Convex Geometry Perspective to the (Standard Model) Effective Field Theory Space

Abstract

We present a convex geometry perspective to the Effective Field Theory (EFT) parameter space. We show that the second $s$ derivatives of the forward EFT amplitudes form a convex cone, whose extremal rays are closely connected with states in the UV theory. For tree-level UV-completions, these rays are simply theories with all UV particles living in at most one irreducible representation of the symmetries of the theory. In addition, all the extremal rays are determined by the symmetries and can be systematically identified via group theoretical considerations. The implications are twofold. First, geometric information encoded in the EFT space can help reconstruct the UV-completion. In particular, we will show that the dim-8 operators are important in reverse-engineering the UV physics from the Standard Model EFT, and thus deserve more theoretical and experimental investigations. Second, theoretical bounds on the Wilson coefficients can be obtained by identifying the boundaries of the cone and are in general stronger than the current positivity bounds. We show explicit examples of these new bounds, and demonstrate that they originate from the scattering amplitudes corresponding to entangled states.

arXiv comment7 pages, 2 figures; version accepted by prl

References in corpus (53)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Effective description of general extensions of the Standard Model: the complete tree-level dictionary
• Positivity Bounds for Scalar Theories
• Theoretical Constraints on the Higgs Effective Couplings
• Beyond Amplitudes' Positivity and the Fate of Massive Gravity
• Softness and Amplitudes' Positivity for Spinning Particles
• Amplitudes' Positivity, Weak Gravity Conjecture, and Modified Gravity
• UV complete me: Positivity Bounds for Particles with Spin
• The Universal One-Loop Effective Action
• Helicity Selection Rules and Non-Interference for BSM Amplitudes
• CoDEx: Wilson coefficient calculator connecting SMEFT to UV theory
• Signs of Analyticity in Single-Field Inflation
• Integrating out heavy particles with functional methods: a simplified framework
• Consistency of the Standard Model Effective Field Theory
• Quantum Gravity Constraints from Unitarity and Analyticity
• Massive Galileon Positivity Bounds
• Positivity Bounds for Massive Spin-1 and Spin-2 Fields
• On the impact of dimension-eight SMEFT operators on Higgs measurements
• Consistency of the Chiral Pion-Pion Scattering Amplitudes with Axiomatic Constraints
• Positivity bounds on vector boson scattering at the LHC
• Covariant diagrams for one-loop matching
• Positivity constraints on aQGC: carving out the physical parameter space
• Extending the Universal One-Loop Effective Action: Heavy-Light Coefficients
• Mixed Heavy-Light Matching in the Universal One-Loop Effective Action
• Positivity of Curvature-Squared Corrections in Gravity
• MatchingTools: a Python library for symbolic effective field theory calculations
• Probing the Scale of New Physics in the $ZZ\gamma$ Coupling at $e^{+}{e}^{-}$ Colliders
• The Chiral Lagrangian parameters, ${\overline{\ell }}_1$, ${\overline{\ell }}_2$, are determined by the $\rho$--resonance
• Patterns of Strong Coupling for LHC Searches
• Measurements of production cross sections of WZ and same-sign WW boson pairs in association with two jets in proton-proton collisions at $\sqrt{s}=$ 13 TeV
• The Speed of Gravity
• Novel angular dependence in Drell-Yan lepton production via dimension-8 operators
• Positivity in the sky
• Positivity Constraints for Pseudo-linear Massive Spin-2 and Vector Galileons
• Search for anomalous electroweak production of vector boson pairs in association with two jets in proton-proton collisions at 13 TeV
• Dispersion Relation Bounds for pi pi Scattering
• ZZ and Zgamma still haven't found what they are looking for
• Bounds on Amplitudes in Effective Theories with Massive Spinning Particles
• Flavor Constraints from Unitarity and Analyticity
• Completing the scalar and fermionic Universal One-Loop Effective Action
• Massive Spin-2 Scattering and Asymptotic Superluminality
• Gauge fixing the Standard Model Effective Field Theory
• Measurement of the cross section for electroweak production of a Z boson, a photon and two jets in proton-proton collisions at $\sqrt{s}=$ 13 TeV and constraints on anomalous quartic couplings
• Massive and Massless Spin-2 Scattering and Asymptotic Superluminality
• Positivity Constraints on Interacting Spin-2 Fields
• Generalized positivity bounds on chiral perturbation theory
• Duality and Axionic Weak Gravity
• The Other Fermion Compositeness
• Constraining Gluonic Quartic Gauge Coupling Operators with $gg\to \gamma \gamma$
• To Positivity and Beyond, where Higgs-Dilaton Inflation has never gone before
• Constraints on Chiral Perturbation Theory Parameters from QCD Inequalities
• Positivity Constraints on Interacting Pseudo-Linear Spin-2 Fields
• Positivity in the effective field theory of cosmological perturbations

Cited by in corpus (69)

