3d physics and the electroweak phase transition: a framework for lattice Monte Carlo analysis

K. Farakos; K. Kajantie; K. Rummukainen; M. Shaposhnikov

REVIEW

3d physics and the electroweak phase transition: a framework for lattice Monte Carlo analysis

K. Farakos, K. Kajantie, K. Rummukainen, M. Shaposhnikov

High Energy Physics - Lattice · Submitted 20 Dec 1994

Pith's verdict: A solid, honest methods paper: the condensate construction and the analytic lattice perturbation theory hold up, but rho is a calibration constant, not a computation, and the 0.3% temperature claim leans on it harder than the data supports.

T0 · AI review

How this review was made: An AI referee (selfhosted/deepseek-v4.1-flash) read the paper on November 11, 2026 and answered a fixed list of questions about it. T0 is the starting level every paper gets. The levels describe how deeply Pith has checked the paper, never the authors.

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

How Pith checks papers →

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

Challenge this review Comment (0) Read on arXiv ↗

Cite ▾

arXiv IDhep-lat/9412091 (version 1)

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

CitationK. Farakos, K. Kajantie, K. Rummukainen, M. Shaposhnikov. "3d physics and the electroweak phase transition: a framework for lattice Monte Carlo analysis." arXiv:hep-lat/9412091 (1994). https://pith.science/paper/MNKIFMXS

Cite this reviewBibTeX for Pith's review of this paper

Claim paper

Why Pith says this

Highlight any text to comment on it.

Editor's note

read the letter

This is the infrastructure paper for the 3d lattice electroweak program, and it does the unglamorous work well. The genuinely new pieces are the gauge-invariant condensates defined as derivatives of the vacuum energy with respect to the five theory parameters (section 4), and their 2-loop evaluation in the broken phase (eqs. 71, 75-78). That construction is clean and it is the right one: it sidesteps the gauge-dependence of the effective potential without hand-waving. The lattice perturbation theory is also real work, not decoration. omega_rho = 0.44 comes out of pure scalar theory (eqs. 110-117), nu_rho = 1.01 out of the SSV diagrams, and both reduce to definite integrals (eqs. 175-176) with quoted numerical values. Anyone can check those. The paper also corrects its own earlier published numbers from ref [4], which is the kind of thing that buys credibility rather than costing it. The distinction between the linear and logarithmic counterterms, and the demonstration that the 1/m^2 poles cancel between one- and two-loop pieces, are handled properly. Where I part company with the harshest reading: the 'exact in the continuum limit' claim is about the form of eqs. 91, 92, 138, 140, and that form is exact by super-renormalizability. rho is a scheme-conversion constant that has to be fixed nonperturbatively; the paper says so. The soft spot is narrower and more specific: the numerical value of rho. It comes from a five-parameter fit to the condensate, with A and B absorbing finite-a corrections and psi-tilde unconstrained over -700 to 700. Nothing in the data separates rho from those except curve collapse across beta_G. The A0-integrated cross-check giving 2.03(5) against 2.18(6) is the honest internal signal, and the authors report it rather than bury it. The systematic from the uncomputed Debye-mass constants is bounded by an assumed inequality, not evaluated. So the 0.3% temperature figure is a statistical reach, not a demonstrated accuracy. Read it as a framework with a calibrated constant, not a finished prediction. Worth a serious referee, and worth citing if you use the condensate relations.

Referee report

Significance

The paper's structural results are genuinely valuable and are stated with unusual care. The 2-loop effective potential (Eq. 34) and the sunset function (Eq. 36) are explicit; the lattice tadpole, one-loop vacuum energy, and sunset expansions (Eqs. 169–174) are given with numerical coefficients; and the two non-trivial 2-loop integrals delta = 1.94 (Eq. 175) and zeta = -0.314 (Eq. 176) are written as definite integrals with numerical values, which makes them independently checkable. The derivation of omega_rho in pure scalar theory (Eqs. 110–117) is a clean step-by-step computation. The claim that the constant-physics curves have no higher-loop contributions follows from 3d super-renormalizability and is correct as a statement about the structure of the matching. The paper also ships an explicit erratum to its own published Letter (the correction of rho and nu_rho in ref. [4], §6.3), which is the kind of self-correction that should be credited. The framework is falsifiable: the fitted rho must be Higgs-mass independent, and the paper tests this at m_H = 160 GeV (Eq. 149).

