The paper delivers the first complete non-redundant dimension-six operator basis for SMEFT at finite temperature using the Hilbert series on R^3 x S^1.
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Dimension-Six Terms in the Standard Model Lagrangian
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abstract
When the Standard Model is considered as an effective low-energy theory, higher dimensional interaction terms appear in the Lagrangian. Dimension-six terms have been enumerated in the classical article by Buchmueller and Wyler [3]. Although redundance of some of those operators has been already noted in the literature, no updated complete list has been published to date. Here we perform their classification once again from the outset. Assuming baryon number conservation, we find 15 + 19 + 25 = 59 independent operators (barring flavour structure and Hermitian conjugations), as compared to 16 + 35 + 29 = 80 in Ref.[3]. The three summed numbers refer to operators containing 0, 2 and 4 fermion fields. If the assumption of baryon number conservation is relaxed, 4 new operators arise in the four-fermion sector.
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representative citing papers
Complete one-loop matching of the general MSSM onto SMEFT in the Warsaw basis, including all SUSY-governed correlations among Wilson coefficients.
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.
Bayesian model selection over SMEFT operator subsets using a genetic algorithm and BIC approximation is applied to electroweak, Higgs, top and diboson data, finding no evidence for new physics and improved Wilson coefficient posteriors compared to global fits.
Yukawa hierarchies are generated from powers of fully anarchic spurions in higher SU(2) and SU(3) flavor representations via progressive rank lifting through composite outer products, with explicit models and predictions for FCNCs and stochastic gravitational waves.
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.
A minimal basis with fewer terms and simpler contractions is given for non-derivative baryon-number-violating operators in SMEFT up to mass dimension 11.
Classification of 440 minimal UV completions for SMEFT dim-9 operators in short-range 0νββ decay, including 324 with vector mediators.
Nucleon energy correlators access linear effects from light-quark dipole operators via azimuthal asymmetries in the target fragmentation region at the EIC.
Formulates nTGC form factors from dim-8 SMEFT operators compatible with electroweak symmetry breaking and applies machine learning to fermion angular distributions to probe new physics scales up to multi-TeV in ZZ production at CEPC, FCC-ee, ILC and CLIC.
Proposes a numerical cross-validation procedure for SMEFT Monte Carlo implementations by comparing linearized EFT amplitudes and their SM interferences at fixed points.
Quantum information observables in LHC top quark pair production are modified by SMEFT dimension-6 operators in ways that depend on their CP properties, offering a complementary probe beyond standard observables.
NLO QCD corrections to pp to ttbar H in the di-lepton channel with SMEFT operators included in both production and top-quark decays.
Leptophilic ALPs with m_a > f_a can explain the electron anomalous magnetic moment tension over a large parameter space and are testable via μ→e conversion.
Doubly charmed baryon decays provide symmetry-protected null tests for nonfactorizable QCD and lepton-universality ratios sensitive to new physics at multi-TeV scales.
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.
Matchotter automates one-loop finite-temperature dimensional reduction and supersoft matching for generic Lagrangians using functional techniques.
A 10 TeV muon collider could improve existing bounds on muon-Higgs-gauge and muon-top interactions by up to an order of magnitude over current limits and FCC-ee projections.
No weak scale triggers exist in the SMEFT up to dimension six (and likely eight) that can solve the hierarchy problem far above the weak scale.
A forward neutrino detector at a muon collider can exceed current and upcoming bounds on non-standard neutrino interactions by exploiting high neutrino flux, known flavor composition, and chirality.
A hybrid NSBI technique is presented for inferring the Higgs trilinear coupling via off-shell production in SMEFT, achieving near-theoretical-optimum sensitivity with expected HL-LHC constraints.
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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.
Proposal for a new observable—dihadron azimuthal asymmetry in unpolarized SIDIS at EIC—that isolates linear dependence on light-quark dipole couplings via SM-dipole interference.
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Finite-temperature operator basis on $\mathbb{R}^3 \times S^1$ for SMEFT
The paper delivers the first complete non-redundant dimension-six operator basis for SMEFT at finite temperature using the Hilbert series on R^3 x S^1.
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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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Exploring the SMEFT landscape: Bayesian Model Selection for indirect discovery
Bayesian model selection over SMEFT operator subsets using a genetic algorithm and BIC approximation is applied to electroweak, Higgs, top and diboson data, finding no evidence for new physics and improved Wilson coefficient posteriors compared to global fits.
