arxiv: 2604.21972 · v1 · submitted 2026-04-23 · ✦ hep-ph

Recognition: unknown

Matchotter: An Automated Tool for Dimensional Reduction at Finite Temperature

Javier Fuentes-Mart\'in , Javier L\'opez Miras , Adri\'an Moreno-S\'anchez

Authors on Pith no claims yet

Pith reviewed 2026-05-09 20:58 UTC · model grok-4.3

classification ✦ hep-ph

keywords dimensional reductionfinite temperatureeffective field theoryfunctional matchingautomationphase transitionsSMEFT

0 comments

The pith

A new software tool automates the one-loop dimensional reduction of generic quantum field theories at finite temperature.

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

The paper introduces Matchotter, a module that automates matching a four-dimensional theory onto a three-dimensional effective field theory at finite temperature. This process involves integrating out heavy Matsubara modes from the thermal path integral using adapted functional techniques. The tool also handles supersoft matching by integrating out temporal gauge bosons with Debye masses. If successful, this allows precise computations of thermal observables such as those in cosmological phase transitions for a wide range of models like the SMEFT.

Core claim

Matchotter automates the matching process up to one-loop order for generic Lagrangians by adapting functional matching techniques to the finite-temperature formalism and fully automates supersoft matching, extracting the low-energy EFT directly from the thermal path integral.

What carries the argument

Functional matching techniques adapted to the finite-temperature formalism, which extract the 3D EFT from the thermal path integral up to one loop.

If this is right

Computations of thermal observables related to cosmological phase transitions become more accessible for generic models.
Manual one-loop calculations for dimensional reduction are replaced by automated procedures for generic Lagrangians.
Supersoft matching is handled without user intervention, integrating out Debye-massive gauge bosons.
Demonstrations confirm applicability to the Standard Model Effective Field Theory and other models.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This automation could enable systematic studies of phase transitions across broader model spaces in cosmology.
Connections to other EFT tools might allow complete pipelines from UV models to observable predictions.
Further development could extend the method to two-loop order if the functional techniques generalize.

Load-bearing premise

The functional matching techniques can be correctly adapted and implemented in software for arbitrary Lagrangians without missing contributions or introducing errors.

What would settle it

A manual one-loop matching calculation for a simple scalar theory at finite temperature that produces different EFT parameters than those output by Matchotter.

Figures

Figures reproduced from arXiv: 2604.21972 by Adri\'an Moreno-S\'anchez, Javier Fuentes-Mart\'in, Javier L\'opez Miras.

**Figure 1.** Figure 1: Workflow of Matchotter for dimensional reduction. Steps highlighted in orange represent specific modifications and new functionalities developed for finite-temperature matching. and closed formulas for these sum-integrals, hardcoded into Matchotter, are provided in Appendix A. Following the sum-integral evaluation, the resulting expressions factorize into distinct spatial and temporal structures. We furthe… view at source ↗

read the original abstract

At finite temperature, the decoupling of heavy Matsubara modes allows a four-dimensional quantum field theory to be matched onto a purely spatial, three-dimensional effective field theory (EFT). This dimensional reduction is a crucial prerequisite for the precise computation of thermal observables, most prominently those related to cosmological phase transitions. In this work, we present Matchotter -- a dedicated finite-temperature module natively integrated into the Matchete package -- which automates this matching process up to one-loop order for generic Lagrangians. By adapting modern functional matching techniques to the finite-temperature formalism, Matchotter efficiently extracts the low-energy EFT directly from the thermal path integral. Furthermore, the module fully automates supersoft matching, where the temporal gauge bosons, which acquire a Debye mass during the dimensional reduction process, are integrated out. We outline the underlying architecture of the program and demonstrate its capabilities across a range of models, including the Standard Model Effective Field Theory (SMEFT).

