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arxiv: 2606.11170 · v1 · pith:6JAQMSGSnew · submitted 2026-06-09 · ✦ hep-ph

MATCHA: A Mathematica package for matching UV models onto HEFT

Raquel G\'omez-Ambrosio , Carlos Quezada-Calonge This is my paper

Pith reviewed 2026-06-27 12:29 UTC · model grok-4.3

classification ✦ hep-ph
keywords HEFT matchingUV to EFTnon-decoupling effectsHiggs Effective Field TheoryMathematica packageFeynRuleseffective field theory
0
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The pith

MATCHA automates leading-order matching of UV models to the Higgs Effective Field Theory for any number of Higgs fields.

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

MATCHA is a Mathematica package built on FeynRules, FeynArts and FormCalc that takes UV model files and an expansion order as input. It computes the leading low-energy couplings in the HEFT Lagrangian that capture non-decoupling O(1) effects. The package works for models containing an arbitrary number of Higgs fields. A reader would care because it replaces manual integration of heavy states with a standardized, minimal-input procedure for deriving the effective theory relevant to Higgs phenomenology.

Core claim

MATCHA performs the matching of non-decoupling effects O(1) to the LO HEFT Lagrangian for an arbitrary number of Higgs fields, providing the leading low-energy couplings capturing non-decoupling effects of HEFT. It requires solely the FeynRules output files and the desired order of expansion, and directly benefits from the established features of FeynArts and FormCalc.

What carries the argument

Automated integration of heavy degrees of freedom at leading order using FeynRules model files to generate HEFT terms via FeynArts and FormCalc.

If this is right

  • Leading HEFT couplings are generated automatically from any UV model supplied as FeynRules output.
  • Non-decoupling O(1) effects are included at LO without separate manual calculation.
  • The procedure extends without modification to models containing multiple Higgs fields.
  • Results inherit the calculational capabilities already present in FeynArts and FormCalc.

Where Pith is reading between the lines

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

  • The package could support systematic scans over families of UV models by converting each to a common HEFT representation.
  • Future versions might incorporate loop-level matching by extending the existing expansion-order input.
  • Direct comparison of HEFT coefficients from different UV completions becomes feasible once the package is run on each model.

Load-bearing premise

The integration of heavy degrees of freedom at leading order can be fully captured by the HEFT Lagrangian terms generated from FeynRules output without additional user-defined counterterms or higher-order corrections.

What would settle it

For a concrete UV model with one heavy scalar, the tree-level HEFT coefficients obtained by hand differ from the numerical values produced by MATCHA on the same model files.

Figures

Figures reproduced from arXiv: 2606.11170 by Carlos Quezada-Calonge, Raquel G\'omez-Ambrosio.

Figure 1
Figure 1. Figure 1: Scalar class definitions in the FeynRules model for the RSE. [PITH_FULL_IMAGE:figures/full_fig_p012_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: UV diagrams for the Real Singlet Extension contributing to the HEFT coefficient [PITH_FULL_IMAGE:figures/full_fig_p016_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: UV diagrams for the Real Singlet Extension involving only light particles which do not contribute [PITH_FULL_IMAGE:figures/full_fig_p017_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: UV diagrams for the Real Singlet Extension involving only heavy particles contributing to [PITH_FULL_IMAGE:figures/full_fig_p018_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: UV diagrams for the 2HDM model involving only heavy particles contributing to [PITH_FULL_IMAGE:figures/full_fig_p023_5.png] view at source ↗
read the original abstract

We present MATChing HEFT Amplitudes (MATCHA), a Mathematica package designed for leading-order (LO) matching of an ultraviolet (UV) model to the Higgs Effective Field Theory (HEFT). MATCHA performs the matching of non-decoupling effects $\mathcal{O}(1)$ to the LO HEFT lagrangian for an arbitrary number of Higgs fields. The main benefit of \heftmatcha is that it is built on existing packages such as \texttt{FeynArts} and \texttt{FormCalc}, which are familiar to the user, and directly benefits from the established features of these packages. In addition, \heftmatcha is designed to require minimal input from the user, requiring solely the \texttt{FeynRules} output files and the desired order of expansion. In this way, \heftmatcha provides the leading low-energy couplings capturing non-decoupling effects of HEFT.

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.

Referee Report

1 major / 0 minor

Summary. The manuscript presents MATCHA, a Mathematica package for leading-order (LO) matching of ultraviolet (UV) models to the Higgs Effective Field Theory (HEFT) Lagrangian. It claims to automate the matching of non-decoupling effects O(1) for an arbitrary number of Higgs fields, using FeynRules output files and a user-specified expansion order as sole inputs, while leveraging FeynArts and FormCalc to output the leading low-energy couplings.

Significance. If the package performs as described, it would provide a practical automation tool for HEFT matching in BSM model building, lowering the barrier for deriving effective couplings from UV completions with non-decoupling Higgs sectors. The design choice to build on established, familiar packages and minimize user input is a clear practical strength.

major comments (1)
  1. [Abstract] Abstract (paragraph describing package functionality): the central claim that MATCHA performs the matching of non-decoupling O(1) effects to the LO HEFT Lagrangian without additional user-defined counterterms or higher-order corrections is asserted but unsupported by any test cases, benchmark results, or explicit matching examples. This is load-bearing for the claim that the generated terms correctly capture the desired effects.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for their detailed review and constructive feedback. We address the single major comment below.

read point-by-point responses

  1. Referee: [Abstract] Abstract (paragraph describing package functionality): the central claim that MATCHA performs the matching of non-decoupling O(1) effects to the LO HEFT Lagrangian without additional user-defined counterterms or higher-order corrections is asserted but unsupported by any test cases, benchmark results, or explicit matching examples. This is load-bearing for the claim that the generated terms correctly capture the desired effects.

    Authors: We agree that the abstract claim would be better supported by explicit examples. In the revised manuscript we will add a dedicated section (or subsection) containing at least two benchmark UV models with explicit matching results. These will demonstrate the automated extraction of the leading non-decoupling O(1) HEFT coefficients directly from FeynRules output, without user-supplied counterterms or higher-order corrections, and will include numerical comparisons to known analytic results where available. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The paper describes a software package (MATCHA) that automates LO matching from FeynRules output to HEFT using established tools (FeynArts/FormCalc). No mathematical derivation, fitted parameters, or predictions are presented that reduce to their own inputs by construction. The workflow is a thin wrapper around external packages with user-specified expansion order; the central claim is implementation of an existing procedure rather than a self-referential result. No self-citation load-bearing steps, ansatze, or uniqueness theorems appear in the provided text.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The paper contributes a computational implementation rather than new physical parameters, axioms, or entities. The matching procedure rests on standard EFT assumptions already present in the literature.

axioms (1)
  • domain assumption Leading-order HEFT Lagrangian suffices to capture O(1) non-decoupling effects when heavy fields are integrated out
    Invoked in the description of what MATCHA computes from FeynRules output.

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