Nonperturbative Bounds on Scattering of Massive Scalar Particles in $d\ge 2$

Abstract

We study two-to-two scattering amplitudes of a scalar particle of mass $m$. For simplicity, we assume the presence of ${\mathbb{Z}}_2$ symmetry and that the particle is ${\mathbb{Z}}_2$ odd. We consider two classes of amplitudes: the fully nonperturbative ones and effective field theory (EFT) ones with a cut-off scale $M$. Using the primal numerical method which allows us to impose full non-linear unitarity, we construct novel bounds on various observables in $2\le d\le 4$ space-time dimensions for both classes of amplitudes. We show that our bounds are much stronger than the ones obtained by using linearized unitarity or positivity only. We discuss applications of our bounds to constraining EFTs. Finally, we compare our bounds to the amplitude in ${\varphi }^4$ theory computed perturbatively at weak coupling, and find that they saturate the bounds.

arXiv comment38 pages + appendices, 23 figures

References in corpus (35)

• Causality, Analyticity and an IR Obstruction to UV Completion
• The S-matrix Bootstrap I: QFT in AdS
• Positive Moments for Scattering Amplitudes
• New positivity bounds from full crossing symmetry
• Sharp Boundaries for the Swampland
• Extremal Effective Field Theories
• Crossing Symmetric Dispersion Relations in QFTs
• The S-matrix Bootstrap II: Two Dimensional Amplitudes
• Unitarity violation at the Wilson-Fisher fixed point in 4-epsilon dimensions
• Where is String Theory?
• Bootstrapping QCD: the Lake, the Peninsula and the Kink
• S-matrix Bootstrap for Effective Field Theories: Massless Pions
• Rigorous Bounds on Light-by-Light Scattering
• Causality Constraints on Gravitational Effective Field Theories
• Flux Tube S-matrix Bootstrap
• Crossing Symmetric Spinning S-matrix Bootstrap: EFT bounds
• Natural Selection Rules: New Positivity Bounds for Massive Spinning Particles
• The S-matrix Bootstrap IV: Multiple Amplitudes
• Positivity Bounds on Dark Energy: When Matter Matters
• Bootstrapping Pions at Large $N$
• Bounding Violations of the Weak Gravity Conjecture
• Bootstrapping Massive Quantum Field Theories
• Adding flavour to the S-matrix bootstrap
• The O(N) S-matrix Monolith
• Relative entropy in scattering and the S-matrix bootstrap
• A note on the S-matrix bootstrap for the 2d O(N) bosonic model
• Dual S-matrix Bootstrap I: 2D Theory
• S-matrix bootstrap in 3+1 dimensions: regularization and dual convex problem
• Rigorous bounds on the Analytic $S$-matrix
• SUSY S-matrix Bootstrap and Friends
• S-matrix bootstrap for resonances
• Selection rules for the S-Matrix bootstrap
• Scattering from production in 2d
• The R-matrix bootstrap for the 2d O(N) bosonic model with a boundary
• Form Factors and Spectral Densities from Lightcone Conformal Truncation

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