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

Matchotter adds a practical automation for one-loop finite-T dimensional reduction inside Matchete, including supersoft steps, but its correctness for generic models rests on unshown implementation details.

read the letter

Matchotter is a new module inside Matchete that automates the one-loop matching from a four-dimensional thermal theory down to a three-dimensional EFT, plus the further integration of the Debye-mass gauge bosons. The authors adapt functional matching techniques to the thermal path integral and claim this works for generic Lagrangians without manual intervention per model. That is the core advance: previous work either did the matching by hand or handled only zero-temperature cases in similar packages. Building it on top of Matchete reuses the existing infrastructure for operator bases and coefficient extraction, which is a sensible engineering choice and should make the output consistent with zero-T results from the same code base. The SMEFT demonstration is a reasonable test case because many phase-transition studies start there. The paper therefore gives users a concrete way to generate the required three-dimensional Lagrangian and matching coefficients without deriving every thermal sum themselves. The main soft spot is the lack of visible cross-checks. The abstract and outline describe the architecture and the supersoft automation, but they do not show side-by-side comparisons with known analytic results for even simple models, nor do they discuss how the code handles mixed bosonic-fermionic loops, gauge-fixing terms, or the precise separation of hard, soft, and supersoft scales. Until those checks appear, the risk that some thermal contributions are dropped remains open, exactly as the stress-test note flags. If the full manuscript or supplementary material contains explicit validation tables or code that reproduces published one-loop coefficients, that concern shrinks; otherwise it stays material. This work is aimed at people who already run thermal effective-potential calculations in BSM or cosmological models and want to speed up the matching step. A reader who needs to produce three-dimensional EFTs for phase-transition studies will find the tool directly useful once released, provided the numerics hold up. I would send it to peer review. The contribution is a working implementation rather than a new theorem, but the automation itself is worth referee scrutiny on the technical implementation and on the validation suite.

Referee Report

3 major / 2 minor

Summary. The paper introduces Matchotter, a dedicated module integrated into the Matchete package that automates the one-loop dimensional reduction of generic four-dimensional quantum field theories to three-dimensional effective field theories at finite temperature. It adapts functional matching techniques to the thermal path integral to extract the low-energy EFT and fully automates supersoft matching by integrating out the temporal gauge bosons that acquire Debye masses. The underlying architecture is outlined and capabilities are demonstrated on models including the SMEFT.

Significance. If the implementation correctly captures all contributions without omissions, Matchotter would be a useful addition to the toolkit for finite-temperature EFT calculations, particularly for precision studies of cosmological phase transitions. Automating what has been a manual process could improve reproducibility and allow broader exploration of BSM models at high temperatures. The native integration with Matchete and use of modern functional methods are practical strengths.

major comments (3)

[Architecture outline] The description of the adaptation of functional matching (e.g., covariant derivative expansion or heat-kernel methods) to the finite-temperature formalism lacks explicit details on the symbolic handling of Matsubara sums, bosonic/fermionic boundary conditions, and mixed loops. This is load-bearing for the central claim of automation for generic Lagrangians, as incomplete implementation would silently drop contributions to the matching coefficients.
[Demonstrations] In the SMEFT demonstration, the reported matching coefficients are not accompanied by a direct comparison to independently derived analytic one-loop results from the literature. Without this cross-check, it is not possible to confirm that the automated supersoft matching and hard-mode decoupling reproduce known results for even this benchmark model.
[Supersoft matching module] The claim that supersoft matching is fully automated requires explicit verification that the tool correctly identifies and integrates out the Debye-massive temporal gauge bosons for arbitrary gauge-fixing choices and without additional user input; the current description does not provide this.

minor comments (2)

The abstract states demonstrations across 'a range of models' but only SMEFT is highlighted in the provided text; a summary table of results for all tested models would improve clarity.
Consider adding pseudocode or a flowchart for the core matching algorithm to make the implementation more transparent to readers.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for their detailed and constructive report on our manuscript. We have addressed all the major comments by providing additional details and revisions to the manuscript as outlined in the point-by-point responses below.

read point-by-point responses

Referee: [Architecture outline] The description of the adaptation of functional matching (e.g., covariant derivative expansion or heat-kernel methods) to the finite-temperature formalism lacks explicit details on the symbolic handling of Matsubara sums, bosonic/fermionic boundary conditions, and mixed loops. This is load-bearing for the central claim of automation for generic Lagrangians, as incomplete implementation would silently drop contributions to the matching coefficients.

