esis”. In: JHEP 07 (2000), p. 018. doi: 10.1088/1126- 6708/2000/07/018 . arXiv: hep-ph/0006119

2000 arXiv
[161]

The electroweak phase transition: a collider target

M. J. Ramsey-Musolf. “The electroweak phase transition: a collider target”. In: JHEP 09 (2020), p. 179. doi: 10.1007/JHEP09(2020)179. arXiv: 1912.07189 [hep-ph]

2020 arXiv
[162]

Relativistic Detonation Waves and Bubble Growth in False Vacuum Decay

P. J. Steinhardt. “Relativistic Detonation Waves and Bubble Growth in False Vacuum Decay”. In: Phys. Rev. D 25 (1982), p. 2074. doi: 10.1103/PhysRevD.25.2074

1982 doi
[163]

The growth of bubbles in cosmological phase transitions

J. Ignatius, K. Kajantie, H. Kurki-Suonio, and M. Laine. “The growth of bubbles in cosmological phase transitions”. In: Phys. Rev. D 49 (1994), pp. 3854–3868. doi: 10.1103/PhysRevD.49.3854. arXiv: astro-ph/9309059

1994 arXiv
[164]

One loop fluctuation - dissipation formula for bubble wall velocity

P. B. Arnold. “One loop fluctuation - dissipation formula for bubble wall velocity”. In: Phys. Rev. D 48 (1993), pp. 1539–1545. doi: 10.1103/PhysRevD.48.1539. arXiv: hep-ph/9302258. 209

1993 arXiv
[165]

Bubble wall velocity in a first order electroweak phase transition

G. D. Moore and T. Prokopec. “Bubble wall velocity in a first order electroweak phase transition”. In: Phys. Rev. Lett. 75 (1995), pp. 777–780. doi: 10.1103/PhysRevLett. 75.777. arXiv: hep-ph/9503296

1995 arXiv
[166]

How fast can the wall move? A Study of the elec- troweak phase transition dynamics

G. D. Moore and T. Prokopec. “How fast can the wall move? A Study of the elec- troweak phase transition dynamics”. In: Phys. Rev. D 52 (1995), pp. 7182–7204. doi: 10.1103/PhysRevD.52.7182. arXiv: hep-ph/9506475

1995 arXiv
[167]

Energy Budget of Cosmolog- ical First-order Phase Transitions

J. R. Espinosa, T. Konstandin, J. M. No, and G. Servant. “Energy Budget of Cosmolog- ical First-order Phase Transitions”. In: JCAP 06 (2010), p. 028. doi: 10.1088/1475- 7516/2010/06/028. arXiv: 1004.4187 [hep-ph]

2010 arXiv
[168]

From Boltzmann equations to steady wall velocities

T. Konstandin, G. Nardini, and I. Rues. “From Boltzmann equations to steady wall velocities”. In: JCAP 09 (2014), p. 028. doi: 10.1088/1475- 7516/2014/09/028 . arXiv: 1407.3132 [hep-ph]

2014 arXiv
[169]

Refining Gravitational Wave and Collider Physics Dialogue via Singlet Scalar Extension

M. J. Ramsey-Musolf, T. V. I. Tenkanen, and V. Q. Tran. “Refining Gravitational Wave and Collider Physics Dialogue via Singlet Scalar Extension”. In: (Sept. 2024). arXiv: 2409.17554 [hep-ph]

2024 arXiv
[170]

Electroweak bubble wall expansion: gravita- tional waves and baryogenesis in Standard Model-like thermal plasma

M. Lewicki, M. Merchand, and M. Zych. “Electroweak bubble wall expansion: gravita- tional waves and baryogenesis in Standard Model-like thermal plasma”. In: JHEP 02 (2022), p. 017. doi: 10.1007/JHEP02(2022)017. arXiv: 2111.02393 [astro-ph.CO]

2022 arXiv
[171]

Bubble wall velocities in local equilibrium

W.-Y. Ai, B. Garbrecht, and C. Tamarit. “Bubble wall velocities in local equilibrium”. In: JCAP 03.03 (2022), p. 015. doi: 10 . 1088 / 1475 - 7516 / 2022 / 03 / 015. arXiv: 2109.13710 [hep-ph]

2022 arXiv
[172]

Dark Matter production from relativistic bubble walls

A. Azatov, M. Vanvlasselaer, and W. Yin. “Dark Matter production from relativistic bubble walls”. In: JHEP 03 (2021), p. 288. doi: 10.1007/JHEP03(2021)288 . arXiv: 2101.05721 [hep-ph]

2021 arXiv
[173]

Friction pressure on relativistic bubble walls

Y. Gouttenoire, R. Jinno, and F. Sala. “Friction pressure on relativistic bubble walls”. In: JHEP 05 (2022), p. 004. doi: 10.1007/JHEP05(2022)004 . arXiv: 2112.07686 [hep-ph]. 210

2022 arXiv
[174]

First principles determination of bubble wall velocity

B. Laurent and J. M. Cline. “First principles determination of bubble wall velocity”. In: Phys. Rev. D 106.2 (2022), p. 023501. doi: 10 . 1103 / PhysRevD . 106 . 023501. arXiv: 2204.13120 [hep-ph]

2022 arXiv
[175]

Bubble wall dynamics at the electroweak phase transition

S. De Curtis, L. D. Rose, A. Guiggiani, Á. G. Muyor, and G. Panico. “Bubble wall dynamics at the electroweak phase transition”. In: JHEP 03 (2022), p. 163. doi: 10. 1007/JHEP03(2022)163. arXiv: 2201.08220 [hep-ph]

2022 arXiv
[176]

Quantisation across bubble walls and friction

A. Azatov, G. Barni, R. Petrossian-Byrne, and M. Vanvlasselaer. “Quantisation across bubble walls and friction”. In: JHEP 05 (2024), p. 294. doi: 10.1007/JHEP05(2024)

2024 doi
[177]

Logarithmically divergent friction on ultrarelativistic bubble walls

W.-Y. Ai. “Logarithmically divergent friction on ultrarelativistic bubble walls”. In: JCAP 10 (2023), p. 052. doi: 10.1088/1475-7516/2023/10/052. arXiv: 2308.10679 [hep-ph]

2023 arXiv
[178]

