Rigorous bounds on the Analytic $S$-matrix

Abstract

We consider a dual $S$-matrix Bootstrap approach in $d\ge 3$ space-time dimensions which relies solely on the rigorously proven analyticity, crossing, and unitarity properties of the scattering amplitudes. As a proof of principle, we provide rigorous upper and lower numerical bounds on the quartic coupling for the scattering of identical scalar particles in four dimensions.

5 + 10 pages, 3 + 6 figures, major revision in the appendices, improved numerics, typos corrected

References in corpus (13)

• The EFT-Hedron
• Positive Moments for Scattering Amplitudes
• New positivity bounds from full crossing symmetry
• Sharp Boundaries for the Swampland
• Extremal Effective Field Theories
• Gravitational Effective Field Theory Islands, Low-Spin Dominance, and the Four-Graviton Amplitude
• Crossing Symmetric Dispersion Relations in QFTs
• Where is String Theory?
• S-matrix Bootstrap for Effective Field Theories: Massless Pions
• Crossing Symmetric Dispersion Relations for Mellin Amplitudes
• S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem
• Selection rules for the S-Matrix bootstrap
• The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary

Cited by in corpus (16)

• Selected Topics in Analytic Conformal Bootstrap: A Guided Journey
• Landau Discriminants
• Nonperturbative Bounds on Scattering of Massive Scalar Particles in $d\ge 2$
• Bootstrapping the $a$-anomaly in $4d$ QFTs
• Bounds on photon scattering
• Locality and Analyticity of the Crossing Symmetric Dispersion Relation
• Positivity Bounds in Scalar Effective Field Theories at One-loop Level
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• Exploring Inelasticity in the S-Matrix Bootstrap
• Bispectrum Islands
• A Celestial Route to AdS Bulk Locality
• From conformal correlators to analytic S-matrices: CFT${}_1$/QFT${}_2$
• Strings from Almost Nothing
• Positivity bounds in scalar-QED EFT at one-loop level
• Primal S-matrix bootstrap with dispersion relations
• Probing multi-particle unitarity with the Landau equations