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Hierarchies from Higher Flavor Spin
Yukawa hierarchies are generated from powers of fully anarchic spurions in higher SU(2) and SU(3) flavor representations via progressive rank lifting through composite outer products, with explicit models and predictions for FCNCs and stochastic gravitational waves.
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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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Basis for non-derivative baryon-number-violating operators
A minimal basis with fewer terms and simpler contractions is given for non-derivative baryon-number-violating operators in SMEFT up to mass dimension 11.
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Complete UV Resonances of SMEFT Dim-9 Operators for Short-range Neutrinoless Double Beta Decay
Classification of 440 minimal UV completions for SMEFT dim-9 operators in short-range 0νββ decay, including 324 with vector mediators.
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Nucleon Energy Correlators as a Probe of Light-Quark Dipole Operators at the Electron-Ion Collider
Nucleon energy correlators access linear effects from light-quark dipole operators via azimuthal asymmetries in the target fragmentation region at the EIC.
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Probing Neutral Triple Gauge Couplings via $ZZ$ Production at $e^+e^-$ Colliders with Machine Learning
Formulates nTGC form factors from dim-8 SMEFT operators compatible with electroweak symmetry breaking and applies machine learning to fermion angular distributions to probe new physics scales up to multi-TeV in ZZ production at CEPC, FCC-ee, ILC and CLIC.
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Proposal for the validation of Monte Carlo implementations of the standard model effective field theory
Proposes a numerical cross-validation procedure for SMEFT Monte Carlo implementations by comparing linearized EFT amplitudes and their SM interferences at fixed points.
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Quantumness of top quark pairs produced at LHC within SMEFT framework
Quantum information observables in LHC top quark pair production are modified by SMEFT dimension-6 operators in ways that depend on their CP properties, offering a complementary probe beyond standard observables.
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SMEFT everywhere: a NLO study of $\boldsymbol{pp \to t\bar{t}H}$ with decaying tops
NLO QCD corrections to pp to ttbar H in the di-lepton channel with SMEFT operators included in both production and top-quark decays.
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Crossing into the $m_a > f_a$ Region for Leptophilic ALPs
Leptophilic ALPs with m_a > f_a can explain the electron anomalous magnetic moment tension over a large parameter space and are testable via μ→e conversion.
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Null Tests and Lepton Universality in $\Xi_{cc}$ Baryon Decays
Doubly charmed baryon decays provide symmetry-protected null tests for nonfactorizable QCD and lepton-universality ratios sensitive to new physics at multi-TeV scales.
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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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Matchotter: An Automated Tool for Dimensional Reduction at Finite Temperature
Matchotter automates one-loop finite-temperature dimensional reduction and supersoft matching for generic Lagrangians using functional techniques.
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Probing Higgs and Top Interactions through the Muon Lens at multi-TeV Muon Colliders
A 10 TeV muon collider could improve existing bounds on muon-Higgs-gauge and muon-top interactions by up to an order of magnitude over current limits and FCC-ee projections.
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Weak Scale Triggers in the SMEFT
No weak scale triggers exist in the SMEFT up to dimension six (and likely eight) that can solve the hierarchy problem far above the weak scale.
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Non-Standard Neutrino Interactions at a Muon Collider Neutrino Detector
A forward neutrino detector at a muon collider can exceed current and upcoming bounds on non-standard neutrino interactions by exploiting high neutrino flux, known flavor composition, and chirality.
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Neural simulation-based inference of the Higgs trilinear self-coupling via off-shell Higgs production
A hybrid NSBI technique is presented for inferring the Higgs trilinear coupling via off-shell production in SMEFT, achieving near-theoretical-optimum sensitivity with expected HL-LHC constraints.
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Amplitudes and partial wave unitarity bounds
Develops spinor-helicity formalism generalizing partial wave unitarity bounds for multi-particle scattering and spin-2 or higher-spin theories.
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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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Dihadron azimuthal asymmetry and light-quark dipole moments at the Electron-Ion Collider
Proposal for a new observable—dihadron azimuthal asymmetry in unpolarized SIDIS at EIC—that isolates linear dependence on light-quark dipole couplings via SM-dipole interference.
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Complete One-Loop Renormalization of the Higgs-Electroweak Chiral Lagrangian
The complete one-loop renormalization of the EWChL is performed, confirming power counting assumptions and operator basis completeness while reproducing known subsector results.
