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

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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

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