The Standard Model as an Effective Field Theory

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.

Version accepted by Physics Reports. Sections on the EFT landscape and the method of regions added. Typos fixed

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• An Effective Guide to Beyond the Standard Model Physics
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• Effective theory calculation of resonant high-energy scattering
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• An improved determination of the width of the top quark
• Sequential Flavour Symmetry Breaking
• Vector-like Fermions and Higgs Effective Field Theory Revisited
• Automatic computations at next-to-leading order in QCD for top-quark flavor-changing neutral processes
• S-Matrix Approach to the $Z$ Line Shape
• Pinning down the large-x gluon with NNLO top-quark pair differential distributions
• Fiducial, total and differential cross-section measurements of $t$-channel single top-quark production in $pp$ collisions at 8 TeV using data collected by the ATLAS detector
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• On Gauge Invariance and Minimal Coupling
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• Scheming in the SMEFT... and a reparameterization invariance!
• Direct and indirect constraints on CP-violating Higgs-quark and Higgs-gluon interactions
• Naive Dimensional Analysis Counting of Gauge Theory Amplitudes and Anomalous Dimensions
• Renormalization group improvement of the NRQCD Lagrangian and heavy quarkonium spectrum
• Evidence for single top-quark production in the $s$-channel in proton-proton collisions at $\sqrt{s}=$8 TeV with the ATLAS detector using the Matrix Element Method
• Dimension-six CP-violating operators of the third-family quarks and their effects at colliders
• Effective field theory approach to LHC Higgs data
• One-loop $W_L{W}_L$ and $Z_L{Z}_L$ scattering from the Electroweak Chiral Lagrangian with a light Higgs-like scalar
• Cross section measurement of t-channel single top quark production in pp collisions at sqrt(s) = 13 TeV
• Composite Higgs Search at the LHC
• How well do we need to measure Higgs boson couplings?
• Non-Perturbative Contribution to the Thrust Distribution in $e^{+}{e}^{-}$ Annihilation
• Hilbert Series for Flavor Invariants of the Standard Model
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• Effective theories of universal theories
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• Standard Model EFT and Extended Scalar Sectors
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• Right-Handed Neutrinos as the Origin of the Electroweak Scale
• Electroweak Higgs boson production in the standard model effective field theory beyond leading order in QCD
• Single Top Production at Next-to-Leading Order in the Standard Model Effective Field Theory
• The Complex-Mass Scheme and Unitarity in perturbative Quantum Field Theory
• Effective Lagrangian approach to neutrinoless double beta decay and neutrino masses
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• Pseudo-observables in Higgs decays
• Measurement of the production cross-section of a single top quark in association with a $W$ boson at 8 TeV with the ATLAS experiment
• Testing Gluon Self-Interactions in Three Jet Events at Hadron Colliders
• Better Higgs Measurements Through Information Geometry
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• Renormalization Group Scaling of the 1/m^2 HQET Lagrangian
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• CP violation with a dynamical Higgs
• Higgs Pair Production at NLO QCD for CP-violating Higgs Sectors
• Constraints on Non-standard Top Quark Couplings
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• Exploring the Anomalous Higgs-top Couplings
• Disentangling Flavor Violation in the Top-Higgs Sector at the LHC
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• Two-Loop Renormalization in the Standard Model Part III: Renormalization Equations and their Solutions
• Flavour with a Light Dynamical "Higgs Particle"
• Width and Partial Widths of Unstable Particles in the Light of the Nielsen Identities
• Pinning down top dipole moments with ultra-boosted tops
• Effective-Lagrangian approach to precision measurements: the anomalous magnetic moment of the muon
• ATLAS sensitivity to Wtb anomalous couplings in top quark decays
• Width and Partial Widths of Unstable Particles
• On the Predictiveness of Single-Field Inflationary Models
• CP Violation in top pair production at an e^+e^- collider
• Neutrino Masses, Grand Unification, and Baryon Number Violation
• Bounding the top and bottom electric dipole moments from neutron experimental data
• Neutrino Masses and Conformal Electro-Weak Symmetry Breaking
• Higgs ultraviolet softening
• The top-quark charge asymmetry at the LHC and Tevatron through NNLO QCD and NLO EW
• Mad-Maximized Higgs Pair Analyses
• Multilepton production via top flavour-changing neutral couplings at the CERN LHC
• Sigma Models with Negative Curvature
• Four-fermion production near the W pair production threshold
• Radiative corrections to WL WL scattering in composite Higgs models
• Higgs couplings: disentangling New Physics with off-shell measurements
• Probing the Top-Yukawa Coupling in Associated Higgs production with a Single Top Quark
• Search for anomalous top-gluon couplings at LHC revisited
• The effective potential in the presence of several mass scales
• A General Analysis of Wtb anomalous Couplings
• Light "Higgs", yet strong interactions
• One-loop corrections to $h\to b\bar{b}$ and $h\to \tau \bar{\tau }$ decays in the Standard Model Dimension-6 EFT: four-fermion operators and the large-$m_t$ limit
• Precision Probes of QCD at High Energies