Major objections (3)

[§7, Eq. (148) and surrounding text] The extraction of rho = 2.18(6) rests on a five-parameter fit (rho, A, B, phi-tilde, psi-tilde) to the scalar condensate at beta_G = 12, 20, 24, 32, 40, with the finite-a correction assumed to have the form A x + B x^2 (Eq. 146) and the 3- and 4-loop continuum corrections assumed to have the form of Eq. (147). The paper itself reports that psi-tilde is unconstrained over -700 < psi-tilde < 700, i.e. the 4-loop coefficient is effectively a free function that can absorb residual finite-a and higher-order effects. The quoted error 2.18(6) is statistical only; the systematic from truncating f(x) at two terms is not quantified, and the paper offers no third-term stability check. This is load-bearing because rho is the single number that calibrates the lattice-to-continuum map for the Higgs mass relation (Eq. 99), and the 0.3% temperature-accuracy claim in §8 depends on it. The authors should either add a third term to f(x) and quote the shift in rho, or state explicitly that the quoted error is statistical and that the systematic from the fit form is not bounded.
[§8, Eq. (165) versus Eq. (148)] The independent cross-check via the A0-integrated-out theory gives rho = 2.03(5), which the authors state is about 2 standard deviations below the direct value 2.18(6). They attribute the discrepancy to the uncomputed 2-loop Debye mass constants c1, c2 in Eq. (30), bounded by the assumed inequality |zeta_g + (lambda_3/g_3^2) zeta_{g lambda}| < 14 (Eq. 156). That bound is asserted, not derived, and the paper does not show where the number 14 comes from. If the true value sits at the edge of the bound, the discrepancy disappears but so does the 0.3% accuracy claim; if it sits near zero, the two routes genuinely disagree at the quoted precision. The paper should either derive the bound or present the 0.3% figure as conditional on it, and should state what value of the combination would be required to reconcile 2.18(6) with 2.03(5).
[§6.3, footnote 14, and the abstract claim of exactness] The abstract (abstract:s3) states that the relations between lattice couplings and continuum parameters are 'exact in the continuum limit', and §6.2 says the constant-physics curves 'do not have any higher loop contributions'. Both statements are correct for the structure of the matching, but the numerical implementation involves truncations that are numerically, not structurally, motivated. Footnote 14 states that f_2D is formally multiplied by log^2(aT), which is singular in the continuum limit, and is dropped because 'in real lattice simulations with beta_G < 40, the value of this log never exceeds 2'. Similarly P_2D = 0 and the O(g^4) terms in Eq. (30) are dropped by power counting, and the paper itself notes that 'the formal suppression of the higher-order terms does not necessarily imply numerical suppression'. The 'exact' language should be qualified to 'exact up to the stated truncations', or the truncations should be shown to vanish in the continuum limit. As written, a reader could take 'exact' to cover the numerical values of rho, nu_rho, omega_rho, which it does not.

Minor objections (7)