Electroweak Bubble Wall Speed Limit

D. Bodeker and G. D. Moore. “Electroweak Bubble Wall Speed Limit”. In: JCAP 05 (2017), p. 025. doi: 10.1088/1475-7516/2017/05/025. arXiv: 1703.08215 [hep-ph]

2017 arXiv
[179]

General bubble expansion at strong coupling

J.-C. Wang, Z.-Y. Yuwen, Y.-S. Hao, and S.-J. Wang. “General bubble expansion at strong coupling”. In: Phys. Rev. D 109.9 (2024), p. 096012. doi: 10.1103/PhysRevD. 109.096012. arXiv: 2311.07347 [hep-ph]

2024 arXiv
[180]

Model-independent bubble wall velocities in local thermal equilibrium

W.-Y. Ai, B. Laurent, and J. van de Vis. “Model-independent bubble wall velocities in local thermal equilibrium”. In: JCAP 07 (2023), p. 002. doi: 10 . 1088 / 1475 - 7516/2023/07/002. arXiv: 2303.10171 [astro-ph.CO]

2023 arXiv
[181]

Thermal pressure on ultrarelativistic bubbles from a semi- classical formalism

A. J. Long and J. Turner. “Thermal pressure on ultrarelativistic bubbles from a semi- classical formalism”. In: JCAP 11 (2024), p. 024. doi: 10.1088/1475- 7516/2024/ 11/024. arXiv: 2407.18196 [hep-ph]

2024 arXiv
[182]

Electroweak phase tran- sition and bubble wall velocity in local thermal equilibrium

C. Branchina, A. Conaci, L. Delle Rose, and S. De Curtis. “Electroweak phase tran- sition and bubble wall velocity in local thermal equilibrium”. In: Phys. Rev. D 112.9 (2025), p. 095008. doi: 10.1103/lkht-1nv1. arXiv: 2504.21213 [hep-ph] . 211

2025 arXiv
[183]

The discriminant power of bubble wall velocities: gravitational waves and electroweak baryogenesis

M. Carena, A. Ireland, T. Ou, and I. R. Wang. “The discriminant power of bubble wall velocities: gravitational waves and electroweak baryogenesis”. In: JHEP 09 (2025), p. 175. doi: 10.1007/JHEP09(2025)175. arXiv: 2504.17841 [hep-ph]

2025 arXiv
[184]

Bubble wall velocity from Kadanoff-Baym equa- tions: fluid dynamics and microscopic interactions

M. J. Ramsey-Musolf and J. Zhu. “Bubble wall velocity from Kadanoff-Baym equa- tions: fluid dynamics and microscopic interactions”. In: (Apr. 2025). arXiv: 2504 . 13724 [hep-ph]

2025
[185]

Bubble wall dynamics from nonequilibrium quantum field theory

W.-Y. Ai, M. Carosi, B. Garbrecht, C. Tamarit, and M. Vanvlasselaer. “Bubble wall dynamics from nonequilibrium quantum field theory”. In: JHEP 08 (2025), p. 077. doi: 10.1007/JHEP08(2025)077. arXiv: 2504.13725 [hep-ph]

2025 arXiv
[186]

The bubble wall velocity in local thermal equilibrium and energy budget with full effective potential

Z. Si, H. Wang, L. Wang, Y. Xiao, and Y. Zhang. “The bubble wall velocity in local thermal equilibrium and energy budget with full effective potential”. In: JHEP 09 (2025), p. 029. doi: 10.1007/JHEP09(2025)029. arXiv: 2505.19584 [hep-ph]

2025 arXiv
[187]

WallGo investigates: Theoretical uncertainties in the bubble wall velocity

J. van de Vis, P. Schicho, L. Niemi, B. Laurent, J. Hirvonen, and O. Gould. “WallGo investigates: Theoretical uncertainties in the bubble wall velocity”. In: (Oct. 2025). arXiv: 2510.27691 [hep-ph]

2025
[188]

Bubble expansion at strong coupling

L. Li, S.-J. Wang, and Z.-Y. Yuwen. “Bubble expansion at strong coupling”. In: Phys. Rev. D 108.9 (2023), p. 096033. doi: 10.1103/PhysRevD.108.096033 . arXiv: 2302. 10042 [hep-th]

2023 doi
[189]

Bubble velocities in local equilibrium from a pseu- dopotential

M. Münzenberg and C. Tamarit. “Bubble velocities in local equilibrium from a pseu- dopotential”. In: (Nov. 2025). arXiv: 2511.22711 [hep-ph]

2025 arXiv
[190]

Laser Interferometer Space Antenna

P. Amaro-Seoane et al. “Laser Interferometer Space Antenna”. In: (Feb. 2017). arXiv: 1702.00786 [astro-ph.IM]

2017 arXiv
[191]

Taiji program: Gravitational- wave sources

W.-H. Ruan, Z.-K. Guo, R.-G. Cai, and Y.-Z. Zhang. “Taiji program: Gravitational- wave sources”. In: Int. J. Mod. Phys. A 35.17 (2020), p. 2050075. doi: 10 . 1142 / S0217751X2050075X. arXiv: 1807.09495 [gr-qc]

2020 arXiv
[192]

TianQin: a space-borne gravitational wave detector

J. Luo et al. “TianQin: a space-borne gravitational wave detector”. In: Class. Quant. Grav. 33.3 (2016), p. 035010. doi: 10.1088/0264-9381/33/3/035010 . arXiv: 1512. 02076 [astro-ph.IM] . 212

2016 doi
[193]

Gravitational Wave Production by Collisions: More Bubbles

S. J. Huber and T. Konstandin. “Gravitational Wave Production by Collisions: More Bubbles”. In: JCAP 09 (2008), p. 022. doi: 10 . 1088 / 1475 - 7516 / 2008 / 09 / 022. arXiv: 0806.1828 [hep-ph]

2008 arXiv
[194]

The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition

C. Caprini, R. Durrer, and G. Servant. “The stochastic gravitational wave background from turbulence and magnetic fields generated by a first-order phase transition”. In: JCAP 12 (2009), p. 024. doi: 10.1088/1475-7516/2009/12/024 . arXiv: 0909.0622 [astro-ph.CO]

2009 arXiv
[195]