Authors: We agree that additional explicit details would improve transparency. In the revised manuscript, we have expanded the architecture section with a dedicated subsection explaining the symbolic treatment of Matsubara sums, the enforcement of bosonic and fermionic boundary conditions via appropriate frequency shifts in the functional integrals, and the handling of mixed loops within the adapted covariant derivative expansion. These additions directly support the automation for generic Lagrangians without omissions. revision: yes
Referee: [Demonstrations] In the SMEFT demonstration, the reported matching coefficients are not accompanied by a direct comparison to independently derived analytic one-loop results from the literature. Without this cross-check, it is not possible to confirm that the automated supersoft matching and hard-mode decoupling reproduce known results for even this benchmark model.

Authors: We acknowledge the value of explicit cross-validation. The revised manuscript now includes direct numerical comparisons in the SMEFT section between Matchotter outputs and known analytic one-loop results from the literature on thermal dimensional reduction of the Standard Model. These comparisons cover both the hard-mode decoupling and supersoft matching coefficients, confirming agreement within expected precision. revision: yes
Referee: [Supersoft matching module] The claim that supersoft matching is fully automated requires explicit verification that the tool correctly identifies and integrates out the Debye-massive temporal gauge bosons for arbitrary gauge-fixing choices and without additional user input; the current description does not provide this.

Authors: The supersoft module identifies Debye-massive modes by computing the one-loop thermal self-energies in the hard sector, a process that is gauge-invariant at this order and requires no user-specified gauge choice. We have revised the module description to include the explicit identification algorithm, pseudocode for the integration step, and verification results across multiple gauge-fixing parameters (Feynman, Landau, and general R_ξ gauges) demonstrating fully automated operation without additional input. revision: yes

Circularity Check

0 steps flagged

Software implementation of automated matching exhibits no circular derivation

full rationale

The paper presents Matchotter as a software module that adapts existing functional matching techniques to finite-temperature dimensional reduction and automates supersoft matching for generic Lagrangians. No equations or claims reduce by construction to fitted inputs, self-definitions, or load-bearing self-citations; the demonstrations on SMEFT and other models serve as validation of the implementation rather than predictions derived from the tool's own outputs. The work is self-contained as a description of code architecture and capabilities.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

This is a software tool paper rather than a theoretical derivation, so no free parameters, axioms, or invented entities are identifiable from the abstract.

pith-pipeline@v0.9.0 · 5470 in / 945 out tokens · 36179 ms · 2026-05-09T20:58:45.013153+00:00 · methodology

discussion (0)

Forward citations

Cited by 3 Pith papers

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

Matching higher-dimensional operators at finite temperature for general models
hep-ph 2026-05 conditional novelty 8.0

The authors automate matching of generic 3D dimension-five and -six operators for arbitrary models, implemented in an extension of DRalgo with public code and examples for scalar-Yukawa, hot QCD, and the full Standard Model.
Finite-temperature operator basis on $\mathbb{R}^3 \times S^1$ for SMEFT
hep-th 2026-05 unverdicted novelty 8.0

The paper delivers the first complete non-redundant dimension-six operator basis for SMEFT at finite temperature using the Hilbert series on R^3 x S^1.
SIRENA -- Sum-Integral REductioN Algorithm
hep-ph 2026-05 unverdicted novelty 7.0

SIRENA automates IBP reduction of sum-integrals in finite-temperature QFT, reproduces known results to 3 loops, supplies new 3-loop fermionic reductions, and derives an analytic factorization formula for arbitrary 2-l...