[§6.2 versus Appendix A, Eq. (170)] The text of §6.2 quotes sigma = 3.17159, while Appendix A, Eq. (170) gives sigma = 3.1759114. These should be reconciled; the value enters Eq. (91) and hence the constant-physics curve.
[Notation, Eq. (102) versus Eq. (169)] The symbol rho is used both for the constant-physics parameter rho = 2.18(6) (Eq. 102) and for the lattice tadpole coefficient rho = 0.15281 (Eq. 169). A different symbol for one of the two would help the reader, especially since both appear in the same section.
[§6.3, erratum to ref. [4]] The erratum corrects ref. [4] to rho = 2.0 and nu_rho = 0.66, whereas this paper quotes rho = 2.18(6) and nu_rho = 1.01. The reader would benefit from a sentence explaining whether the difference is due to improved fits, a different data set, or a different truncation.
[Figs. 5 and 6] The vertical axis is labelled 'Delta R^2 beta_H beta_G / x' and the horizontal axis 'x = phi/(g T beta_G)'. Since the collapse of points at different beta_G onto a single curve is the visual evidence for the fit, the caption should state explicitly what normalization is applied and what the units of the vertical axis are.
[§2.2.2] The estimates of '10^3 larger 3d volumes' and '3 to 4 orders of magnitude gain in computer time' rest on assumed values m/T ~ 0.2 and p = 10%. These assumptions should be stated in the text at the point where the numbers are quoted, not only in the surrounding prose.
[Appendix A] The numerical constants rho = 0.15281, zeta = -0.6, delta = 1.94, and zeta = -0.314 are quoted without an indication of the integration method or the numerical precision. Since these enter the central results, a sentence on how they were obtained and to what accuracy would be appropriate.
[Abstract and §9] The abstract's 'will be able to reliably determine' and the 0.3% temperature-accuracy figure in §8 are projections; the actual determination of T_c is deferred to ref. [3], listed as 'in preparation'. This is appropriate for a framework paper, but the abstract should make clear that the 0.3% figure is an estimate of the accuracy the framework will deliver, not a demonstrated result of this paper.

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

The paper

The paper claims

The paper argues that the electroweak phase transition can be computed reliably by simulating a three-dimensional effective theory on the lattice, because the map between lattice couplings and continuum couplings — the constant physics曲线 —,

The reading

The paper asks how to compute, from first principles, the numbers that characterise the electroweak phase transition: the temperature at which it happens, the size of the jump in the order parameter, and the latent heat. Its answer is a two-stage strategy. First, replace the full four-dimensional finite-temperature Standard Model with a three-dimensional effective theory in which the heavy thermal modes have been integrated out analytically; second, simulate that 3d theory on the lattice, where the strongly coupled infrared physics is handled numerically. The bridge between the two stages is a set of relations — the constant physics curves — connecting lattice couplings to continuum couplings, and the paper's claim is that these relations, together with the relations between lattice and $overline{mathrm{MS}}$ condensates, are exact in the continuum limit. If that holds, a lattice simulation stops being a model of a model and becomes a numerically controlled statement about the hot Standard Model, with the residual error budget set by ordinary perturbation theory rather than by the lattice.

What carries the argument

The load-bearing mechanism is super-renormalizability of the 3d theory: because only one- and two-loop graphs diverge, the difference between lattice and continuum regularization can only be a linear counterterm, a logarithmic counterterm, and a constant. That reduces the entire matching problem to three numbers multiplying $g_3^4$, $lambda_3 g_3^2$ and $lambda_3^2$ in the mass polynomial, which is what makes an exact-in-the-continuum-limit relation possible at all. The second piece of machinery is the gauge-invariant condensate: differentiating the finite vacuum energy density with respect to $m_3^2$, $m_D^2$, $lambda_3$, $lambda_A$ and $g_3^2$ produces order parameters that are computable at two loops and measurable on the lattice with small statistical error, sidestepping the gauge dependence of the effective potential itself.

Extended reading notes

Core claim

The central claim is that the 3d gauge-Higgs theory is super-renormalizable, so its ultraviolet divergences occur only at one and two loops and all scheme dependence collapses into a small set of constants. Consequently the lattice-to-continuum map can be written exactly in the continuum limit and is parametrized by just three pure numbers, denoted $rho$, $nu_rho$ and $omega_rho$. The authors compute $nu_rho=1.01$ and $omega_rho=0.44$ analytically in lattice perturbation theory, and extract $rho=2.18(6)$ by matching Monte Carlo measurements of the scalar condensate $langle R_L^2 rangle$ against the two-loop continuum prediction, fitting simultaneously for the finite-lattice-spacing coefficients $A=5.09(25)$, $B=-3.40(23)$ and a higher-order coefficient $tilde{phi}=-162(22)$. They also define gauge-invariant condensates as derivatives of the renormalized vacuum energy density with respect to the couplings, so that the latent heat of a first-order transition is just the jump of the scalar condensate between phases. As a cross-check they integrate out the $A_0$ field, obtain $rho'=1.62(7)$ from a separate simulation, and convert it analytically to $rho=2.03(5)$ — a value the authors themselves note is about two standard deviations below the direct determination.

