Positive Moments for Scattering Amplitudes

Abstract

We find the complete set of conditions satisfied by the forward $2\to 2$ scattering amplitude in unitarity and causal theories. These are based on an infinite set of energy dependent quantities -- the arcs -- which are dispersively expressed as moments of a positive measure defined at (arbitrarily) higher energies. We identify optimal finite subsets of constraints, suitable to bound Effective Field Theories (EFTs), at any finite order in the energy expansion. At tree-level arcs are in one-to-one correspondence with Wilson coefficients. We establish under which conditions this approximation applies, identifying seemingly viable EFTs where it never does. In all cases, we discuss the range of validity in both couplings and energy. We also extend our results to the case of small but finite~$t$. A consequence of our study is that EFTs in which the scattering amplitude in some regime grows in energy faster than $E^6$ cannot be UV-completed.

15 pages, v2 matches published version

References in corpus (9)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Galileons as Wess-Zumino Terms
• Convex Geometry Perspective to the (Standard Model) Effective Field Theory Space
• Symmetries, Sum Rules and Constraints on Effective Field Theories
• Falsifying Models of New Physics Via WW Scattering
• Carving out the Space of Open-String S-matrix
• The Other Fermion Compositeness
• Goldstones with Extended Shift Symmetries
• Causal vs. Analytic constraints on anomalous quartic gauge couplings

Cited by in corpus (67)

• Sharp Boundaries for the Swampland
• Analyticity and Unitarity for Cosmological Correlators
• Cosmological Cutting Rules
• Crossing Symmetric Dispersion Relations in QFTs
• Causality constraints on corrections to Einstein gravity
• From Locality and Unitarity to Cosmological Correlators
• Where is String Theory?
• AdS Bulk Locality from Sharp CFT Bounds
• 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
• Natural Selection Rules: New Positivity Bounds for Massive Spinning Particles
• Landau Discriminants
• Towards the renormalisation of the Standard Model effective field theory to dimension eight: Bosonic interactions I
• Positivity Bounds on Dark Energy: When Matter Matters
• Positivity in Multi-Field EFTs
• Massless Positivity in Graviton Exchange
• Bootstrapping Pions at Large $N$
• Positivity bounds in the Standard Model effective field theory beyond tree level
• Bounding Violations of the Weak Gravity Conjecture
• Causal Effective Field Theories
• Gravitational Regge bounds
• Causality Constraints on Black Holes beyond GR
• Cornering Large-$N_c$ QCD with Positivity Bounds
• Classical vs Quantum Eikonal Scattering and its Causal Structure
• Triple crossing positivity bounds for multi-field theories
• Positivity bounds on Minimal Flavor Violation
• Positivity and Geometric Function Theory Constraints on Pion Scattering
• Positivity Bounds without Boosts
• Nonsingular cosmological models with strong gravity in the past
• 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
• Rigorous bounds on the Analytic $S$-matrix
• QFT, EFT and GFT
• Dispersion Formulas in QFTs, CFTs, and Holography
• On the unitarity and low energy expansion of the Coon amplitude
• UV graviton scattering and positivity bounds from IR dispersion relations
• Building blocks of the flavourful SMEFT RG
• Bulk locality from the celestial amplitude
• Positivity bounds from multiple vacua and their cosmological consequences
• Scattering from production in 2d
• 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
• Bounds on Crossing Symmetry
• The shape of Scalar Gauss-Bonnet Gravity
• Bounds on photon scattering
• Finite energy sum rules for gravitational Regge amplitudes
• Monolepton production in SMEFT to $\mathcal{O}(1/{\Lambda }^4)$ and beyond
• Spinning Sum Rules for the Dimension-Six SMEFT
• RG of GR from On-shell Amplitudes
• The Color-Dual Fates of $F^3$, $R^3$, and $\mathcal{N}=4$ Supergravity
• Dispersive Sum Rules in AdS${}_2$
• Renormalisation of SMEFT bosonic interactions up to dimension eight by LNV operators
• NNLO Positivity Bounds on Chiral Perturbation Theory for a General Number of Flavours
• Origin of Neutrino Masses on the Convex Cone of Positivity Bounds
• Effective Field Theory Islands from Perturbative and Nonperturbative Four-Graviton Amplitudes
• Positivity bounds in vector theories
• Locality and Analyticity of the Crossing Symmetric Dispersion Relation
• Positivity bounds at one-loop level: the Higgs sector
• Causality constraints on nonlinear supersymmetry
• Unitarity and unstable-particle scattering amplitudes
• The IR-Side of Positivity Bounds