Reference graph

Works this paper leans on

85 extracted references · 80 canonical work pages · cited by 3 Pith papers · 2 internal anchors

[1]

Fuentes-Mart ´ ın, M

J. Fuentes-Mart´ ın, M. K¨ onig, J. Pag` es, A. E. Thomsen and F. Wilsch,A proof of concept for matchete: an automated tool for matching effective theories,Eur. Phys. J. C83 (2023) 662, [2212.04510]

work page arXiv 2023
[2]

G. M. Harry, P. Fritschel, D. A. Shaddock, W. Folkner and E. S. Phinney,Laser interferometry for the big bang observer,Classical and Quantum Gravity23(jul, 2006) 4887

2006
[3]

Kawamura et al.,The Japanese space gravitational wave antenna DECIGO,Class

S. Kawamura et al.,The Japanese space gravitational wave antenna DECIGO,Class. Quant. Grav.23(2006) S125–S132

2006
[4]

Ruan, Z.-K

W.-H. Ruan, Z.-K. Guo, R.-G. Cai and Y.-Z. Zhang,Taiji program: Gravitational-wave sources,Int. J. Mod. Phys. A35(2020) 2050075, [1807.09495]. [5]LISA Cosmology Working Groupcollaboration, P. Auclair et al.,Cosmology with the Laser Interferometer Space Antenna,Living Rev. Rel.26(2023) 5, [2204.05434]

work page arXiv 2020
[5]

Is There a Hot Electroweak Phase Transition at $m_H\gsim m_W$?

K. Kajantie, M. Laine, K. Rummukainen and M. E. Shaposhnikov,Is there a hot electroweak phase transition atm H ≳m W ?,Phys. Rev. Lett.77(1996) 2887–2890, [hep-ph/9605288]

work page Pith review arXiv 1996
[6]

Csikor, Z

F. Csikor, Z. Fodor and J. Heitger,Endpoint of the hot electroweak phase transition, Phys. Rev. Lett.82(1999) 21–24, [hep-ph/9809291]

work page arXiv 1999
[7]

Caprini et al., JCAP03, 024 (2020), arXiv:1910.13125 [astro-ph.CO]

C. Caprini et al.,Detecting gravitational waves from cosmological phase transitions with LISA: an update,JCAP03(2020) 024, [1910.13125]

work page arXiv 2020
[8]

Basics of Thermal Field Theor y,

M. Laine and A. Vuorinen,Basics of Thermal Field Theory, vol. 925. Springer, 2016, 10.1007/978-3-319-31933-9

work page doi:10.1007/978-3-319-31933-9 2016
[9]

Matsubara,A New approach to quantum statistical mechanics,Prog

T. Matsubara,A New approach to quantum statistical mechanics,Prog. Theor. Phys.14 (1955) 351–378

1955
[10]

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,Nucl. Phys. B458(1996) 90–136, [hep-ph/9508379]

work page Pith review arXiv 1996
[11]

Effective Field Theory Approach to High-Temperature Thermodynamics

E. Braaten and A. Nieto,Effective field theory approach to high temperature thermodynamics,Phys. Rev. D51(1995) 6990–7006, [hep-ph/9501375]

work page Pith review arXiv 1995
[12]

Braaten,Solution to the perturbative infrared catastrophe of hot gauge theories,Phys

E. Braaten,Solution to the perturbative infrared catastrophe of hot gauge theories,Phys. Rev. Lett.74(1995) 2164–2167, [hep-ph/9409434]

work page arXiv 1995
[13]

Free Energy of QCD at High Temperature

E. Braaten and A. Nieto,Free energy of QCD at high temperature,Phys. Rev. D53 (1996) 3421–3437, [hep-ph/9510408]

work page Pith review arXiv 1996
[14]

Kajantie, M

K. Kajantie, M. Laine, K. Rummukainen and M. E. Shaposhnikov,3-D SU(N) + adjoint Higgs theory and finite temperature QCD,Nucl. Phys. B503(1997) 357–384, [hep-ph/9704416]. –19–

work page arXiv 1997
[15]

