Abstract
We review unitarity and crossing constraints on scattering amplitudes for particles with spin in four dimensional quantum field theories. As an application we study two to two scattering of neutral spin 1/2 fermions in detail. Assuming Mandelstam analyticity of its scattering amplitude, we use the numerical S-matrix bootstrap method to estimate various non-perturbative bounds on quartic and cubic (Yukawa) couplings.
Highlights
The space of Quantum Field Theories (QFT) is vast and uncharted
We review unitarity and crossing constraints on scattering amplitudes for particles with spin in four dimensional quantum field theories
We develop the formalism to study 2 to 2 scattering amplitudes of particles with spin in four dimensional QFTs
Summary
The space of Quantum Field Theories (QFT) is vast and uncharted. The numerical S-matrix Bootstrap is a nonperturbative approach to explore this space [1,2,3,4,5,6,7,8,9,10,11,12,13,14]. We develop the formalism to study 2 to 2 scattering amplitudes of particles with spin in four dimensional QFTs. The main idea of the numerical S-matrix Bootstrap [2, 3] is to write a generic analytic and Lorentz invariant ansatz for the scattering amplitude and impose the constraints from crossing symmetry and unitarity. In the case of generic spin, (1.4) remains valid for center of mass amplitudes, if the Legendre polynomial is replaced by the small Wigner d-matrix given in (2.9) in full generality We include several appendices that fill in the details of the presentation in the main text
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