New positivity bounds from full crossing symmetry

Abstract

Positivity bounds are powerful tools to constrain effective field theories. Utilizing the partial wave expansion in the dispersion relation and the full crossing symmetry of the scattering amplitude, we derive several sets of generically nonlinear positivity bounds for a generic scalar effective field theory: We refer to these as the $PQ$, $D^{\mathrm{su}}$, $D^{\mathrm{stu}}$ and ${\bar{D}}^{\mathrm{stu}}$ bounds. While the $PQ$ bounds and $D^{\mathrm{su}}$ bounds only make use of the $s\leftrightarrow u$ dispersion relation, the $D^{\mathrm{stu}}$ and ${\bar{D}}^{\mathrm{stu}}$ bounds are obtained by further imposing the $s\leftrightarrow t$ crossing symmetry. In contradistinction to the linear positivity for scalars, these inequalities can be applied to put upper and lower bounds on Wilson coefficients, and are much more constraining as shown in the lowest orders. In particular we are able to exclude theories with soft amplitude behaviour such as weakly broken Galileon theories from admitting a standard UV completion. We also apply these bounds to chiral perturbation theory and we find these bounds are stronger than the previous bounds in constraining its Wilson coefficients.

arXiv comment39 pages, 8 figures; v2: published in JHEP, various small edits, in particular minor improvement due to use of vanishing odd partial waves

References in corpus (57)

• 4D Gravity on a Brane in 5D Minkowski Space
• The galileon as a local modification of gravity
• Resummation of Massive Gravity
• Generalization of the Fierz-Pauli Action
• Massive Gravity
• Causality, Analyticity and an IR Obstruction to UV Completion
• ππscattering
• Strong Interactions and Stability in the DGP Model
• Galileon inflation
• DBI and the Galileon reunited
• Elastic $\pi \pi$ scattering to two loops
• Effective Field Theories from Soft Limits
• Energy's and amplitudes' positivity
• Positivity Bounds for Scalar Theories
• A Periodic Table of Effective Field Theories
• 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
• 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
• Consistency of the Chiral Pion-Pion Scattering Amplitudes with Axiomatic Constraints
• Positivity bounds on vector boson scattering at the LHC
• Weakly Broken Galileon Symmetry
• Positivity constraints on aQGC: carving out the physical parameter space
• Convex Geometry Perspective to the (Standard Model) Effective Field Theory Space
• Improved Positivity Bounds and Massive Gravity
• Positivity of Curvature-Squared Corrections in Gravity
• Positivity Bounds and the Massless Spin-2 Pole
• Positive Signs in Massive Gravity
• The Chiral Lagrangian parameters, ${\overline{\ell }}_1$, ${\overline{\ell }}_2$, are determined by the $\rho$--resonance
• $K_{\ell 4}$ Form-Factors and $\pi$-$\pi$ Scattering
• Falsifying Models of New Physics Via WW Scattering
• The Speed of Gravity
• Gravitational positivity bounds
• Positivity Constraints for Pseudo-linear Massive Spin-2 and Vector Galileons
• Positivity in the sky
• 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
• Thermodynamics of 4D Dilatonic Black Holes and the Weak Gravity Conjecture
• Carving out the Space of Open-String S-matrix
• Positivity Constraints on Interacting Spin-2 Fields
• Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings
• Generalized positivity bounds on chiral perturbation theory
• Unitarity bounds on charged/neutral state mass ratio
• The Other Fermion Compositeness
• Positivity in electron-positron scattering: testing the axiomatic quantum field theory principles and probing the existence of UV states
• Goldstones with Extended Shift Symmetries
• Causal vs. Analytic constraints on anomalous quartic gauge couplings
• Constraints on Chiral Perturbation Theory Parameters from QCD Inequalities
• Road Signs for UV-Completion
• Positivity Constraints on Interacting Pseudo-Linear Spin-2 Fields
• Comment on the Prediction of Two-loop Standard Chiral Perturbation Theory for Low-Energy ππScattering

Cited by in corpus (102)