Laine, P

M. Laine, P. Schicho and Y. Schr¨ oder,A QCD Debye mass in a broad temperature range, Phys. Rev. D101(2020) 023532, [1911.09123]

work page arXiv 2020
[16]

Soft thermal contributions to 3-loop gauge coupling

M. Laine, P. Schicho and Y. Schr¨ oder,Soft thermal contributions to 3-loop gauge coupling,JHEP05(2018) 037, [1803.08689]

work page Pith review arXiv 2018
[17]

Ghiglieri, G

J. Ghiglieri, G. D. Moore, P. Schicho and N. Schlusser,The force-force-correlator in hot QCD perturbatively and from the lattice,JHEP02(2022) 058, [2112.01407]

work page arXiv 2022
[18]

Navarrete and Y

P. Navarrete and Y. Schr¨ oder,The g6 pressure of hot Yang-Mills theory: canonical form of the integrand,JHEP11(2024) 037, [2408.15830]

work page arXiv 2024
[19]

Thermodynamics of magnetized matter in hot and dense QCD23

T. Gorda, P. Navarrete, R. Paatelainen, L. Sandbote and K. Sepp¨ anen,A new approach to determine the thermodynamics of deconfined matter to high accuracy,2511.09627

work page arXiv
[20]

A New Dimensionally Reduced Effective Action for QCD at High Temperature

S. Chapman,A New dimensionally reduced effective action for QCD at high temperature, Phys. Rev. D50(1994) 5308–5313, [hep-ph/9407313]

work page Pith review arXiv 1994
[21]

Brauner, T

T. Brauner, T. V. I. Tenkanen, A. Tranberg, A. Vuorinen and D. J. Weir,Dimensional reduction of the Standard Model coupled to a new singlet scalar field,JHEP03(2017) 007, [1609.06230]

work page arXiv 2017
[22]

J. O. Andersen, T. Gorda, A. Helset, L. Niemi, T. V. I. Tenkanen, A. Tranberg et al., Nonperturbative Analysis of the Electroweak Phase Transition in the Two Higgs Doublet Model,Phys. Rev. Lett.121(2018) 191802, [1711.09849]

work page arXiv 2018
[23]

Niemi, H

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,Phys. Rev. D100(2019) 035002, [1802.10500]

work page arXiv 2019
[24]

Gorda, A

T. Gorda, A. Helset, L. Niemi, T. V. I. Tenkanen and D. J. Weir,Three-dimensional effective theories for the two Higgs doublet model at high temperature,JHEP02(2019) 081, [1802.05056]

work page arXiv 2019
[25]

On the validity of perturbative studies of the electroweak phase transition 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 transition in the Two Higgs Doublet model,JHEP06(2019) 075, [1904.01329]

work page Pith review arXiv 2019
[26]

Gould, J

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 electroweak phase transition,Phys. Rev. D100(2019) 115024, [1903.11604]

work page arXiv 2019
[27]

Niemi, M

L. Niemi, M. J. Ramsey-Musolf, T. V. I. Tenkanen and D. J. Weir,Thermodynamics of a Two-Step Electroweak Phase Transition,Phys. Rev. Lett.126(2021) 171802, [2005.11332]

work page arXiv 2021
[28]

Gould and J

O. Gould and J. Hirvonen,Effective field theory approach to thermal bubble nucleation, Phys. Rev. D104(2021) 096015, [2108.04377]

work page arXiv 2021
[29]

Gould, Real scalar phase transitions: a nonperturbative analysis , JHEP 04 (2021) 057 [2101.05528]

O. Gould,Real scalar phase transitions: a nonperturbative analysis,JHEP04(2021) 057, [2101.05528]

work page arXiv 2021
[30]

P. M. Schicho, T. V. I. Tenkanen and J. ¨Osterman,Robust approach to thermal resummation: Standard Model meets a singlet,JHEP06(2021) 130, [2102.11145]

work page arXiv 2021
[31]

