SUSY meets SMEFT: Complete one-loop matching of the general MSSM
Pith reviewed 2026-05-19 10:56 UTC · model grok-4.3
The pith
The general MSSM matches onto the SMEFT at one loop with all supersymmetry-governed correlations among Wilson coefficients preserved.
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
Core claim
The central claim is that the complete set of one-loop matching conditions from the MSSM to the SMEFT has been derived for the most general case, including all correlations among the SMEFT Wilson coefficients that are dictated by supersymmetry in the 124-parameter model with conserved R-parity.
What carries the argument
The one-loop matching procedure that integrates out all superpartners simultaneously while preserving the general flavor structure and reducing redundant operators to the Warsaw basis.
If this is right
- All supersymmetry-induced correlations among SMEFT Wilson coefficients are now available and can be used directly in global fits.
- The matching forms a basis for systematic and global studies of the full MSSM parameter space with effective field theory methods.
- The detailed Higgs sector treatment ensures accurate electroweak symmetry breaking in the reduced effective Lagrangian.
- The alternative matching to the two-Higgs-doublet-model EFT supplies relations for scenarios where the second Higgs doublet remains in the low-energy spectrum.
Where Pith is reading between the lines
- These correlations could be applied to reinterpret existing experimental limits on SMEFT operators in terms of underlying supersymmetric parameters.
- The method could be extended to derive similar matchings for other supersymmetric models or to include additional effects like R-parity violation.
- The relations might simplify numerical scans over the MSSM parameter space by reducing the effective degrees of freedom at low energies.
Load-bearing premise
The integration of superpartners preserves the general flavor structure and the reduction of operators to the Warsaw basis introduces no uncontrolled errors in the Higgs sector treatment.
What would settle it
A direct one-loop calculation of the matching conditions for a chosen non-degenerate MSSM parameter point with specific superpartner masses would show a discrepancy in the predicted Wilson coefficient correlations if the claim is incorrect.
read the original abstract
We present the complete one-loop matching of the Minimal Supersymmetric Standard Model (MSSM) onto the Standard Model Effective Field Theory (SMEFT), considering the most general case for the MSSM with conserved $R$-parity, which has 124 free parameters. The matching is performed with the Matchete package, which integrates out all superpartners at once with non-degenerate masses, while also retaining the most general flavor structure. Our results include all correlations among the different SMEFT Wilson coefficients that are governed by supersymmetry and thus provide a basis for future systematic and global studies of the MSSM parameter space employing EFT methods. A detailed discussion is provided on the treatment of the Higgs sector and electroweak symmetry breaking, along with the reduction of redundant operators in the EFT Lagrangian to the Warsaw basis. Furthermore, we validate against existing results in the literature and present a minimal phenomenological example. As an alternative low-energy scenario, we also provide the complete one-loop matching of the MSSM onto the two-Higgs-doublet-model EFT, where the second Higgs doublet is retained in the infrared spectrum. Extensive auxiliary material, including the code utilized for the matching, is available on GitHub.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper claims to deliver the complete one-loop matching of the general MSSM (124 parameters, R-parity conserved) onto SMEFT via the Matchete package, integrating out all superpartners simultaneously with non-degenerate masses and retaining general flavor structure. It supplies the full set of correlated Wilson coefficients, includes a detailed treatment of the Higgs sector and electroweak symmetry breaking, reduces redundant operators to the Warsaw basis, validates results against existing literature, presents a minimal phenomenological example, and additionally provides the matching onto the two-Higgs-doublet-model EFT. Public code and auxiliary material are made available on GitHub.
Significance. If the matching and reduction are free of artifacts, the result is significant because it supplies the complete set of SUSY-governed correlations among SMEFT Wilson coefficients for the most general MSSM. This directly enables systematic global EFT analyses of the MSSM parameter space. The automated implementation with public code, literature validation, and the alternative 2HDM-EFT matching are concrete strengths that enhance reproducibility and utility.
major comments (1)
- [Higgs sector treatment] Higgs sector and EWSB discussion: the manuscript states that a detailed treatment of the two-Higgs-doublet structure, vev alignment, and tadpole cancellation is provided, yet it should include explicit verification (e.g., a table of selected Warsaw-basis coefficients or a check of the effective Higgs potential) that the projection onto the single-Higgs SMEFT introduces no residual basis artifacts in operators such as Q_H or Q_HD. Without this concrete cross-check, the claim of completeness for the full 124-parameter case remains difficult to assess.
minor comments (2)
- The abstract and main text should explicitly state the number of independent operators retained after reduction to the Warsaw basis for the general-flavor case.