General Properties of the Gravitational Wave Spectrum from Phase Transitions

C. Caprini, R. Durrer, T. Konstandin, and G. Servant. “General Properties of the Gravitational Wave Spectrum from Phase Transitions”. In: Phys. Rev. D 79 (2009), p. 083519. doi: 10.1103/PhysRevD.79.083519. arXiv: 0901.1661 [astro-ph.CO]

2009 arXiv
[196]

arXiv: hep-ph/0606298

doi: 10.1016/j.nuclphysb.2006.09.003. arXiv: hep-ph/0606298. 208

2006 arXiv
[197]

Numerical simulations of acoustically generated gravitational waves at a first order phase transition

M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir. “Numerical simulations of acoustically generated gravitational waves at a first order phase transition”. In: Phys. Rev. D 92.12 (2015), p. 123009. doi: 10.1103/PhysRevD.92.123009 . arXiv: 1504.03291 [astro-ph.CO]

2015 arXiv
[198]

Bubble wall velocity with out-of-equilibrium corrections

C. Branchina, A. Conaci, L. Delle Rose, and S. De Curtis. “Bubble wall velocity with out-of-equilibrium corrections”. In: Phys. Rev. D 113.3 (2026), p. 035024. doi: 10.1103/nmkw-7kgk. arXiv: 2510.21942 [hep-ph]

2026
[199]

The Gravitational-Wave Physics

R.-G. Cai, Z. Cao, Z.-K. Guo, S.-J. Wang, and T. Yang. “The Gravitational-Wave Physics”. In: Natl. Sci. Rev. 4.5 (2017), pp. 687–706. doi: 10 . 1093 / nsr / nwx029. arXiv: 1703.00187 [gr-qc]

2017 arXiv
[200]

Gravitational Wave Signals of Electroweak Phase Transition Triggered by Dark Matter

W. Chao, H.-K. Guo, and J. Shu. “Gravitational Wave Signals of Electroweak Phase Transition Triggered by Dark Matter”. In: JCAP 09 (2017), p. 009. doi: 10.1088/ 1475-7516/2017/09/009. arXiv: 1702.02698 [hep-ph] . 213

2017 arXiv
[201]

Shape of the acoustic gravitational wave power spectrum from a first order phase transition

M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir. “Shape of the acoustic gravitational wave power spectrum from a first order phase transition”. In: Phys. Rev. D 96.10 (2017). [Erratum: Phys.Rev.D 101, 089902 (2020)], p. 103520. doi: 10.1103/ PhysRevD.96.103520. arXiv...

2017 arXiv
[202]

Detecting gravitational waves from cosmological phase transitions with LISA: an update

C. Caprini et al. “Detecting gravitational waves from cosmological phase transitions with LISA: an update”. In: JCAP 03 (2020), p. 024. doi: 10.1088/1475-7516/2020/ 03/024. arXiv: 1910.13125 [astro-ph.CO]

2020 arXiv
[203]

Gravitational Waves from First- Order Phase Transition in a Simple Axion-Like Particle Model

P. S. B. Dev, F. Ferrer, Y. Zhang, and Y. Zhang. “Gravitational Waves from First- Order Phase Transition in a Simple Axion-Like Particle Model”. In: JCAP 11 (2019), p. 006. doi: 10.1088/1475-7516/2019/11/006. arXiv: 1905.00891 [hep-ph]

2019 arXiv
[204]

Phase Transitions in an Expanding Universe: Stochastic Gravitational Waves in Standard and Non-Standard Histories

H.-K. Guo, K. Sinha, D. Vagie, and G. White. “Phase Transitions in an Expanding Universe: Stochastic Gravitational Waves in Standard and Non-Standard Histories”. In: JCAP 01 (2021), p. 001. doi: 10.1088/1475-7516/2021/01/001 . arXiv: 2007. 08537 [hep-ph]

2021 doi
[205]

arXiv: 2203.01561 [hep-ph]

arXiv
[206]

Gravitational waves from the sound of a first order phase transition

M. Hindmarsh, S. J. Huber, K. Rummukainen, and D. J. Weir. “Gravitational waves from the sound of a first order phase transition”. In: Phys. Rev. Lett. 112 (2014), p. 041301. doi: 10.1103/PhysRevLett.112.041301. arXiv: 1304.2433 [hep-ph]

2014 arXiv
[207]

Speed of sound in cosmological phase transi- tions and effect on gravitational waves

T. V. I. Tenkanen and J. van de Vis. “Speed of sound in cosmological phase transi- tions and effect on gravitational waves”. In: JHEP 08 (2022), p. 302. doi: 10.1007/ JHEP08(2022)302. arXiv: 2206.01130 [hep-ph]

2022 arXiv
[208]

Gravitational waves from bubble collisions: An analytic derivation

R. Jinno and M. Takimoto. “Gravitational waves from bubble collisions: An analytic derivation”. In: Phys. Rev. D 95.2 (2017), p. 024009. doi: 10.1103/PhysRevD.95. 024009. arXiv: 1605.01403 [astro-ph.CO]

2017 arXiv
[209]

Grav- itational waves from first-order phase transitions: from weak to strong

C. Caprini, R. Jinno, T. Konstandin, A. Roper Pol, H. Rubira, and I. Stomberg. “Grav- itational waves from first-order phase transitions: from weak to strong”. In: JHEP 07 (2025), p. 217. doi: 10.1007/JHEP07(2025)217. arXiv: 2409.03651 [gr-qc]

2025 arXiv
[210]

Measuring gravita- tional wave spectrum from electroweak phase transition and Higgs self-couplings

S. Guan, H.-K. Guo, D. Jiao, Q. Liang, L. Wu, and Y. Zhang. “Measuring gravita- tional wave spectrum from electroweak phase transition and Higgs self-couplings”. In: Phys. Rev. D 113.7 (2026), p. 075014. doi: 10.1103/2xy8-9y1r . arXiv: 2511.00996 [hep-ph]

2026 arXiv
[211]

Supersymmetry, Supergravity and Particle Physics

H. P. Nilles. “Supersymmetry, Supergravity and Particle Physics”. In: Phys. Rept. 110 (1984), pp. 1–162. doi: 10.1016/0370-1573(84)90008-5

1984 doi
[212]