• Positive Moments for Scattering Amplitudes
• New positivity bounds from full crossing symmetry
• The Weak Gravity Conjecture: A Review
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Causality, Unitarity, and the Weak Gravity Conjecture
• Into the EFThedron and UV constraints from IR consistency
• QED positivity bounds
• Natural Selection Rules: New Positivity Bounds for Massive Spinning Particles
• Positivity in Multi-Field EFTs
• The Flavor of UV Physics
• Bootstrapping Pions at Large $N$
• Bounding Violations of the Weak Gravity Conjecture
• Positivity bounds in the Standard Model effective field theory beyond tree level
• Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings
• Causality, Unitarity and Symmetry in Effective Field Theory
• Positivity bounds on Minimal Flavor Violation
• Triple crossing positivity bounds for multi-field theories
• Positivity Bounds without Boosts
• SMEFTs living on the edge: determining the UV theories from positivity and extremality
• Moments for positivity: using Drell-Yan data to test positivity bounds and reverse-engineer new physics
• Signs, Spin, SMEFT: Sum Rules at Dimension Six
• Exploring the SMEFT at dimension-8 with Drell-Yan transverse momentum measurements
• Unambiguously Testing Positivity at Lepton Colliders
• Constraints on anomalous quartic gauge couplings via $W\gamma jj$ production at the LHC
• The study of neutral triple gauge couplings in the process $e^{+}{e}^{-}\to Z\gamma$ including unitarity bounds
• Low-Energy Effective Field Theory below the Electroweak Scale: Dimension-8 Operators
• Generalized elastic positivity bounds on interacting massive spin-2 theories
• Sum Rules in the Standard Model Effective Field Theory from Helicity Amplitudes
• Constraints on anomalous quartic gauge couplings via $Z\gamma jj$ production at the LHC
• Swampland Conditions for Higher Derivative Couplings from CFT
• Using a nested anomaly detection machine learning algorithm to study the neutral triple gauge couplings at an \texorpdfstring{$e^{+}{e}^{-}$}{e+e-} collider
• Detecting anomalous quartic gauge couplings using the isolation forest machine learning algorithm
• Searching for anomalous quartic gauge couplings at muon colliders using principle component analysis
• Tri-photon at muon collider: a new process to probe the anomalous quartic gauge couplings
• Computing Tools for Effective Field Theories
• Amplitude's positivity vs. subluminality: Causality and Unitarity Constraints on dimension 6 & 8 Gluonic operators in the SMEFT
• Spinning Sum Rules for the Dimension-Six SMEFT
• Extract the energy scale of anomalous $\gamma \gamma \to W^{+}{W}^{-}$ scattering in the vector boson scattering process using artificial neural networks
• Four-fermion operators at dimension 6: dispersion relations and UV completions
• Effective Field Theories as Lagrange Spaces
• A Note on Gauge Anomaly Cancellation in Effective Field Theories
• Origin of Neutrino Masses on the Convex Cone of Positivity Bounds
• Positivity Bounds on parity-violating scalar-tensor EFTs
• Positivity bounds in vector theories
• Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes
• Positivity Bounds on Massive Vectors
• Multipositivity Bounds for Scattering Amplitudes
• Positivity Bounds in Scalar Effective Field Theories at One-loop Level
• Using k-means assistant event selection strategy to study anomalous quartic gauge couplings at muon colliders
• Detect anomalous quartic gauge couplings at muon colliders with quantum kernel k-means
• Searching for gluon quartic gauge couplings at muon colliders using the auto-encoder
• Quantum Corrections to Pair Production of Charged Black Holes in de Sitter Space
• Optimize the event selection strategy to study the anomalous quartic gauge couplings at muon colliders using the support vector machine and quantum support vector machine
• Positivity bounds at one-loop level: the Higgs sector
• Lectures in Quantum Gravity
• Positively Identifying HEFT or SMEFT
• Positivity Bounds on Higgs-Portal Dark Matter
• Causality constraints on nonlinear supersymmetry
• Positivity bounds in scalar-QED EFT at one-loop level
• Search for Neutral Triple Gauge Couplings with $ZZ$ Production at Future Electron Positron Colliders
• Positivity in Amplitudes and Quantum Entanglement
• Search for anomalous quartic gauge couplings in the process ${\mu }^{+}{\mu }^{-}\to \bar{\nu }\nu \gamma \gamma$ with a nested local outlier factor
• Constraining dimension-6 SMEFT with higher-order predictions for $pp\to tW$
• Seesaw Models of Neutrino Masses on the Convex Cone of Positivity Bounds
• A quantum machine learning classifier to search for new physics
• General form of effective operators from hidden sectors
• Primal S-matrix bootstrap with dispersion relations
• Positivity and partial wave unitarity bounds on ALP theories via amplitude methods
• Dilepton production in the SMEFT at $\mathcal{O}(1/{\Lambda }^4)$