- Figure captions and table headings in the phenomenological example should clarify which MSSM parameters are varied and which SMEFT coefficients are shown.
Simulated Author's Rebuttal
We thank the referee for the positive assessment of our work and the recommendation for minor revision. We address the major comment below.
read point-by-point responses
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Referee: [Higgs sector treatment] Higgs sector and EWSB discussion: the manuscript states that a detailed treatment of the two-Higgs-doublet structure, vev alignment, and tadpole cancellation is provided, yet it should include explicit verification (e.g., a table of selected Warsaw-basis coefficients or a check of the effective Higgs potential) that the projection onto the single-Higgs SMEFT introduces no residual basis artifacts in operators such as Q_H or Q_HD. Without this concrete cross-check, the claim of completeness for the full 124-parameter case remains difficult to assess.
Authors: We thank the referee for highlighting this point. While the manuscript already contains a detailed discussion of the two-Higgs-doublet structure, vev alignment, and tadpole cancellation, we agree that an explicit numerical cross-check would improve clarity and allow readers to more readily assess the absence of basis artifacts. In the revised manuscript we will add a table of selected Warsaw-basis coefficients (including those involving Q_H and Q_HD) obtained after the projection, together with a short verification that the effective Higgs potential is free of residual artifacts. This addition will be placed in the Higgs-sector section and will be supported by the existing Matchete output files already provided on GitHub. revision: yes
Circularity Check
Direct computational matching produces independent Wilson coefficients
full rationale
The paper's central result is the output of an automated one-loop integration performed by the Matchete package on the general 124-parameter MSSM, retaining full flavor structure and non-degenerate masses. Wilson coefficients and SUSY-induced correlations are generated by this external tool rather than being algebraically defined in terms of the input parameters or fitted to the same dataset. The discussion of Higgs-sector EWSB, vev alignment, and reduction to the Warsaw basis describes the computational pipeline and operator-basis choices but does not create a self-referential loop; the final coefficients remain the direct numerical/analytic output of the integration. Validation against existing literature supplies an external benchmark. No load-bearing self-citation, self-definitional relation, or fitted-input-renamed-as-prediction reduces the claimed matching to its own inputs by construction.
Axiom & Free-Parameter Ledger
axioms (2)
- domain assumption The most general R-parity conserving MSSM has 124 free parameters.
- domain assumption Matchete correctly performs the one-loop integration of all superpartners while retaining general flavor structure.
Lean theorems connected to this paper
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IndisputableMonolith/Foundation/RealityFromDistinction.leanreality_from_one_distinction unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
We present the complete one-loop matching of the Minimal Supersymmetric Standard Model (MSSM) onto the Standard Model Effective Field Theory (SMEFT), considering the most general case for the MSSM with conserved R-parity, which has 124 free parameters. The matching is performed with the Matchete package...
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IndisputableMonolith/Foundation/AlphaCoordinateFixation.leanJ_uniquely_calibrated_via_higher_derivative unclear?
unclearRelation between the paper passage and the cited Recognition theorem.
A detailed discussion is provided on the treatment of the Higgs sector and electroweak symmetry breaking, along with the reduction of redundant operators in the EFT Lagrangian to the Warsaw basis.
What do these tags mean?
- matches
- The paper's claim is directly supported by a theorem in the formal canon.
- supports
- The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
- extends
- The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
- uses
- The paper appears to rely on the theorem as machinery.
- contradicts
- The paper's claim conflicts with a theorem or certificate in the canon.
- unclear
- Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.
Forward citations
Cited by 1 Pith paper
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When Two Loops Matter: Electroweak Precision in the SMEFT
A modification to the top-Higgs Yukawa coupling in SMEFT induces a two-loop shift in the W mass through a large anomalous dimension, providing a new indirect probe via electroweak precision observables.
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discussion (0)
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