The Search for Supersymmetry: Probing Physics Beyond the Standard Model

H. E. Haber and G. L. Kane. “The Search for Supersymmetry: Probing Physics Beyond the Standard Model”. In: Phys. Rept. 117 (1985), pp. 75–263. doi: 10.1016/0370- 1573(85)90051-1

1985 doi
[213]

The Sphaleron at finite mixing angle

F. R. Klinkhamer and R. Laterveer. “The Sphaleron at finite mixing angle”. In: Z. Phys. C 53 (1992), pp. 247–252. doi: 10.1007/BF01597560

1992 doi
[214]

Static Minimum Energy Path From a Vac- uum to a Sphaleron in the Weinberg-Salam Model

T. Akiba, H. Kikuchi, and T. Yanagida. “Static Minimum Energy Path From a Vac- uum to a Sphaleron in the Weinberg-Salam Model”. In: Phys. Rev. D 38 (1988), pp. 1937–1941. doi: 10.1103/PhysRevD.38.1937

1988 doi
[215]

Phase transition dynamics and gravitational wave spectra of strong first-order phase transition in supercooled universe

X. Wang, F. P. Huang, and X. Zhang. “Phase transition dynamics and gravitational wave spectra of strong first-order phase transition in supercooled universe”. In: JCAP 05 (2020), p. 045. doi: 10 . 1088 / 1475 - 7516 / 2020 / 05 / 045. arXiv: 2003 . 08892 [hep-ph]

2020
[216]

The Gravitational-wave physics II: Progress

L. Bian et al. “The Gravitational-wave physics II: Progress”. In: Sci. China Phys. Mech. Astron. 64 (2021), p. 120401. doi: 10 . 1007 / s11433 - 021 - 1781 - x. arXiv: 2106.10235 [gr-qc]

2021 arXiv
[217]

Improved sphaleron decoupling condition and the Higgs coupling constants in the real singlet-extended standard model

K. Fuyuto and E. Senaha. “Improved sphaleron decoupling condition and the Higgs coupling constants in the real singlet-extended standard model”. In: Phys. Rev. D 90.1 (2014), p. 015015. doi: 10.1103/PhysRevD.90.015015. arXiv: 1406.0433 [hep-ph] . 215

2014 arXiv
[218]

Gravitational waves from supercooled phase transitions: dimensional transmutation meets dimen- sional reduction

M. Kierkla, B. Swiezewska, T. V. I. Tenkanen, and J. van de Vis. “Gravitational waves from supercooled phase transitions: dimensional transmutation meets dimen- sional reduction”. In: JHEP 02 (2024), p. 234. doi: 10 . 1007 / JHEP02(2024 ) 234. arXiv: 2312.12413 [hep-ph] . 214

2024 arXiv
[219]

Bloch Wave Function for the Periodic Sphaleron Potential and Unsuppressed Baryon and Lepton Number Violating Processes

S. .-. H. Tye and S. S. C. Wong. “Bloch Wave Function for the Periodic Sphaleron Potential and Unsuppressed Baryon and Lepton Number Violating Processes”. In: Phys. Rev. D 92.4 (2015), p. 045005. doi: 10 . 1103 / PhysRevD . 92 . 045005. arXiv: 1505.03690 [hep-th]

2015 arXiv
[220]

Electroweak sphaleron with dimension-six operators

X. Gan, A. J. Long, and L.-T. Wang. “Electroweak sphaleron with dimension-six operators”. In: Phys. Rev. D 96.11 (2017), p. 115018. doi: 10.1103/PhysRevD.96. 115018. arXiv: 1708.03061 [hep-ph]

2017 arXiv
[221]

Role of Bloch Waves in baryon-number violating pro- cesses

Y.-C. Qiu and S. H. H. Tye. “Role of Bloch Waves in baryon-number violating pro- cesses”. In: Phys. Rev. D 100.3 (2019), p. 033006. doi: 10 . 1103 / PhysRevD . 100 . 033006. arXiv: 1812.07181 [hep-ph]

2019 arXiv
[222]

Connecting the electroweak sphaleron with gravi- tational waves

R. Zhou, L. Bian, and H.-K. Guo. “Connecting the electroweak sphaleron with gravi- tational waves”. In: Phys. Rev. D 101.9 (2020), p. 091903. doi: 10.1103/PhysRevD. 101.091903. arXiv: 1910.00234 [hep-ph]

2020 arXiv
[223]

Obtaining the sphaleron field configurations with gra- dient flow

Y. Hamada and K. Kikuchi. “Obtaining the sphaleron field configurations with gra- dient flow”. In: Phys. Rev. D 101.9 (2020), p. 096014. doi: 10.1103/PhysRevD.101. 096014. arXiv: 2003.02070 [hep-th]

2020 arXiv
[224]

Higgs boson coupling as a probe of the sphaleron property

S. Kanemura and M. Tanaka. “Higgs boson coupling as a probe of the sphaleron property”. In: Phys. Lett. B 809 (2020), p. 135711. doi: 10.1016/j.physletb.2020. 135711. arXiv: 2005.05250 [hep-ph]

2020 arXiv
[226]

Sphalerons and the Electroweak Phase Transition in Models with Higher Scalar Representations

A. Ahriche, T. A. Chowdhury, and S. Nasri. “Sphalerons and the Electroweak Phase Transition in Models with Higher Scalar Representations”. In: JHEP 11 (2014), p. 096. doi: 10.1007/JHEP11(2014)096. arXiv: 1409.4086 [hep-ph]

2014 arXiv
[227]

Sphaleron in the Higgs Triplet Model

J. Hu, B. Yu, and S. Zhou. “Sphaleron in the Higgs Triplet Model”. In: JHEP 10 (2023), p. 004. doi: 10.1007/JHEP10(2023)004. arXiv: 2307.04713 [hep-ph]

2023 arXiv
[228]

Sphaleron and critical bubble in the scale invariant two Higgs doublet model

K. Fuyuto and E. Senaha. “Sphaleron and critical bubble in the scale invariant two Higgs doublet model”. In: Phys. Lett. B 747 (2015), pp. 152–157. doi: 10.1016/j. physletb.2015.05.061. arXiv: 1504.04291 [hep-ph]

2015 arXiv
[229]

