Complete one-loop matching of the general MSSM onto SMEFT in the Warsaw basis, including all SUSY-governed correlations among Wilson coefficients.
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The Standard Model as an Effective Field Theory
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abstract
Projecting measurements of the interactions of the known Standard Model (SM) states into an effective field theory (EFT) framework is an important goal of the LHC physics program. The interpretation of measurements of the properties of the Higgs-like boson in an EFT allows one to consistently study the properties of this state, while the SM is allowed to eventually break down at higher energies. In this review, basic concepts relevant to the construction of such EFTs are reviewed pedagogically. Electroweak precision data is discussed as a historical example of some importance to illustrate critical consistency issues in interpreting experimental data in EFTs. A future precision Higgs phenomenology program can benefit from the projection of raw experimental results into consistent field theories such as the SM, the SM supplemented with higher dimensional operators (the SMEFT) or an Electroweak chiral Lagrangian with a dominantly $J^P = 0^+$ scalar (the HEFT). We discuss the developing SMEFT and HEFT approaches, that are consistent versions of such EFTs, systematically improvable with higher order corrections, and comment on the pseudo-observable approach. We review the challenges that have been overcome in developing EFT methods for LHC studies, and the challenges that remain.
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representative citing papers
Complete one-loop SMEFT dim-6 dictionary for arbitrary heavy fermion and scalar UV completions, added to the SOLD package with example application to B to K nu nu anomaly.
S-matrix consistency forces the complete gluon amplitude structure and requires Yang-Mills Lie algebra plus Higgs mechanism for unitarised massive vector boson scattering.
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.
Quantum tomography of diboson spin density matrices yields superior sensitivity to CP-even and CP-odd SMEFT contributions, including quadratic new-physics terms not captured by traditional angular observables.
Complete positivity bounds for the 22 aQGC coefficients in SMEFT restrict the viable parameter space to approximately 0.0313% of the naive total.
The work supplies a modular SMEFT likelihood for EWPD that includes NLO effects and five input schemes, then combines it with LHC measurements to tighten constraints on lepton-flavor universality and quark coupling asymmetries.
A chiral EFT framework is constructed for |ΔB|=2 interactions that matches SMEFT operators to low-energy baryon processes and identifies new dinucleon decay channels sensitive to previously unconstrained operator structures.
NLO QCD and EW corrections in dimension-6 SMEFT are provided for all 2- and 4-body Higgs decays, Z/W decays with EW precision observables, and e+e- to ZH at 240, 365, and 500 GeV, including the total Higgs width and a differential distribution, all in POPxf format.
HEFT admits two consistent power counting schemes, one with a single low-energy scale v and one with two scales v < f, each allowing systematic truncation of operators and amplitudes for any normalization choice.
High-energy amplitude ratios for longitudinal di-boson production approach unity in the SM and dimension-6 SMEFT but not necessarily in HEFT, making the W±_L Z_L to W±_L h cross section ratio a promising discriminator between linear and non-linear electroweak symmetry at the HL-LHC.
A simultaneous fit to multiple ATLAS datasets constrains 48 SMEFT Wilson coefficients and matches subsets to 2HDM and heavy-vector models, finding consistency with the Standard Model.
Future e+e- colliders can constrain new physics through precision Higgs and electroweak measurements in Higgs-coupling, EFT, and SMEFT frameworks, with updated SMEFiT code released.
High-energy astrophysical neutrinos can constrain the running of neutrino mixing parameters with energy, with future multi-detector setups forecast to set strong bounds despite astrophysical uncertainties.
Higher-order QCD predictions for pp to tW enable three-parameter SMEFT fits that constrain effective new-physics scales to 0.5–2 TeV using LHC Run II and III data.
CMS performs a combined SMEFT fit to multiple LHC measurements and precision data, yielding individual constraints on 64 Wilson coefficients and 43 linear combinations.
In the flavor-gauged two Higgs doublet model, h to Z gamma receives unique modifications from f fbar Z vertex corrections while both decays are sensitive to charged Higgs loops, with viable parameter space identified under current limits.
Obtains 95% CL exclusion and 3σ/5σ sensitivity limits on a_τ and d_τ from PbPb collisions at FCC-hh with comparisons to other future colliders.
The review summarizes the baseline SM+GR+Lambda-CDM framework, lists major anomalies and missing pieces, surveys theoretical and experimental approaches, and outlines a staged roadmap organized by decision points.
Reviews advances toward global SMEFT fits across top, Higgs, and electroweak sectors including NLO QCD effects and multi-sector combinations.
A review summarizing recent theory, tools, and phenomenology in the Standard Model Effective Field Theory.
citing papers explorer
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SUSY meets SMEFT: Complete one-loop matching of the general MSSM
Complete one-loop matching of the general MSSM onto SMEFT in the Warsaw basis, including all SUSY-governed correlations among Wilson coefficients.
