Softness and amplitudes’ positivity for spinning particles

Brando Bellazzini (1)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681

We derive positivity bounds for scattering amplitudes of particles with arbitrary spin using unitarity, analyticity and crossing symmetry. The bounds imply the positivity of certain low-energy coefficients of the effective action that controls the dynamics of the light degrees of freedom. We show that low-energy amplitudes strictly softer than O(p$^{4}$) do not admit unitary ultraviolet completions unless the theory is free. This enforces a bound on the energy growth of scattering amplitudes in the region of validity of the effective theory. We discuss explicit examples including the Goldstino from spontaneous supersymmetry breaking, and the theory of a spin-1/2 fermion with a shift symmetry.

Mots clés: Effective field theories; Scattering Amplitudes; Spontaneous Symmetry Breaking; Beyond Standard Model; symmetry: crossing; particle: spin; supersymmetry: spontaneous symmetry breaking; scattering amplitude; unitarity; analytic properties; effective action; Goldstino; energy: low

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique des Hautes Energies - Phénoménologie [hep-ph]

Brando Bellazzini. Softness and amplitudes’ positivity for spinning particles. Journal of High Energy Physics, 2017, 02, pp.034. ⟨10.1007/JHEP02(2017)034⟩. ⟨hal-01554986⟩