Positive moments for scattering amplitudes

We find the complete set of conditions satisfied by the forward 2 -> 2 scattering amplitude in unitary and causal theories. These are based on an infinite set of energy dependent quantities (the arcs) which are dispersively expressed as moments of a positive measure defined at (arbitrarily) higher energies. We identify optimal finite subsets of constraints, suitable to bound effective field theories (EFTs), at any finite order in the energy expansion. At tree level arcs are in a one to one correspondence with Wilson coefficients. We establish under which conditions this approximation applies, identifying seemingly viable EFTs where it never does. In all cases, we discuss the range of validity in both energy and couplings, where the latter has to satisfy two-sided bounds. We also extend our results to the case of small but finite t. A consequence of our study is that EFTs in which the scattering amplitude in some regime grows in energy faster than E-6 cannot be UV completed.

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Riccardo Rattazzi, Francesco Riva, Marc Riembau Saperas
2021
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Abstract

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https://infoscience.epfl.ch/record/288568?ln=en

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Related concepts (4)

Effective field theory

In physics, an effective field theory is a type of approximation, or effective theory, for an underlying physical theory, such as a quantum field theory or a statistical mechanics model. An effective field theory includes the appropriate degrees of freedom to describe physical phenomena occurring at a chosen length scale or energy scale, while ignoring substructure and degrees of freedom at shorter distances (or, equivalently, at higher energies).

Energy

In physics, energy () is the quantitative property that is transferred to a body or to a physical system, recognizable in the performance of work and in the form of heat and light. Energy is a conserved quantity—the law of conservation of energy states that energy can be converted in form, but not created or destroyed. The unit of measurement for energy in the International System of Units (SI) is the joule (J).

Scattering amplitude

In quantum physics, the scattering amplitude is the probability amplitude of the outgoing spherical wave relative to the incoming plane wave in a stationary-state scattering process. The plane wave is described by the wavefunction where is the position vector; ; is the incoming plane wave with the wavenumber k along the z axis; is the outgoing spherical wave; θ is the scattering angle; and is the scattering amplitude. The dimension of the scattering amplitude is length.