Scattering from production in 2d

Abstract

In 1968, Atkinson proved the existence of functions that satisfy all S-matrix axioms in four spacetime dimensions. His proof is constructive and to our knowledge it is the only result of this type. Remarkably, the methods to construct such functions used in the proof were never implemented in practice. In the present paper, we test the applicability of those methods in the simpler setting of two-dimensional S-matrices. We solve the problem of reconstructing the scattering amplitude starting from a given particle production probability. We do this by implementing two numerical iterative schemes (fixed-point iteration and Newton's method), which, by iterating unitarity and dispersion relations, converge to solutions to the S-matrix axioms. We characterize the region in the amplitude-space in which our algorithms converge, and discover a fractal structure connected to the so-called CDD ambiguities which we call "CDD fractal". To our surprise, the question of convergence naturally connects to the recent study of the coupling maximization in the two-dimensional S-matrix bootstrap. The methods exposed here pave the way for applications to higher dimensions, and expose some of the potential challenges that will have to be overcome.

34 pages, 12 figures

References in corpus (10)

• The EFT-Hedron
• Positive Moments for Scattering Amplitudes
• New positivity bounds from full crossing symmetry
• Extremal Effective Field Theories
• Crossing Symmetric Dispersion Relations in QFTs
• S-matrix Bootstrap for Effective Field Theories: Massless Pions
• High-energy gravitational scattering and black hole resonances
• Dual S-matrix Bootstrap I: 2D Theory
• Scattering from production in 2d
• Towards the saturation of the Froissart bound

Cited by in corpus (10)

• Scattering from production in 2d
• Constraints on Sequential Discontinuities from the Geometry of On-shell Spaces
• Nonperturbative Bounds on Scattering of Massive Scalar Particles in $d\ge 2$
• Swampland Conditions for Higher Derivative Couplings from CFT
• Bootstrapping the $a$-anomaly in $4d$ QFTs
• Bounds on Crossing Symmetry
• Bounds on photon scattering
• Real-Time Scattering in Ising Field Theory using Matrix Product States
• Bootstrapping 2d ${\varphi }^4$ Theory with Hamiltonian Truncation Data
• From conformal correlators to analytic S-matrices: CFT${}_1$/QFT${}_2$