• Measurement of the W boson helicity fractions in the decays of top quark pairs to lepton + jets final states produced in pp collisions at sqrt(s) = 8 TeV
• Measurement of the $t\bar{t}W$ and $t\bar{t}Z$ production cross sections in $pp$ collisions at $\sqrt{s}=8\mathrm{Te}\mathrm{V}$ with the ATLAS detector
• Integrating out the Standard Higgs Field in the Path Integral
• Zt and γt production via top flavour-changing neutral couplings at the Fermilab Tevatron
• Measurement of the t t-bar production cross section using events in the e mu final state in pp collisions at sqrt(s) = 13 TeV
• Nonstandard Higgs Couplings from Angular Distributions in $h\to Z{\ell }^{+}{\ell }^{-}$
• Pseudoscalar top-Higgs coupling: Exploration of $\mathrm{CP}$-odd observables to resolve the sign ambiguity
• On the renormalization of the electroweak chiral Lagrangian with a Higgs
• Note on Anomalous Higgs-Boson Couplings in Effective Field Theory
• Differences Between the Pole and On-Shell Masses and Widths of the Higgs Boson
• Minimal conformal extensions of the Higgs sector
• The top quark forward-backward asymmetry at approximate N${}^3$LO
• Measurement of the $W$ boson polarisation in $t\bar{t}$ events from $pp$ collisions at $\sqrt{s}$ = 8 TeV in the lepton+jets channel with ATLAS
• Standard Model Extended by a Heavy Singlet: Linear vs. Nonlinear EFT
• Measurement of the t t-bar production cross section using events with one lepton and at least one jet in pp collisions at sqrt(s) = 13 TeV
• Probing the Top-Quark Electric Dipole Moment at a Photon Linear Collider
• Higgs form factors in Associated Production
• Deriving Non-decoupling Effects of Heavy Fields from the Path Integral: a Heavy Higgs Field in an SU(2) Gauge Theory
• Genuine CP-odd Observables at the LHC
• Sigma Decomposition
• Pseudo-observables in electroweak Higgs production
• On the consistent use of Constructed Observables
• Unitarity, analyticity, dispersion relations and resonances in strongly interacting $W_L{W}_L$, $Z_L{Z}_L$ and $hh$ scattering
• The Neutrino Option
• Measurements of the t-tbar production cross section in lepton+jets final states in pp collisions at 8 TeV and ratio of 8 to 7 TeV cross sections
• Single Top Production in $e^{+}{e}^{-}$, $e^{-}{e}^{-}$, $\gamma e$ and $\gamma \gamma$ Collisions
• Interpreting $W$ mass measurements in the SMEFT
• Anomalous Couplings of the Third Generation in Rare B Decays
• Top effective operators at the ILC
• One-loop renormalization of the electroweak chiral Lagrangian with a light Higgs
• Latest constraint on non-standard top-gluon couplings at hadron colliders and its future prospect
• Flavor Changing Neutral Coupling Mediated Radiative Top Quark Decays at Next-to-Leading Order in QCD
• Constraining $qqtt$ operators from four-top production: a case for enhanced EFT sensitivity
• (Dys)Zphilia or a custodial breaking Higgs at the LHC
• Top Partners and Higgs Boson Production
• Molien Function for Duality
• QCD radiative corrections for $h\to b\bar{b}$ in the Standard Model Dimension-6 EFT
• Energy Spectrum of Secondary Leptons in $e^{+}{e}^{-}\to t\bar{t}$ - Non-standard Interactions and CP Violation -
• A Direct Measurement of the Total Decay Width of the Top Quark
• New directions for top quark polarization in the $t$-channel process
• Searching for New Physics in the Three-Body Decays of the Higgs-like Particle
• The minimal linear sigma model for the Goldstone Higgs
• Effective Lagrangian approach to Higgs-mediated FCNC top quark decays
• Further numerical results on non-factorizable corrections to e+e- --> 4fermions
• Dimension six FCNC operators and top production at the LHC
• Probing chromomagnetic and chromoelectric couplings of the top quark using its polarization in pair production at hadron colliders
• Single top-quark production at the Tevatron and the LHC
• Through precision straits to next standard model heights
• Flavour changing strong interaction effects on top quark physics at the LHC
• Zt, gamma t and t production at hadron colliders via strong flavour-changing neutral couplings
• Four-Fermi Effective Operators in Top-Quark Production and Decay
• Effective Field Theory for Nonstandard Top Quark Couplings
• Probing top anomalous couplings at the LHC with trilepton signatures in the single top mode
• A Probe of New Physics in Top Quark Pair Production at $e^{-}{e}^{+}$ Colliders
• Measurement of the semileptonic tt-bar gamma production cross section in pp collisions at sqrt(s) = 8 TeV
• Combined effects of strong and electroweak FCNC effective operators in top quark physics at the LHC
• Pole Mass, Width, and Propagators of Unstable Fermions
• Bounding the top Yukawa with Higgs-associated single-top production
• Gamma-Z box corrections to weak charges of heavy nuclei in atomic parity violation
• Probing CP-violating Higgs and gauge boson couplings in the Standard Model effective field theory
• Using Final State Pseudorapidities to Improve s-channel Resonance Observables at the LHC
• Studying the $Wtb$ vertex structure using recent LHC results
• Lepton Flavour Violating top decays at the LHC
• Constraints on flavor-changing neutral-current $Htq$ couplings from the signal of $tH$ associated production with QCD next-to-leading order accuracy at the LHC
• New physics in t-> b W decay at next-to-leading order in QCD
• CP Violation in the Top-Quark Pair Production at a Next Linear Collider
• Measurement of differential cross-sections of a single top quark produced in association with a $W$ boson at $\sqrt{s}=13$ TeV with ATLAS
• Searching for t->c(u)h with dipole moments
• On the non-minimal character of the SMEFT
• Higgs boson pair production at NNLO in QCD including dimension 6 operators
• Probing Top-Quark Couplings at Polarized NLC
• Electric dipole moment of top quark and CP-violating asymmetries in gamma gamma -> t tbar
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