Electroweak sphaleron revisited. II. Study of decay dynamics

K. T. Matchev and S. Verner. “Electroweak sphaleron revisited. II. Study of decay dynamics”. In: Phys. Rev. D 112.11 (2025), p. 113010. doi: 10 . 1103 / pxt7 - hhlz. arXiv: 2505.05608 [hep-ph]

2025 arXiv
[230]

An Effective Sphaleron Awakens

X.-X. Li, M. J. Ramsey-Musolf, T. V. I. Tenkanen, and Y. Wu. “An Effective Sphaleron Awakens”. In: (June 2025). arXiv: 2506.01585 [hep-ph]

2025 arXiv
[231]

Nonperturbative determination of the sphaleron rate for first-order phase transitions

J. Annala, K. Rummukainen, and T. V. I. Tenkanen. “Nonperturbative determination of the sphaleron rate for first-order phase transitions”. In: Phys. Rev. D 113.1 (2026), p. 016014. doi: 10.1103/q1jq-gq9m. arXiv: 2506.04939 [hep-ph]

2026
[232]

The Sphaleron Rate in SU(N) Gauge Theory

G. D. Moore and M. Tassler. “The Sphaleron Rate in SU(N) Gauge Theory”. In: JHEP 02 (2011), p. 105. doi: 10.1007/JHEP02(2011)105. arXiv: 1011.1167 [hep-ph]

2011 arXiv
[233]

SU(3) sphaleron: Numerical solution

F. R. Klinkhamer and P. Nagel. “SU(3) sphaleron: Numerical solution”. In: Phys. Rev. D 96.1 (2017), p. 016006. doi: 10.1103/PhysRevD.96.016006 . arXiv: 1704.07756 [hep-ph]

2017 arXiv
[234]

Sphaleron rate from Euclidean lattice correlators: An exploration

L. Altenkort, A. M. Eller, O. Kaczmarek, L. Mazur, G. D. Moore, and H.-T. Shu. “Sphaleron rate from Euclidean lattice correlators: An exploration”. In: Phys. Rev. D 103.11 (2021), p. 114513. doi: 10.1103/PhysRevD.103.114513 . arXiv: 2012.08279 [hep-lat]

2021 arXiv
[235]

The sphaleron rate from 4D Euclidean lat- tices

M. Barroso Mancha and G. D. Moore. “The sphaleron rate from 4D Euclidean lat- tices”. In: JHEP 01 (2023), p. 155. doi: 10.1007/JHEP01(2023)155 . arXiv: 2210. 05507 [hep-lat]

2023 doi
[236]

arXiv: 2504.07705 [hep-ph]

arXiv
[237]

On sphaleron heating in the presence of fermions

M. Drewes and S. Zell. “On sphaleron heating in the presence of fermions”. In: JCAP 06 (2024), p. 038. doi: 10 . 1088 / 1475 - 7516 / 2024 / 06 / 038. arXiv: 2312 . 13739 [hep-ph]. 216

2024
[238]

Electroweak sphaleron revisited. I. Static solutions, energy barrier, and unstable modes

K. T. Matchev and S. Verner. “Electroweak sphaleron revisited. I. Static solutions, energy barrier, and unstable modes”. In: Phys. Rev. D 112.11 (2025), p. 113009. doi: 10.1103/nsrp-hwkg. arXiv: 2505.05607 [hep-ph]

2025 arXiv
[239]

Revisiting the sphaleron and axion production rates in QCD at high temperatures

S. Guin and S. Sharma. “Revisiting the sphaleron and axion production rates in QCD at high temperatures”. In: (Apr. 2026). arXiv: 2604.07256 [hep-lat]

2026 arXiv
[240]

The Riddle of high-energy baryon number violation

M. P. Mattis. “The Riddle of high-energy baryon number violation”. In: Phys. Rept. 214 (1992). Ed. by E. Gava, K. Narain, S. Randjbar-Daemi, E. Sezgin, and Q. Shafi, pp. 159–221. doi: 10.1016/0370-1573(92)90033-V

1992 doi
[242]

Search for Sphalerons in Proton-Proton Collisions

J. Ellis and K. Sakurai. “Search for Sphalerons in Proton-Proton Collisions”. In: JHEP 04 (2016), p. 086. doi: 10.1007/JHEP04(2016)086. arXiv: 1601.03654 [hep-ph]

2016 arXiv
[243]

Search for black holes and sphalerons in high-multiplicity final states in proton-proton collisions at √s = 13 TeV

A. M. Sirunyan et al. “Search for black holes and sphalerons in high-multiplicity final states in proton-proton collisions at √s = 13 TeV”. In: JHEP 11 (2018), p. 042. doi: 10.1007/JHEP11(2018)042. arXiv: 1805.06013 [hep-ex]

2018 arXiv
[244]

Limits on Electroweak Instanton- Induced Processes with Multiple Boson Production

A. Ringwald, K. Sakurai, and B. R. Webber. “Limits on Electroweak Instanton- Induced Processes with Multiple Boson Production”. In: JHEP 11 (2018), p. 105. doi: 10.1007/JHEP11(2018)105. arXiv: 1809.10833 [hep-ph]

2018 arXiv
[245]

Sphaleron rate from lattice QCD

C. Bonanno, F. D’Angelo, M. D’Elia, L. Maio, and M. Naviglio. “Sphaleron rate from lattice QCD”. In: Nucl. Part. Phys. Proc. 343 (2024), pp. 113–119. doi: 10.1016/j. nuclphysbps.2023.09.019. arXiv: 2309.13327 [hep-lat]

2024 arXiv
[246]

Sphaleron Rate of Nf=2+1 QCD

C. Bonanno, F. D’Angelo, M. D’Elia, L. Maio, and M. Naviglio. “Sphaleron Rate of Nf=2+1 QCD”. In: Phys. Rev. Lett. 132.5 (2024), p. 051903. doi: 10 . 1103 / PhysRevLett.132.051903. arXiv: 2308.01287 [hep-lat] . 217

2024 arXiv
[247]

Sphaleron freeze-in baryogenesis with gravitational waves from the QCD transition

F. Gao, J. Harz, C. Hati, Y. Lu, I. M. Oldengott, and G. White. “Sphaleron freeze-in baryogenesis with gravitational waves from the QCD transition”. In: Phys. Lett. B 869 (2025), p. 139849. doi: 10.1016/j.physletb.2025.139849 . arXiv: 2309.00672 [hep-ph]