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NLO EW and QCD dimension-6 SMEFT results for Higgs and gauge boson decays in POPxf format
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Probing SMEFT Operators through $t\bar{t}t\bar{t}$ Production with Hyper-Graph Neural Networks at the LHC
A hyper-graph neural network improves discrimination of four-top production at 13 TeV, raising expected significance from 5.13 to 9.11 and enabling projected 95% CL limits on five dimension-six SMEFT Wilson coefficients at current and HL-LHC luminosities.
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Electroweak Restoration: SMEFT and HEFT
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Six classes of CP-violating operators near the QCD scale produce distinct EDM patterns that enable discrimination of their origins and distinguish high-scale versus low-energy sources of the axion vacuum expectation value.
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Solving Cosmological Puzzles using Finite Temperature $\nu$SMEFT
A minimal extension of the Standard Model with three heavy Majorana neutrinos simultaneously realizes fermionic dark matter, a strong first-order electroweak phase transition, and low-scale resonant leptogenesis consistent with neutrino data.
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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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Probing $\tau$ lepton dipole moments at future Lepton Colliders
Future lepton colliders can improve existing constraints on the tau lepton's dipole moments by several orders of magnitude through complementary channels.
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The Spurion Massive EFT (SMEFT)
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CPT Violation, Mirror World and Implications for Baryon Asymmetry
A globally CPT-symmetric paired-universe model with local violations produces inflaton mass splitting that modifies reheating and accounts for observed matter-antimatter asymmetry.
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Probing invisible particles with charm
Rare charm hadron decays offer clean null tests of the standard model that can reach branching ratios up to 10^{-3} for dark photons and 10^{-4} for ALPs in unconstrained parameter spaces.
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Improved Standard-Model predictions for $\eta^{(\prime)}\to \ell^+ \ell^-$
Updated SM predictions yield Br(η→e⁺e⁻)=5.37(4)(2)[4]×10⁻⁹, Br(η→μ⁺μ⁻)=4.54(4)(2)[4]×10⁻⁶, Br(η'→e⁺e⁻)=1.80(2)(3)[3]×10⁻¹⁰, and Br(η'→μ⁺μ⁻)=1.22(2)(2)[3]×10⁻⁷, with a mild 1.6σ tension in the η→μ⁺μ⁻ channel.
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Higgs pair production in gluon fusion to higher orders in Higgs Effective Field Theory
Consistent NLO power counting in HEFT for di-Higgs gluon fusion requires higher-dimensional operators beyond leading order, affecting kinematic benchmarks used in experiments.
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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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Constraining the four-light quark operators in the SMEFT with multijet and VBF processes at linear level
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Derives new physics scale constraints in a six-dimensional EFT subspace for μ to e transitions using data from μ→eγ, μ→3e, and nuclear conversion experiments while highlighting their complementarity.
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Correlated $b \to s$ and $s \to d$ Rare Semileptonic Transitions in the Standard Model Effective Field Theory
SMEFT global fit to b→s anomalies with complex Wilson coefficients shows left-handed four-fermion operators preferred and demonstrates that U(3)^5 or U(2)^5 flavor symmetry restores consistency with kaon data.
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The Higgs-top-$Z$ mass coincidence relation after NNLO matching
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Exploring new resonances with direct top flavor changing interactions
Three new physics resonances with top flavor-changing couplings are mapped to SMEFT operators at the electroweak scale and their phenomenology is analyzed.
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Spin effects in the tau-lepton pair induced by anomalous magnetic and electric dipole moments
Anomalous dipole moments of the tau lepton produce measurable effects on tau polarization and spin correlations in gamma-gamma and quark-antiquark induced pair production.
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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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Revisiting $\mu$-$e$ conversion in $R$-parity violating SUSY
RG running changes limits on certain RPV SUSY λ and λ' couplings by up to 80 percent, with upcoming μ-e conversion experiments expected to set stronger bounds than μ→eγ or μ→eee decays.
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Impact of Higgs-boson measurements on SMEFT fits
Higgs precision data now meaningfully tightens SMEFT constraints and increases the lower bound on new physics scales across different flavor assumptions.
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Lepton flavor violating top quark FCNC processes at the $\mu$TRISTAN
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Combination and interpretation of differential Higgs boson production cross sections in proton-proton collisions at $\sqrt{s}$ = 13 TeV
Combined differential and total Higgs boson production cross sections at 13 TeV are measured and found consistent with Standard Model expectations, with a total cross section of 53.4 pb.