Load-bearing premise

The number $rho$ is not measured directly: it is inferred from a five-parameter fit in which the finite-lattice-spacing coefficients $A$ and $B$ and an unconstrained higher-order coefficient float alongside it, so $rho$ is identified only by requiring data at different lattice spacings to collapse onto a single curve.

Editorial extensions

If this is right

The transition temperature can be located to roughly 0.3 percent, which at $m_H=80$ GeV means an uncertainty of about 0.5 GeV — fine enough to decide whether electroweak baryogenesis survives for a given Higgs mass.
The latent heat and the order-parameter jump follow directly from the difference of the scalar condensate between the broken and symmetric phases, with no need for a four-dimensional lattice simulation.
A 3d lattice with $beta_G$ between 12 and 40 reaches the same finite-spacing accuracy as a 4d simulation at a cost roughly three to four orders of magnitude smaller in computer time.
Comparing measured condensates with the two-loop prediction yields an empirical estimate of the neglected three-loop contribution, quoted as $phi=-49(22)$, which is a direct check on how well perturbation theory works in the broken phase.
The same constant physics curves can be written for the theory with the $A_0$ field integrated out, giving an independent route to the same physics and a consistency test of the matching procedure.

Reading between the lines

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

The roughly two-sigma gap between $rho=2.18(6)$ and the $A_0$-eliminated value $2.03(5)$ is the most informative number in the paper for anyone judging the programme: if it survives better statistics, it points to the neglected $g^4$ contributions to the Debye screening mass being numerically larger than power counting suggests, which would be a cheap diagnostic for the whole dimensional-reduction
Because finite-spacing effects in 3d start at order $a$ rather than $a^2$, the practical reach of this method is set by how tightly the linear coefficient $A$ can be pinned — a generic feature of simulating any super-renormalizable 3d theory, not something specific to the electroweak case.
The trick of defining order parameters as derivatives of the vacuum energy with respect to couplings is portable: any super-renormalizable 3d theory one wishes to simulate, hot QCD somewhat above its transition being the obvious neighbour, admits the same construction.
The framework buys precision only on the broken side; the paper concedes that the symmetric phase is strongly coupled and inaccessible to perturbation theory, so the most cosmologically interesting regime is precisely where this machinery hands off rather than delivers.

Original abstract

We discuss a framework relying on both perturbative and non-perturbative lattice computations which will be able to reliably determine the parameters of the EW phase transition. A motivation for the use of 3d effective theory in the lattice simulations, rather than the complete 4d one, is provided. We introduce and compute on the 2-loop level a number of gauge-invariant order parameters -- condensates, which can be measured with high accuracy in MC simulations. The relation between MSbar and lattice condensates is found, together with the relation between lattice couplings and continuum parameters (the constant physics curves). These relations are exact in the continuum limit.

The compiled record

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

Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,213 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.04 · states limitation 0.19 · human participants 0.01 · controlled comparison 0.03 · randomized assignment 0.01 · states quantitative result 0.12 · compares with prior results 0.18 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