2025
[248]

QCD corrections to the electroweak sphaleron rate

D. Bödeker and P. Klose. “QCD corrections to the electroweak sphaleron rate”. In: JHEP 05 (2026), p. 024. doi: 10 . 1007 / JHEP05(2026 ) 024. arXiv: 2510 . 20594 [hep-ph]

2026
[249]

Electroweak sphaleron in a strong magnetic field

D. L. J. Ho and A. Rajantie. “Electroweak sphaleron in a strong magnetic field”. In: Phys. Rev. D 102.5 (2020), p. 053002. doi: 10.1103/PhysRevD.102.053002 . arXiv: 2005.03125 [hep-th]

2020 arXiv
[250]

Electroweak sphaleron in a magnetic field

J. Annala and K. Rummukainen. “Electroweak sphaleron in a magnetic field”. In: Phys. Rev. D 107.7 (2023), p. 073006. doi: 10.1103/PhysRevD.107.073006 . arXiv: 2301.08626 [hep-ph]

2023 arXiv
[251]

Annihilation of electroweak dumbbells

T. Patel and T. Vachaspati. “Annihilation of electroweak dumbbells”. In: JHEP 02 (2024), p. 164. doi: 10.1007/JHEP02(2024)164. arXiv: 2311.00026 [hep-ph]

2024 arXiv
[252]

Impact of primordial magnetic fields on the first- order electroweak phase transition

Y. Di, L. Bian, and R.-G. Cai. “Impact of primordial magnetic fields on the first- order electroweak phase transition”. In: Phys. Rev. D 113.4 (2026), p. 043529. doi: 10.1103/jrd3-s1h2. arXiv: 2508.07416 [hep-ph]

2026 arXiv
[253]

Speculations on primordial magnetic helicity

J. M. Cornwall. “Speculations on primordial magnetic helicity”. In: Phys. Rev. D 56 (1997), pp. 6146–6154. doi: 10.1103/PhysRevD.56.6146. arXiv: hep-th/9704022

1997 arXiv
[254]

Estimate of the primordial magnetic field helicity

T. Vachaspati. “Estimate of the primordial magnetic field helicity”. In: Phys. Rev. Lett. 87 (2001), p. 251302. doi: 10.1103/PhysRevLett.87.251302 . arXiv: astro- ph/0101261

2001
[255]

On the phenomenology of sphaleron- induced processes at the LHC and beyond

A. Papaefstathiou, S. Plätzer, and K. Sakurai. “On the phenomenology of sphaleron- induced processes at the LHC and beyond”. In: JHEP 12 (2019), p. 017. doi: 10. 1007/JHEP12(2019)017. arXiv: 1910.04761 [hep-ph]

2019 arXiv
[256]

The Sphaleron at nonzero Weinberg angle

M. E. R. James. “The Sphaleron at nonzero Weinberg angle”. In: Z. Phys. C 55 (1992), pp. 515–524. doi: 10.1007/BF01565115. 218

1992 doi
[257]

Sphalerons at finite mixing angle

J. Kunz, B. Kleihaus, and Y. Brihaye. “Sphalerons at finite mixing angle”. In: Phys. Rev. D 46 (1992), pp. 3587–3600. doi: 10.1103/PhysRevD.46.3587

1992 doi
[258]

arXiv: hep-lat/9510020

doi: 10.1016/0550-3213(96)00052-1. arXiv: hep-lat/9510020

arXiv
[259]

The Sphaleron in a magnetic field and electroweak baryogenesis

D. Comelli, D. Grasso, M. Pietroni, and A. Riotto. “The Sphaleron in a magnetic field and electroweak baryogenesis”. In: Phys. Lett. B 458 (1999), pp. 304–309. doi: 10.1016/S0370-2693(99)00381-0. arXiv: hep-ph/9903227

1999 arXiv
[260]

Generic rules for high temperature dimensional reduction and their application to the standard model

K. Kajantie, M. Laine, K. Rummukainen, and M. E. Shaposhnikov. “Generic rules for high temperature dimensional reduction and their application to the standard model”. In: Nucl. Phys. B 458 (1996), pp. 90–136. doi: 10.1016/0550- 3213(95)00549- 8 . arXiv: hep-ph/9508379

1996 arXiv
[261]

Effective field theory approach to high temperature ther- modynamics

E. Braaten and A. Nieto. “Effective field theory approach to high temperature ther- modynamics”. In: Phys. Rev. D 51 (1995), pp. 6990–7006. doi: 10.1103/PhysRevD. 51.6990. arXiv: hep-ph/9501375

1995 arXiv
[262]

Nonperturbative Analysis of the Electroweak Phase Transition in the Two Higgs Doublet Model

J. O. Andersen, T. Gorda, A. Helset, L. Niemi, T. V. I. Tenkanen, A. Tranberg, A. Vuorinen, and D. J. Weir. “Nonperturbative Analysis of the Electroweak Phase Transition in the Two Higgs Doublet Model”. In: Phys. Rev. Lett. 121.19 (2018), p. 191802. doi: 10.1103/PhysRevLett.12...

2018 arXiv
[263]

Theoretical un- certainties for cosmological first-order phase transitions

D. Croon, O. Gould, P. Schicho, T. V. I. Tenkanen, and G. White. “Theoretical un- certainties for cosmological first-order phase transitions”. In: JHEP 04 (2021), p. 055. doi: 10.1007/JHEP04(2021)055. arXiv: 2009.10080 [hep-ph]

2021 arXiv
[264]

Effective field theory approach to thermal bubble nu- cleation

O. Gould and J. Hirvonen. “Effective field theory approach to thermal bubble nu- cleation”. In: Phys. Rev. D 104.9 (2021), p. 096015. doi: 10.1103/PhysRevD.104. 096015. arXiv: 2108.04377 [hep-ph] . 220

2021 arXiv
[265]

Helical Magnetic Fields from Sphaleron Decay and Baryogenesis

C. J. Copi, F. Ferrer, T. Vachaspati, and A. Achucarro. “Helical Magnetic Fields from Sphaleron Decay and Baryogenesis”. In: Phys. Rev. Lett. 101 (2008), p. 171302. doi: 10.1103/PhysRevLett.101.171302. arXiv: 0801.3653 [astro-ph]