• Sharp Boundaries for the Swampland
• Analyticity and Unitarity for Cosmological Correlators
• Cosmological Cutting Rules
• Crossing Symmetric Dispersion Relations in QFTs
• From Locality and Unitarity to Cosmological Correlators
• Causality constraints on corrections to Einstein gravity
• Celestial Amplitudes from UV to IR
• Where is String Theory?
• AdS Bulk Locality from Sharp CFT Bounds
• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• The Inflationary Wavefunction from Analyticity and Factorization
• Into the EFThedron and UV constraints from IR consistency
• QED positivity bounds
• S-matrix Bootstrap for Effective Field Theories: Massless Pions
• Rigorous Bounds on Light-by-Light Scattering
• Reverse Bootstrapping: IR lessons for UV physics
• Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds
• Crossing Symmetric Dispersion Relations for Mellin Amplitudes
• Natural Selection Rules: New Positivity Bounds for Massive Spinning Particles
• Landau Discriminants
• Positivity Bounds on Dark Energy: When Matter Matters
• Positivity in Multi-Field EFTs
• Bootstrapping Pions at Large $N$
• Bounding Violations of the Weak Gravity Conjecture
• Causal Effective Field Theories
• Graviton partial waves and causality in higher dimensions
• Gravitational Regge bounds
• Positivity bounds on effective field theories with spontaneously broken Lorentz invariance
• Causality Constraints on Black Holes beyond GR
• Causality, Unitarity and Symmetry in Effective Field Theory
• Quantum field theory and the Bieberbach conjecture
• Cornering Large-$N_c$ QCD with Positivity Bounds
• Positivity bounds on Minimal Flavor Violation
• Triple crossing positivity bounds for multi-field theories
• Positivity and Geometric Function Theory Constraints on Pion Scattering
• Positivity Bounds without Boosts
• SMEFTs living on the edge: determining the UV theories from positivity and extremality
• Massive Gravity is not Positive
• What is the $i\epsilon$ for the S-matrix?
• Rigorous bounds on the Analytic $S$-matrix
• Moments for positivity: using Drell-Yan data to test positivity bounds and reverse-engineer new physics
• QFT, EFT and GFT
• On the unitarity and low energy expansion of the Coon amplitude
• Testing gravitational wave propagation with multiband detections
• A cautionary case of casual causality
• Positivity bounds from multiple vacua and their cosmological consequences
• Scattering from production in 2d
• Bulk locality from the celestial amplitude
• Nonperturbative Bounds on Scattering of Massive Scalar Particles in $d\ge 2$
• Swampland Conditions for Higher Derivative Couplings from CFT
• Scalar Fields Near Compact Objects: Resummation versus UV Completion
• Crossing antisymmetric Polyakov blocks + Dispersion relation
• Bounds on Crossing Symmetry
• Bounds on photon scattering
• Finite energy sum rules for gravitational Regge amplitudes
• RG of GR from On-shell Amplitudes
• Spinning Sum Rules for the Dimension-Six SMEFT
• The EFT Bootstrap at Finite $M_{PL}$
• Celestial insights into the S-matrix bootstrap
• Horndeski stars
• Dispersive Sum Rules in AdS${}_2$
• Non-topological solitons and quasi-solitons
• NNLO Positivity Bounds on Chiral Perturbation Theory for a General Number of Flavours
• Origin of Neutrino Masses on the Convex Cone of Positivity Bounds
• Positivity Bounds on parity-violating scalar-tensor EFTs
• Positivity bounds in vector theories
• Positivity Bounds on Massive Vectors
• A Well-Posed UV Completion for Simulating Scalar Galileons
• Non-Forward UV/IR Relations
• Multipositivity Bounds for Scattering Amplitudes
• Locality and Analyticity of the Crossing Symmetric Dispersion Relation
• Feynman Integrals from Positivity Constraints
• Positivity Bounds in Scalar Effective Field Theories at One-loop Level
• Gravity-Induced Photon Interactions and Infrared Consistency in any Dimensions
• Supersymmetric Massive Gravity
• Positivity, low twist dominance and CSDR for CFTs
• Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry
• Dispersion relations, knot polynomials and the $q$-deformed harmonic oscillator
• Post-Newtonian Dynamics of Spinning Black Hole Binaries in Einstein-Scalar-Gauss-Bonnet Gravity
• Bispectrum Islands
• Causality and Stability from Acoustic Geometry
• Positivity bounds at one-loop level: the Higgs sector
• Effective Field Theory of Chiral Gravitational Waves
• Lectures in Quantum Gravity
• Impossible Symmetries and Conformal Gravity
• Five-point Superluminality Bounds
• Causality constraints on nonlinear supersymmetry
• Unitarity and unstable-particle scattering amplitudes
• A Celestial Route to AdS Bulk Locality
• Strings from Almost Nothing
• Positivity bounds in scalar-QED EFT at one-loop level
• IR side of bounds on Theories with Spontaneously Broken Lorentz Symmetry
• Theoretical priors in scalar-tensor cosmologies: Shift-symmetric Horndeski models
• Spectral Constraints on Theories of Colored Particles and Gravity
• Primal S-matrix bootstrap with dispersion relations
• A Note on the Analytic Structure of Celestial Amplitudes
• Quantifying EFT Uncertainties in LHC Searches
• Five-point partial waves, splitting constraints and hidden zeros
• The Rise of Linear Trajectories
• String Theory from Maximal Supersymmetry
• The IR-Side of Positivity Bounds
• Positivity vs. Lorentz-violation: an explicit example