We discuss a framework relying on both perturbative and non-perturbative lattice computations which will be able to reliably determine the parameters of the EW phase transition. A motivation for the use of 3d effective theory in the lattice simulations, rather than the complete 4d one, is provided. We introduce and compute on the 2-loop level a number of gauge-invariant order parameters -- condensates, which can be measured with high accuracy in MC simulations. The relation between MSbar and lattice condensates is found, together with the relation between lattice couplings and continuum parameters (the constant physics curves). These relations are exact in the continuum limit.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We discuss a framework relying on both perturbative and non-perturbative lattice computations which will be able to reliably determine the parameters of the EW phase transition.	contribution 0.86	0.38	0.42	hedged possibility 0.79
s1	A motivation for the use of 3d effective theory in the lattice simulations, rather than the complete 4d one, is provided.	method 0.57	0.59	0.06	asserted 0.94
s2	We introduce and compute on the 2-loop level a number of gauge-invariant order parameters -- condensates, which can be measured with high accuracy in MC simulations.	contribution 0.97	0.95	0.11	asserted 0.99
s3	The relation between MSbar and lattice condensates is found, together with the relation between lattice couplings and continuum parameters (the constant physics curves).	result 0.88	0.91	0.14	asserted 1.00
s4	These relations are exact in the continuum limit.	result 0.53	0.66	0.13	asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.95 · evidence from simulation or computation 0.76.

What was examined, and what was not

sources read

arXiv listing abstract v1

not examined

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

levels run

P abstract

not run

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

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

Figures

**Figure 1.** The vacuum 2-loop diagrams used in the computation of . 1

**Figure 2.** The Higgs self-energy 2-loop diagrams used in the computation of . 45

**Figure 3.** The scalar-gauge vertices in lattice perturbation theory. 46

**Figure 4.** The evolution of the distribution of hR2 Li with H . 47

**Figure 5.** The quantity 2 amT as a function of x = amT =2. 48

**Figure 6.** The same as Fig.5, for a theory without A0 eld. 49

**Figure 7.** The A0 contribution to the e ective potential. 50

Figures reproduced from arXiv:hep-lat/9412091 by the authors.

References

Forward citations

Cited by 37 Pith papers

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

The Electroweak Phase Transition: A Non-Perturbative Analysis
hep-lat 1995-10 accept novelty 8.0 of 10

Lattice simulations of the 3d SU(2)+Higgs model give continuum values for the electroweak phase transition and show that perturbation theory misestimates its strength.
Hot news on the phase structure of the SMEFT
hep-ph 2025-07 conditional novelty 7.0 of 10

A full O(g^4) dimensional reduction of the dimension-six SMEFT shows that the top-Higgs operator O_tphi can trigger a first-order electroweak phase transition with zero (phi-dagger phi)^3 coupling at zero temperature.
An Effective Sphaleron Awakens
hep-ph 2025-06 conditional novelty 7.0 of 10

A consistent 3D EFT computation of the Higgs phase sphaleron rate yields universal baryon preservation bounds x ≈ 0.025 (strong) and x ≈ 0.036 (weak), and shows two-loop corrections eliminate strong one-step transitio...
Phase Transitions in Dimensional Reduction up to Three Loops
hep-ph 2025-05 conditional novelty 7.0 of 10

In a toy complex-scalar model, 1-loop dimension-6 matching corrections compete with 2-loop quartic corrections and dominate 3-loop thermal-mass corrections for strong phase transitions.
Theoretical uncertainties for cosmological first-order phase transitions
hep-ph 2020-09 accept novelty 7.0 of 10

Dimensional reduction reduces the renormalisation-scale uncertainty in gravitational wave predictions for a Standard Model effective theory by one to two orders of magnitude compared to daisy resummation, while also f...

Show 32 more citing papers

Electroweak Bubble Nucleation, Nonperturbatively
hep-ph 2000-09 accept novelty 7.0 of 10

A multicanonical lattice method plus Langevin real-time evolution yields the electroweak bubble nucleation rate nonperturbatively, and shows two-loop perturbation theory overestimates supercooling by a factor of two.
The universality class of the electroweak theory
hep-lat 1998-05 accept novelty 7.0 of 10

The endpoint of the first-order electroweak phase transition in the 3d SU(2)+Higgs theory falls into the 3d Ising universality class, with the Standard Model endpoint at m_H = 72(2) GeV.
The MSSM Electroweak Phase Transition on the Lattice
hep-lat 1998-04 conditional novelty 7.0 of 10