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From the EFT to the UV: the complete SMEFT one-loop dictionary
Complete one-loop SMEFT dim-6 dictionary for arbitrary heavy fermion and scalar UV completions, added to the SOLD package with example application to B to K nu nu anomaly.
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Consistent Scattering Amplitudes, Yang-Mills, the Higgs Mechanism and the EFTs Beyond
S-matrix consistency forces the complete gluon amplitude structure and requires Yang-Mills Lie algebra plus Higgs mechanism for unitarised massive vector boson scattering.
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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.
-
Odd Physics Off the Diagonal: Constraining CP-violating SMEFT with Quantum Tomography
Quantum tomography of diboson spin density matrices yields superior sensitivity to CP-even and CP-odd SMEFT contributions, including quadratic new-physics terms not captured by traditional angular observables.
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Full positivity bounds for anomalous quartic gauge couplings in SMEFT
Complete positivity bounds for the 22 aQGC coefficients in SMEFT restrict the viable parameter space to approximately 0.0313% of the naive total.
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An EWPD SMEFT likelihood for the LHC -- and how to improve it with measurements of W and Z boson properties
The work supplies a modular SMEFT likelihood for EWPD that includes NLO effects and five input schemes, then combines it with LHC measurements to tighten constraints on lepton-flavor universality and quark coupling asymmetries.
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EFT Pathways to $|\Delta B| =2$: Chiral Constructions and Phenomenology
A chiral EFT framework is constructed for |ΔB|=2 interactions that matches SMEFT operators to low-energy baryon processes and identifies new dinucleon decay channels sensitive to previously unconstrained operator structures.
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NLO EW and QCD dimension-6 SMEFT results for Higgs and gauge boson decays in POPxf format
NLO QCD and EW corrections in dimension-6 SMEFT are provided for all 2- and 4-body Higgs decays, Z/W decays with EW precision observables, and e+e- to ZH at 240, 365, and 500 GeV, including the total Higgs width and a differential distribution, all in POPxf format.
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The Art of Counting: a reappraisal of the HEFT expansion
HEFT admits two consistent power counting schemes, one with a single low-energy scale v and one with two scales v < f, each allowing systematic truncation of operators and amplitudes for any normalization choice.
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Electroweak Restoration: SMEFT and HEFT
High-energy amplitude ratios for longitudinal di-boson production approach unity in the SM and dimension-6 SMEFT but not necessarily in HEFT, making the W±_L Z_L to W±_L h cross section ratio a promising discriminator between linear and non-linear electroweak symmetry at the HL-LHC.
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Effective field theory interpretation of ATLAS measurements involving the Higgs boson, electroweak bosons and the top quark
A simultaneous fit to multiple ATLAS datasets constrains 48 SMEFT Wilson coefficients and matches subsets to 2HDM and heavy-vector models, finding consistency with the Standard Model.
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New Physics Reach through Precision at Future Colliders: a Multi-Pronged Approach
Future e+e- colliders can constrain new physics through precision Higgs and electroweak measurements in Higgs-coupling, EFT, and SMEFT frameworks, with updated SMEFiT code released.
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Astrophysical bounds on the high-energy evolution of neutrino mixing
High-energy astrophysical neutrinos can constrain the running of neutrino mixing parameters with energy, with future multi-detector setups forecast to set strong bounds despite astrophysical uncertainties.
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Constraining dimension-6 SMEFT with higher-order predictions for $p p \to t W$
Higher-order QCD predictions for pp to tW enable three-parameter SMEFT fits that constrain effective new-physics scales to 0.5–2 TeV using LHC Run II and III data.
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Combined effective field theory interpretation of Higgs boson, electroweak vector boson, top quark, and multi-jet measurements
CMS performs a combined SMEFT fit to multiple LHC measurements and precision data, yielding individual constraints on 64 Wilson coefficients and 43 linear combinations.
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Higgs Decays to $Z\gamma$ and $\gamma\gamma$ in the Flavor-Gauged Two Higgs Doublet Model
In the flavor-gauged two Higgs doublet model, h to Z gamma receives unique modifications from f fbar Z vertex corrections while both decays are sensitive to charged Higgs loops, with viable parameter space identified under current limits.
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Probing electromagnetic moments of the tau lepton in PbPb collisions at the FCC-hh
Obtains 95% CL exclusion and 3σ/5σ sensitivity limits on a_τ and d_τ from PbPb collisions at FCC-hh with comparisons to other future colliders.
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Fundamental Physics in 2025: Status, Decisive Targets, and Path Forward
The review summarizes the baseline SM+GR+Lambda-CDM framework, lists major anomalies and missing pieces, surveys theoretical and experimental approaches, and outlines a staged roadmap organized by decision points.
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Towards global fits in EFT's and New Physics implications
Reviews advances toward global SMEFT fits across top, Higgs, and electroweak sectors including NLO QCD effects and multi-sector combinations.
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Recent Developments in SMEFT: Theory, Tools, and Phenomenology
A review summarizing recent theory, tools, and phenomenology in the Standard Model Effective Field Theory.