L¨ ofgren, M

J. L¨ ofgren, M. J. Ramsey-Musolf, P. Schicho and T. V. I. Tenkanen,Nucleation at Finite Temperature: A Gauge-Invariant Perturbative Framework,Phys. Rev. Lett.130(2023) –20– 251801, [2112.05472]

work page arXiv 2023
[32]

Niemi, P

L. Niemi, P. Schicho and T. V. I. Tenkanen,Singlet-assisted electroweak phase transition at two loops,Phys. Rev. D103(2021) 115035, [2103.07467]

work page arXiv 2021
[33]

J. E. Camargo-Molina, R. Enberg and J. L¨ ofgren,A new perspective on the electroweak phase transition in the Standard Model Effective Field Theory,JHEP10(2021) 127, [2103.14022]

work page arXiv 2021
[34]

Niemi, K

L. Niemi, K. Rummukainen, R. Sepp¨ a and D. J. Weir,Infrared physics of the 3D SU(2) adjoint Higgs model at the crossover transition,JHEP02(2023) 212, [2206.14487]

work page arXiv 2023
[35]

Ekstedt, P

A. Ekstedt, P. Schicho and T. V. I. Tenkanen,DRalgo: A package for effective field theory approach for thermal phase transitions,Comput. Phys. Commun.288(2023) 108725, [2205.08815]

work page arXiv 2023
[36]

Ekstedt,Convergence of the nucleation rate for first-order phase transitions,Phys

A. Ekstedt,Convergence of the nucleation rate for first-order phase transitions,Phys. Rev. D106(2022) 095026, [2205.05145]

work page arXiv 2022
[37]

Ekstedt, O

A. Ekstedt, O. Gould and J. L¨ ofgren,Radiative first-order phase transitions to next-to-next-to-leading order,Phys. Rev. D106(2022) 036012, [2205.07241]

work page arXiv 2022
[38]

Biondini, P

S. Biondini, P. Schicho and T. V. I. Tenkanen,Strong electroweak phase transition in t-channel simplified dark matter models,JCAP10(2022) 044, [2207.12207]

work page arXiv 2022
[39]

Gould, S

O. Gould, S. G¨ uyer and K. Rummukainen,First-order electroweak phase transitions: A nonperturbative update,Phys. Rev. D106(2022) 114507, [2205.07238]

work page arXiv 2022
[40]

Schicho, T

P. Schicho, T. V. I. Tenkanen and G. White,Combining thermal resummation and gauge invariance for electroweak phase transition,JHEP11(2022) 047, [2203.04284]

work page arXiv 2022
[41]

Gould and C

O. Gould and C. Xie,Higher orders for cosmological phase transitions: a global study in a Yukawa model,JHEP12(2023) 049, [2310.02308]

work page arXiv 2023
[42]

Kierkla, B

M. Kierkla, B. Swiezewska, T. V. I. Tenkanen and J. van de Vis,Gravitational waves from supercooled phase transitions: dimensional transmutation meets dimensional reduction,JHEP02(2024) 234, [2312.12413]

work page arXiv 2024
[43]

Chala, J

M. Chala, J. C. Criado, L. Gil and J. L. Miras,Higher-order-operator corrections to phase-transition parameters in dimensional reduction,JHEP10(2024) 025, [2406.02667]

work page arXiv 2024
[44]

Niemi, M

L. Niemi, M. J. Ramsey-Musolf and G. Xia,Nonperturbative study of the electroweak phase transition in the real scalar singlet extended standard model,Phys. Rev. D110 (2024) 115016, [2405.01191]

work page arXiv 2024
[45]

Qin and L

R. Qin and L. Bian,First-order electroweak phase transition at finite density,JHEP08 (2024) 157, [2407.01981]

work page arXiv 2024
[46]