Lattice simulations of the dimensionally reduced MSSM show the electroweak phase transition is up to 45% stronger than two-loop perturbation theory, and that a two-stage transition survives non-perturbatively at small...
Gauge-invariant Higgs mechanism via gradient-flow regularization
hep-ph 2026-09 accept novelty 6.0 of 10

The paper defines the Higgs mechanism gauge-invariantly using gradient flow, providing a one-loop matching to MS and a framework that eliminates the contact-term divergences of composite operators.
Hard thermal contributions to phase transition observables at NNLO
hep-ph 2026-02 conditional novelty 6.0 of 10

Three-loop thermal masses and two-loop quartic couplings complete the O(g^6) high-temperature EFT of U(1) and SU(N) gauge-Higgs models, with a missing contribution identified in a known three-loop master integral.
What happens when supercooling is terminated by curvature flipping of the effective potential?
hep-ph 2024-12 conditional novelty 6.0 of 10

Supercooling terminated by curvature flipping still proceeds by bubble nucleation and expansion, not by smooth phase mixing, according to 3D lattice simulations.
Perturbative effective field theory expansions for cosmological phase transitions
hep-ph 2023-09 accept novelty 6.0 of 10

Matching a chain of effective field theories down to a newly named supersoft scale yields gauge-invariant, real perturbative thermodynamics for a two-step electroweak phase transition that agrees well with lattice data.
DRalgo: a package for effective field theory approach for thermal phase transitions
hep-ph 2022-05 conditional novelty 6.0 of 10

DRalgo automates next-to-leading-order dimensional reduction for generic renormalizable particle models, producing the three-dimensional effective couplings, thermal masses, beta functions, and two-loop effective pote...
First-order electroweak phase transitions: a nonperturbative update
hep-lat 2022-05 accept novelty 6.0 of 10

Continuum-extrapolated lattice Monte Carlo of the 3d SU(2) Higgs model yields the phase boundary, condensate jumps, surface tension and bubble nucleation rate for first-order electroweak transitions, and shows next-to...
Computing the gauge-invariant bubble nucleation rate in finite temperature effective field theory
hep-ph 2021-12 conditional novelty 6.0 of 10

The two leading exponent terms of the finite-temperature bubble nucleation rate are gauge invariant when computed in a dimensionally reduced effective field theory with a consistent power counting.
Nucleation at finite temperature: a gauge-invariant, perturbative framework
hep-ph 2021-12 conditional novelty 6.0 of 10

A power-counted, gauge-invariant procedure for the leading exponential of the thermal bubble nucleation rate, proven independent of the gauge-fixing parameter via Nielsen identities in the Abelian Higgs model.
Singlet-assisted electroweak phase transition at two loops
hep-ph 2021-03 conditional novelty 6.0 of 10

Two-loop corrections shift the singlet-extended electroweak phase transition's critical temperature and strength by 20 to 50 percent relative to one-loop resummed results, and can erase radiatively generated barriers ...
Robust approach to thermal resummation: Standard Model meets a singlet
hep-ph 2021-02 conditional novelty 6.0 of 10

The authors derive the next-to-leading-order three-dimensional effective field theory for the Standard Model extended by a real singlet scalar, including two-loop matching relations, so that phase-transition thermodyn...
Real scalar phase transitions: a nonperturbative analysis
hep-ph 2021-01 accept novelty 6.0 of 10

Lattice Monte Carlo and three-loop renormalisation-group-improved perturbation theory agree to a few percent for the thermal first-order phase transition of a real scalar field, even where unimproved perturbation theo...
On the validity of perturbative studies of the electroweak phase transition in the Two Higgs Doublet model
hep-ph 2019-04 conditional novelty 6.0 of 10

Nonperturbative lattice simulations of the Two Higgs Doublet electroweak phase transition show the conventional one-loop resummed effective potential gets the critical temperature wrong by 20 to 30 percent, while a tw...
Nonperturbative analysis of the gravitational waves from a first-order electroweak phase transition
hep-ph 2019-03 conditional novelty 6.0 of 10

