Positivity Bounds for Scalar Theories

Abstract

Assuming the existence of a local, analytic, unitary UV completion in a Poincaré invariant scalar field theory with a mass gap, we derive an infinite number of positivity requirements using the known properties of the amplitude at and away from the forward scattering limit. These take the form of bounds on combinations of the pole subtracted scattering amplitude and its derivatives. In turn, these positivity requirements act as constraints on the operator coefficients in the low energy effective theory. For certain theories these constraints can be used to place an upper bound on the mass of the next lightest state that must lie beyond the low energy effective theory if such a UV completion is to ever exist.

5 pages

References in corpus (5)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Massive Galileon Positivity Bounds
• Symmetries, Sum Rules and Constraints on Effective Field Theories
• Dispersion Relation Bounds for pi pi Scattering
• Causal vs. Analytic constraints on anomalous quartic gauge couplings

Cited by in corpus (110)

• Implications of the Neutron Star Merger GW170817 for Cosmological Scalar-Tensor Theories
• A systematic approach to generalisations of General Relativity and their cosmological implications
• The EFT-Hedron
• Positive Moments for Scattering Amplitudes
• New positivity bounds from full crossing symmetry
• Extremal Effective Field Theories
• Operator bases, $S$-matrices, and their partition functions
• Beyond Amplitudes' Positivity and the Fate of Massive Gravity
• The Weak Gravity Conjecture: A Review
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• UV complete me: Positivity Bounds for Particles with Spin
• Cosmological Cutting Rules
• Crossing Symmetric Dispersion Relations in QFTs
• Massive Galileon Positivity Bounds
• Causality constraints on corrections to Einstein gravity
• Celestial Amplitudes from UV to IR
• Positivity bounds on vector boson scattering at the LHC
• 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
• Cosmological parameter constraints for Horndeski scalar-tensor gravity
• Positivity Bounds and the Massless Spin-2 Pole
• Into the EFThedron and UV constraints from IR consistency
• The Speed of Gravity
• QED positivity bounds
• S-matrix Bootstrap for Effective Field Theories: Massless Pions
• Positivity in the sky
• Causality in Curved Spacetimes: The Speed of Light & Gravity
• Reverse Bootstrapping: IR lessons for UV physics
• Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds
• Natural Selection Rules: New Positivity Bounds for Massive Spinning Particles
• Carving out the Space of Open-String S-matrix
• 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
• Positivity Constraints on Interacting Spin-2 Fields
• Causal Effective Field Theories
• Elastic positivity vs extremal positivity bounds in SMEFT: a case study in transversal electroweak gauge-boson scatterings
• Graviton partial waves and causality in higher dimensions
• Gravitational Regge bounds
• Generalized positivity bounds on chiral perturbation theory
• Relative entropy in scattering and the S-matrix bootstrap
• Causality Constraints on Black Holes beyond GR
• Cornering Large-$N_c$ QCD with Positivity Bounds
• Positivity in electron-positron scattering: testing the axiomatic quantum field theory principles and probing the existence of UV states
• Triple crossing positivity bounds for multi-field theories
• Dynamical Constraints on RG Flows and Cosmology
• Positivity and Geometric Function Theory Constraints on Pion Scattering
• Positivity Bounds without Boosts
• Heavy Spinning Particles from Signs of Primordial Non-Gaussianities: Beyond the Positivity Bounds
• 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
• To Positivity and Beyond, where Higgs-Dilaton Inflation has never gone before
• QFT, EFT and GFT
• Dispersion Formulas in QFTs, CFTs, and Holography
• Positivity Constraints on Interacting Pseudo-Linear Spin-2 Fields
• Unambiguously Testing Positivity at Lepton Colliders
• A cautionary case of casual causality
• Shift symmetries, soft limits, and the double copy beyond leading order
• UV graviton scattering and positivity bounds from IR dispersion relations
• Generalized elastic positivity bounds on interacting massive spin-2 theories
• Sum Rules in the Standard Model Effective Field Theory from Helicity Amplitudes
• Positivity bounds from multiple vacua and their cosmological consequences
• Swampland Conditions for Higher Derivative Couplings from CFT
• Scalar Fields Near Compact Objects: Resummation versus UV Completion
• Positivity in the effective field theory of cosmological perturbations
• Spin-2 and the Weak Gravity Conjecture
• The shape of Scalar Gauss-Bonnet Gravity
• Cutting the Coon Amplitude
• 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
• The Color-Dual Fates of $F^3$, $R^3$, and $\mathcal{N}=4$ Supergravity
• Perturbative unitarity and NEC violation in genesis cosmology
• Horndeski stars
• Celestial insights into the S-matrix bootstrap
• The EFT Bootstrap at Finite $M_{PL}$
• Dispersive Sum Rules in AdS${}_2$
• Positivity Bounds on parity-violating scalar-tensor EFTs
• UV Constraints on Massive Spinning Particles: Lessons from the Gravitino
• Origin of Neutrino Masses on the Convex Cone of Positivity Bounds
• Matter Coupling in Massive Gravity
• Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes
• Positivity Bounds on Massive Vectors
• Positivity bounds in vector theories
• Non-Forward UV/IR Relations
• Black Hole Extremality in Nonlinear Electrodynamics: A Lesson for Weak Gravity and Festina Lente Bounds
• Positivity bounds on reconstructed Horndeski models
• Locality and Analyticity of the Crossing Symmetric Dispersion Relation
• Are $f(R,\mathrm{Matter})$ theories really relevant to cosmology?
• Gravitational Positivity for Phenomenologists: Dark Gauge Boson in the Swampland
• Gravitational Properties of the Proca Field
• Positivity Bounds in Scalar Effective Field Theories at One-loop Level
• Bispectrum Islands
• Superstring Amplitudes, Unitarity, and Hankel Determinants of Multiple Zeta Values
• Lectures in Quantum Gravity
• Positivity bounds at one-loop level: the Higgs sector
• Unitarity and unstable-particle scattering amplitudes
• Causality constraints on nonlinear supersymmetry
• A Celestial Route to AdS Bulk Locality
• Positivity bounds in scalar-QED EFT at one-loop level
• Theoretical priors in scalar-tensor cosmologies: Shift-symmetric Horndeski models
• IR side of bounds on Theories with Spontaneously Broken Lorentz Symmetry
• A Bit Rate Bound on Superluminal Communication
• A Note on the Analytic Structure of Celestial Amplitudes
• Primal S-matrix bootstrap with dispersion relations
• Quantifying EFT Uncertainties in LHC Searches
• Propagator positivity bounds for cosmological correlators
• Five-point partial waves, splitting constraints and hidden zeros
• The IR-Side of Positivity Bounds