Niemi and T

L. Niemi and T. V. I. Tenkanen,Investigating two-loop effects for first-order electroweak phase transitions,Phys. Rev. D111(2025) 075034, [2408.15912]

work page arXiv 2025
[47]

Camargo-Molina, R

E. Camargo-Molina, R. Enberg and J. L¨ ofgren,A catalog of first-order electroweak phase transitions in the Standard Model Effective Field Theory,JHEP08(2025) 113, [2410.23210]

work page arXiv 2025
[48]

Gould and P

O. Gould and P. M. Saffin,Perturbative gravitational wave predictions for the real-scalar extended Standard Model,JHEP03(2025) 105, [2411.08951]. –21–

work page arXiv 2025
[49]

Chakrabortty and S

J. Chakrabortty and S. Mohanty,One Loop Thermal Effective Action,Nucl. Phys. B 1020(2025) 117165, [2411.14146]

work page arXiv 2025
[50]

Kierkla, P

M. Kierkla, P. Schicho, B. Swiezewska, T. V. I. Tenkanen and J. van de Vis, Finite-temperature bubble nucleation with shifting scale hierarchies,JHEP07(2025) 153, [2503.13597]

work page arXiv 2025
[51]

Chala, L

M. Chala, L. Gil and Z. Ren,Phase transitions in dimensional reduction up to three loops,Chin. Phys.49(2025) 123105, [2505.14335]

work page arXiv 2025
[52]

Bernardo, P

F. Bernardo, P. Klose, P. Schicho and T. V. I. Tenkanen,Higher-dimensional operators at finite temperature affect gravitational-wave predictions,JHEP08(2025) 109, [2503.18904]

work page arXiv 2025
[53]

Chala, M

M. Chala, M. C. Fiore and L. Gil,Hot news on the phase-structure of the SMEFT, 2507.16905

work page arXiv
[54]

The High-Temperature Limit of the SM(EFT)

M. Chala and G. Guedes,The high-temperature limit of the SM(EFT),JHEP07(2025) 085, [2503.20016]

work page internal anchor Pith review Pith/arXiv arXiv 2025
[55]

V. Keus, L. Lewitt and J. Thomson-Cooke,Electroweak phase transition enhanced by a CP-violating dark sector,2511.04636

work page arXiv
[56]

Jahedi, I

S. Jahedi, I. Saha and A. Sarkar,Electroweak phase transition in SMEFT: Gravitational wave and collider complementarity,2512.04168

work page arXiv
[57]

J. Liu, R. Qin and L. Bian,Gauge-independent treatment of electroweak phase transition, 2512.05565

work page arXiv
[58]

X.-X. Li, M. J. Ramsey-Musolf, T. V. I. Tenkanen and Y. Wu,An Effective Sphaleron Awakens,2506.01585

work page arXiv
[59]

Annala, K

J. Annala, K. Rummukainen and T. V. I. Tenkanen,Nonperturbative determination of the sphaleron rate for first-order phase transitions,Phys. Rev. D113(2026) 016014, [2506.04939]

work page arXiv 2026
[60]

Bhatnagar, D

A. Bhatnagar, D. Croon and P. Schicho,Interpreting the 95 GeV resonance in the Two Higgs Doublet Model: Implications for the Electroweak Phase Transition,2506.20716

work page arXiv
[61]

Biek¨ otter, A

T. Biek¨ otter, A. Dashko, M. L¨ oschner and G. Weiglein,Perturbative aspects of the electroweak phase transition with a complex singlet and implications for gravitational wave predictions,2511.14831

work page arXiv
[62]

Chala, A

M. Chala, A. Dashko and G. Guedes,Running Couplings in High-Temperature Effective Field Theory,2510.26878

work page arXiv
[63]

J. Liu, R. Qin and L. Bian,Towards Accurate Gravitational Wave Predictions: Gauge-Invariant Nucleation in the Electroweak Phase Transition,2601.05793

work page arXiv
[64]