Any beyond-Standard-Model theory that reduces to the Standard Model's long-distance effective theory at the electroweak transition gives gravitational waves too weak to detect at LISA or any planned detector.
Primordial gravitational waves, precisely: The role of thermodynamics in the Standard Model
hep-ph 2018-03 conditional novelty 6.0 of 10

Including Standard Model particle interactions in the cosmic equation of state raises the predicted primordial gravitational wave amplitude by 1 to 2 percent at DECIGO frequencies and adds new damping features from fr...
3d SU(N) + adjoint Higgs theory and finite temperature QCD
hep-ph 1997-04 accept novelty 6.0 of 10

Two-loop matching plus lattice simulation of the 3d SU(2) adjoint-Higgs theory shows non-perturbative corrections to the Debye mass are about three times the leading perturbative value, and that this effective theory ...
How fast can the wall move? A study of the electroweak phase transition dynamics
hep-ph 1995-06 conditional novelty 6.0 of 10

Coupled Boltzmann and Higgs equations give a subsonic electroweak bubble wall, with velocity 0.36 to 0.44 and thickness 23 to 29 inverse temperature units, for Higgs masses up to 90 GeV.
Bubble Wall Velocity at the Electroweak Phase Transition
hep-ph 1995-03 conditional novelty 6.0 of 10

Modeling friction from out-of-equilibrium top quarks with a three-moment fluid Ansatz, the authors find the electroweak bubble wall moves at roughly 0.7c and is significantly thicker than its equilibrium profile.
Thermal Resummation for Very Strong First-order Phase Transitions
hep-ph 2026-07 conditional novelty 5.0 of 10

A 2PI-based real-time resummation yields an NLO Abelian-Higgs effective potential for strong phase transitions that passes the leading-order Nielsen gauge-independence test.
One Loop Thermal Effective Action
hep-th 2024-11 reject novelty 5.0 of 10

The paper derives a one-loop finite-temperature effective action via heat-kernel coefficients up to dimension-6 operators with Polyakov loop dependence, but the fermionic generalization rests on an invalid Matsubara i...
On the perturbative expansion at high temperature and implications for cosmological phase transitions
hep-ph 2021-04 accept novelty 5.0 of 10

At high temperature the widely used one-loop daisy-resummed effective potential carries an uncancelled renormalisation-scale dependence at O(g^4), removable only by two-loop terms, and this shifts predicted gravitatio...
The Sphaleron Rate through the Electroweak Cross-over
hep-ph 2012-07 conditional novelty 5.0 of 10

The sphaleron rate falls by roughly ten orders of magnitude across the electroweak cross-over, following a clean exponential in the broken phase rather than an instantaneous shut-off.
Thermodynamics of SU(N) Yang-Mills theories in 2+1 dimensions I - The confining phase
hep-lat 2011-05 conditional novelty 5.0 of 10

The confining-phase equation of state of 2+1 dimensional SU(N) Yang-Mills theory is computed for N=2 to 6 and matches a free glueball gas at low temperature and a closed bosonic string spectral density near the deconf...
A Non-Perturbative Analysis of the Finite T Phase Transition in SU(2)xU(1) Electroweak Theory
hep-lat 1996-12 conditional novelty 5.0 of 10

Including the U(1) hypercharge field in lattice simulations of the 3d electroweak effective theory strengthens the first-order phase transition by close to the perturbatively expected amount and leaves the phase diagr...
Combining thermal resummation and gauge invariance for electroweak phase transition
hep-ph 2022-03 conditional novelty 4.0 of 10

A minimal 3d effective-field-theory setup combines a gauge-invariant expansion around leading-order minima with next-to-leading-order dimensional reduction, and applied to the complex-singlet Standard Model it shows t...
Electroweak Phase Transition with an SU(2) Dark Sector
hep-ph 2020-12 conditional novelty 4.0 of 10

A two-scalar SU(2) dark sector with a Higgs portal yields vector dark matter, dark radiation, and a first-order dark phase transition whose gravitational wave signal may reach the proposed BBO detector for one benchma...
Precise WIMP Dark Matter Abundance and Standard Model Thermodynamics
hep-ph 2020-05 conditional novelty 4.0 of 10