2008 arXiv
[266]

Phase Structure of Electroweak Vacuum in a Strong Magnetic Field: The Lattice Results

M. N. Chernodub, V. A. Goy, and A. V. Molochkov. “Phase Structure of Electroweak Vacuum in a Strong Magnetic Field: The Lattice Results”. In: Phys. Rev. Lett. 130.11 (2023), p. 111802. doi: 10 . 1103 / PhysRevLett . 130 . 111802. arXiv: 2206 . 14008 [hep-lat]. 219

2023
[267]

Strongly interacting matter in extreme magnetic fields

P. Adhikari et al. “Strongly interacting matter in extreme magnetic fields”. In: Prog. Part. Nucl. Phys. 146 (2026), p. 104199. doi: 10.1016/j.ppnp.2025.104199. arXiv: 2412.18632 [nucl-th]

2026
[269]

High-Temperature Yang-Mills Theories and Three- Dimensional Quantum Chromodynamics

T. Appelquist and R. D. Pisarski. “High-Temperature Yang-Mills Theories and Three- Dimensional Quantum Chromodynamics”. In: Phys. Rev. D 23 (1981), p. 2305. doi: 10.1103/PhysRevD.23.2305

1981 doi
[270]

Towards Accurate Gravitational Wave Predictions: Gauge-Invariant Nucleation in the Electroweak Phase Transition

J. Liu, R. Qin, and L. Bian. “Towards Accurate Gravitational Wave Predictions: Gauge-Invariant Nucleation in the Electroweak Phase Transition”. In: (Jan. 2026). arXiv: 2601.05793 [hep-ph]

2026
[271]

Approximate Computation of the Small Fluctuation Determinant Around a Sphaleron

L. Carson and L. D. McLerran. “Approximate Computation of the Small Fluctuation Determinant Around a Sphaleron”. In: Phys. Rev. D 41 (1990), p. 647. doi: 10.1103/ PhysRevD.41.647

1990
[272]

Exact Computation of the Small Fluctuation Determinant Around a Sphaleron

L. Carson, X. Li, L. D. McLerran, and R.-T. Wang. “Exact Computation of the Small Fluctuation Determinant Around a Sphaleron”. In: Phys. Rev. D 42 (1990), pp. 2127–

1990
[273]

Quantum fluctuations around the electroweak sphaleron

J. Baacke and S. Junker. “Quantum fluctuations around the electroweak sphaleron”. In: Phys. Rev. D 49 (1994), pp. 2055–2073. doi: 10.1103/PhysRevD.49.2055. arXiv: hep-ph/9308310

1994 arXiv
[274]

Quantum fluctuations of the electroweak sphaleron: Erratum and addendum

J. Baacke and S. Junker. “Quantum fluctuations of the electroweak sphaleron: Erratum and addendum”. In: Phys. Rev. D 50 (1994), pp. 4227–4228. doi: 10.1103/PhysRevD. 50.4227. arXiv: hep-th/9402078

1994 arXiv
[275]

Computing the gauge-invariant bubble nucleation rate in finite temperature effective field theory

J. Hirvonen, J. Löfgren, M. J. Ramsey-Musolf, P. Schicho, and T. V. I. Tenkanen. “Computing the gauge-invariant bubble nucleation rate in finite temperature effective field theory”. In: JHEP 07 (2022), p. 135. doi: 10.1007/JHEP07(2022)135 . arXiv: 2112.08912 [hep-ph]

2022 arXiv
[276]

DRalgo: A package for effective field theory approach for thermal phase transitions

A. Ekstedt, P. Schicho, and T. V. I. Tenkanen. “DRalgo: A package for effective field theory approach for thermal phase transitions”. In: Comput. Phys. Commun. 288 (2023), p. 108725. doi: 10.1016/j.cpc.2023.108725. arXiv: 2205.08815 [hep-ph]

2023
[277]

Radiative first-order phase transitions to next- to-next-to-leading order

A. Ekstedt, O. Gould, and J. Löfgren. “Radiative first-order phase transitions to next- to-next-to-leading order”. In: Phys. Rev. D 106.3 (2022). [Erratum: Phys.Rev.D 110, 019901 (2024)], p. 036012. doi: 10.1103/PhysRevD.106.036012. arXiv: 2205.07241 [hep-ph]

2022 arXiv
[278]

Perturbative effective field theory expansions for cos- mological phase transitions

O. Gould and T. V. I. Tenkanen. “Perturbative effective field theory expansions for cos- mological phase transitions”. In: JHEP 01 (2024), p. 048. doi: 10.1007/JHEP01(2024)

2024 doi
[279]

arXiv: 2309.01672 [hep-ph]

arXiv
[280]

Cosmological phase transitions at three loops: The final verdict on perturbation theory

A. Ekstedt, P. Schicho, and T. V. I. Tenkanen. “Cosmological phase transitions at three loops: The final verdict on perturbation theory”. In: Phys. Rev. D 110.9 (2024), p. 096006. doi: 10.1103/PhysRevD.110.096006. arXiv: 2405.18349 [hep-ph]

2024 arXiv
[281]

On the Gauge Dependence of Spontaneous Symmetry Breaking in Gauge Theories

N. K. Nielsen. “On the Gauge Dependence of Spontaneous Symmetry Breaking in Gauge Theories”. In: Nucl. Phys. B 101 (1975), pp. 173–188. doi: 10.1016/0550- 3213(75)90301-6

1975 doi
[282]

Gauge Invariance in the Effective Action and Potential

R. Fukuda and T. Kugo. “Gauge Invariance in the Effective Action and Potential”. In: Phys. Rev. D 13 (1976), p. 3469. doi: 10.1103/PhysRevD.13.3469. 222

1976 doi
[283]

Gauge independence of the bubble nucleation rate in theories with radiative symmetry breaking

D. Metaxas and E. J. Weinberg. “Gauge independence of the bubble nucleation rate in theories with radiative symmetry breaking”. In: Phys. Rev. D 53 (1996), pp. 836–843. doi: 10.1103/PhysRevD.53.836. arXiv: hep-ph/9507381

1996 arXiv
[284]

Baryon Washout, Electroweak Phase Transi- tion, and Perturbation Theory

H. H. Patel and M. J. Ramsey-Musolf. “Baryon Washout, Electroweak Phase Transi- tion, and Perturbation Theory”. In: JHEP 07 (2011), p. 029. doi: 10.1007/JHEP07(2011)