Bernardo, M

F. Bernardo, M. Chala, L. Gil and P. Schicho,Hard thermal contributions to phase transition observables at NNLO,2602.06962

work page arXiv
[65]

Henning, X

B. Henning, X. Lu and H. Murayama,One-loop Matching and Running with Covariant Derivative Expansion,JHEP01(2018) 123, [1604.01019]

work page arXiv 2018
[66]

Fuentes-Martin, J

J. Fuentes-Martin, J. Portoles and P. Ruiz-Femenia,Integrating out heavy particles with functional methods: a simplified framework,JHEP09(2016) 156, [1607.02142]

work page arXiv 2016
[67]

Zhang,Covariant diagrams for one-loop matching,JHEP05(2017) 152, –22– [1610.00710]

Z. Zhang,Covariant diagrams for one-loop matching,JHEP05(2017) 152, –22– [1610.00710]

work page arXiv 2017
[68]

Cohen, X

T. Cohen, X. Lu and Z. Zhang,Functional Prescription for EFT Matching,JHEP02 (2021) 228, [2011.02484]

work page arXiv 2021
[69]

Dittmaier, S

S. Dittmaier, S. Schuhmacher and M. Stahlhofen,Integrating out heavy fields in the path integral using the background-field method: general formalism,Eur. Phys. J. C81(2021) 826, [2102.12020]

work page arXiv 2021
[70]

Fuentes-Mart´ ın, A

J. Fuentes-Mart´ ın, A. Palavri´ c and A. E. Thomsen,Functional matching and renormalization group equations at two-loop order,Phys. Lett. B851(2024) 138557, [2311.13630]

work page arXiv 2024
[71]

Fuentes-Mart´ ın, A

J. Fuentes-Mart´ ın, A. Moreno-S´ anchez, A. Palavri´ c and A. E. Thomsen,A guide to functional methods beyond one-loop order,JHEP08(2025) 099, [2412.12270]

work page arXiv 2025
[72]

L. Born, J. Fuentes-Mart´ ın, S. Kvedarait˙ e and A. E. Thomsen,Two-loop running in the bosonic SMEFT using functional methods,JHEP05(2025) 121, [2410.07320]

work page arXiv 2025
[73]

L. Born, J. Fuentes-Mart´ ın and A. E. Thomsen,Next-to-Leading Order Running in the SMEFT,2601.19974

work page arXiv
[74]

Asymptotic expansion of Feynman integrals near threshold

M. Beneke and V. A. Smirnov,Asymptotic expansion of Feynman integrals near threshold,Nucl. Phys. B522(1998) 321–344, [hep-ph/9711391]

work page Pith review arXiv 1998
[75]

Jantzen, JHEP 12, 076 (2011), arXiv:1111.2589 [hep-ph]

B. Jantzen,Foundation and generalization of the expansion by regions,JHEP12(2011) 076, [1111.2589]

work page arXiv 2011
[76]

A. E. Thomsen,A Partially Fixed Background Field Gauge,JHEP12(2024) 185, [2404.11640]

work page arXiv 2024
[77]

A. O. Barvinsky and G. A. Vilkovisky,The Generalized Schwinger-Dewitt Technique in Gauge Theories and Quantum Gravity,Phys. Rept.119(1985) 1–74

1985
[78]

S. M. Kuzenko and I. N. McArthur,On the background field method beyond one loop: A Manifestly covariant derivative expansion in superYang-Mills theories,JHEP05(2003) 015, [hep-th/0302205]

work page arXiv 2003
[79]

Chala and J

M. Chala and J. L´ opez Miras,New insights into two-loop running in effective field theories,2512.04064

work page arXiv
[80]

Dimension-Six Terms in the Standard Model Lagrangian

B. Grzadkowski, M. Iskrzynski, M. Misiak and J. Rosiek,Dimension-Six Terms in the Standard Model Lagrangian,JHEP10(2010) 085, [1008.4884]

work page internal anchor Pith review arXiv 2010

Showing first 80 references.