Using an updated Standard Model equation of state, the predicted WIMP relic abundance shifts by about 5 to 10 percent relative to conventional estimates for dark matter masses of 1 to 1000 GeV.
Cosmological phase transitions: from perturbative particle physics to gravitational waves
hep-ph 2023-05 accept novelty 3.0 of 10

This review assembles the full calculational chain from a particle physics model to gravitational waves from cosmological first-order phase transitions, with new pedagogical derivations of the JMAK equation and the ef...
Electroweak baryogenesis
hep-ph 2012-06 accept novelty 3.0 of 10

Electroweak baryogenesis requires new TeV-scale particles that make the electroweak phase transition strongly first order and supply CP violation, and this review argues those requirements make the scenario testable b...
Detection of Early-Universe Gravitational Wave Signatures and Fundamental Physics
gr-qc 2022-03 accept novelty 2.0 of 10

A community survey mapping which early-Universe mechanisms could produce gravitational waves detectable by current and planned observatories, and what each mechanism would reveal about fundamental physics.

How the literature uses it

52 arXiv papers cite this in 106 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 86 sentences without a confident label

Builds on it 1 paper

In this work at hand, we have unified, generalised and expanded most of this progress to a revised EFT framework for equilibrium thermodynamics that builds from the dimensionally reduced 3d EFTs [ref] , but also consistently applies strict power-counting expansions in perturbation theory [ref] .

Perturbative effective field theory expansions for cosmological phase transitions · Discussion · 0.96

Uses its method or tool 9 papers

We simulate a 3-dimensional effective field theory containing the light bosonic field (the zero Matsubara mode), which we write as $ϕ$ , with the remaining heavy fields integrated out [ref] .

What happens when supercooling is terminated by curvature flipping of the effective potential? · Setup · 0.81
Finally, we compute the latent heat in a strict expansion akin to Refs. [ref] , that is [equation] where the eta-function $η(σ̃_3) ≡T dσ̃_3/dT$ at $T_c$ [ref] and the jump in the scalar condensate [ref] admits a strict expansion [equation] Here, we use the shorthand notation $v_0 ≡√(-6 m̃^2_ϕ,3/λ_3)$ for the order parameter with $m̃^2_ϕ,3 = m^2_ϕ,3 - g^2_3/(2λ_3)$ and the effective expansion parameter $α_3 ≡√(λ_3)/(4π|v_0|)$.

Cosmological phase transitions without high-temperature expansions · Thermodynamics using 3d EFT in a high-T expansion · 0.95
First, at temperatures lower than the critical temperature of the electroweak crossover, the thermodynamic quantities can be evaluated by using the one-loop [ref] or two-loop [ref] Coleman-Weinberg potential.

Precise WIMP Dark Matter Abundance and Standard Model Thermodynamics · Effective Degrees of Freedom in the Standard Model · 0.84

Uses its data or values 1 paper

It is given analytically in Eq. (170) of Ref. [ref] , and its numerical value is $Σ=3.17591153562522...$.

Real scalar phase transitions: a nonperturbative analysis · Lattice-continuum relations · 0.98

Cites it as background 9 papers

Such EFTs are commonly referred as “ultrasoft” scale EFTs, and have been studied using non-perturbative lattice simulations e.g. in [ref] .

Perturbative effective field theory expansions for cosmological phase transitions · Cosmological phase transitions · 0.91
This 3d EFT [ref] has been studied extensively both perturbatively and nonperturbatively in Refs. [ref] .

First-order electroweak phase transitions: a nonperturbative update · Electroweak physics at high temperatures · 0.97
The dynamics of the phase transition is determined by the effective potential at the finite temperature (see, e.g., Ref. [ref] for a recent review), which can be calculated perturbatively or non-perturbatively on the lattice with dimensional reduction [ref] .

Electroweak Phase Transition with an SU(2) Dark Sector · Electroweak phase transition · 0.95

Discussion

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