2011 doi
[285]

On the gauge dependence of vacuum transitions at finite temperature

M. Garny and T. Konstandin. “On the gauge dependence of vacuum transitions at finite temperature”. In: JHEP 07 (2012), p. 189. doi: 10.1007/JHEP07(2012)189 . arXiv: 1205.3392 [hep-ph]

2012 arXiv
[286]

Consistent Use of the Standard Model Effective Potential

A. Andreassen, W. Frost, and M. D. Schwartz. “Consistent Use of the Standard Model Effective Potential”. In: Phys. Rev. Lett. 113.24 (2014), p. 241801. doi: 10 . 1103 / PhysRevLett.113.241801. arXiv: 1408.0292 [hep-ph]

2014 arXiv
[287]

Theory of the condensation point

J. S. Langer. “Theory of the condensation point”. In: Annals Phys. 41 (1967), pp. 108–

1967
[288]

doi: 10.1016/0003-4916(67)90200-X

doi
[289]

Statistical theory of the decay of metastable states

J. S. Langer. “Statistical theory of the decay of metastable states”. In: Annals Phys. 54 (1969), pp. 258–275. doi: 10.1016/0003-4916(69)90153-5

1969 doi
[290]

The Fate of the False Vacuum. 1. Semiclassical Theory

S. R. Coleman. “The Fate of the False Vacuum. 1. Semiclassical Theory”. In: Phys. Rev. D 15 (1977). [Erratum: Phys.Rev.D 16, 1248 (1977)], pp. 2929–2936. doi: 10. 1103/PhysRevD.16.1248

1977
[291]

The Fate of the False Vacuum. 2. First Quantum Corrections

C. G. Callan Jr. and S. R. Coleman. “The Fate of the False Vacuum. 2. First Quantum Corrections”. In: Phys. Rev. D 16 (1977), pp. 1762–1768. doi: 10.1103/PhysRevD. 16.1762

1977 doi
[292]

Fate of the False Vacuum at Finite Temperature: Theory and Applica- tions

A. D. Linde. “Fate of the False Vacuum at Finite Temperature: Theory and Applica- tions”. In: Phys. Lett. B 100 (1981), pp. 37–40. doi: 10.1016/0370-2693(81)90281- 1

1981 doi
[293]

Quantum Statistical Metastability

I. Affleck. “Quantum Statistical Metastability”. In: Phys. Rev. Lett. 46 (1981), p. 388. doi: 10.1103/PhysRevLett.46.388

1981 doi
[294]

arXiv: 2310.06972 [hep-ph]

arXiv
[298]

arXiv: 1101.4665 [hep-ph]

arXiv
[2019]

doi: 10.1201/9780429492860

isbn: 978-0-429-49286-0, 978-0-201-62674-2. doi: 10.1201/9780429492860

doi
[2021]

Mar. 2022. arXiv: 2203.05010 [hep-ph]

2022 arXiv
[2143]

doi: 10.1103/PhysRevD.42.2127. 221

doi
[2890]

arXiv: hep-ph/9605288

doi: 10.1103/PhysRevLett.77.2887. arXiv: hep-ph/9605288

arXiv
[3873]

arXiv: hep-ph/9609240

arXiv

Pith tools

Reviewed July 31, 2026 · model on record in the stance chip above.

[1] [1]

A Saddle Point Solution in the Weinberg-Salam Theory

F. R. Klinkhamer and N. S. Manton. “A Saddle Point Solution in the Weinberg-Salam Theory”. In: Phys. Rev. D 30 (1984), p. 2212. doi: 10.1103/PhysRevD.30.2212

doi:10.1103/physrevd.30.2212 1984

[2] [2]

Topology in the Weinberg-Salam Theory

N. S. Manton. “Topology in the Weinberg-Salam Theory”. In: Phys. Rev. D 28 (1983), p. 2019. doi: 10.1103/PhysRevD.28.2019

doi:10.1103/physrevd.28.2019 1983

[3] [3]

Recent progress in baryogenesis

A. Riotto and M. Trodden. “Recent progress in baryogenesis”. In: Ann. Rev. Nucl. Part. Sci. 49 (1999), pp. 35–75. doi: 10 . 1146 / annurev . nucl . 49 . 1 . 35. arXiv: hep-ph/9901362

arXiv 1999

[4] [4]

The Origin of the matter - antimatter asymmetry

M. Dine and A. Kusenko. “The Origin of the matter - antimatter asymmetry”. In: Rev. Mod. Phys. 76 (2003), p. 1. doi: 10.1103/RevModPhys.76.1. arXiv: hep-ph/0303065

arXiv 2003

[5] [5]

Baryogenesis from the weak scale to the grand unifi- cation scale

D. Bodeker and W. Buchmuller. “Baryogenesis from the weak scale to the grand unifi- cation scale”. In: Rev. Mod. Phys. 93.3 (2021), p. 035004. doi: 10.1103/RevModPhys. 93.035004. arXiv: 2009.07294 [hep-ph]

arXiv 2021

[6] [6]

Planck 2018 results. VI. Cosmological parameters

N. Aghanim et al. “Planck 2018 results. VI. Cosmological parameters”. In: Astron. Astrophys. 641 (2020). [Erratum: Astron.Astrophys. 652, C4 (2021)], A6. doi: 10 . 1051/0004-6361/201833910. arXiv: 1807.06209 [astro-ph.CO]

arXiv 2018

[7] [7]

Big-Bang Nucleosynthesis after Planck

B. D. Fields, K. A. Olive, T.-H. Yeh, and C. Young. “Big-Bang Nucleosynthesis after Planck”. In: JCAP 03 (2020). [Erratum: JCAP 11, E02 (2020)], p. 010. doi: 10.1088/ 1475-7516/2020/03/010. arXiv: 1912.01132 [astro-ph.CO]

arXiv 2020

[8] [8]

A Matter - antimatter universe?

A. G. Cohen, A. De Rujula, and S. L. Glashow. “A Matter - antimatter universe?” In: Astrophys. J. 495 (1998), pp. 539–549. doi: 10 . 1086 / 305328. arXiv: astro - ph/9707087

arXiv 1998