Full Unitarity and the Moments of Scattering Amplitudes

TL;DR

This paper investigates how full unitarity constrains the moments of forward scattering amplitudes, introducing semiarcs and revealing that unitarity forbids large hierarchies between moments, with implications for EFT bounds.

Contribution

It introduces semiarcs as calculable quantities related to UV amplitudes and analyzes the impact of full unitarity on moment hierarchies and EFT bounds.

Findings

Large hierarchies between moments are forbidden by unitarity.

Full unitarity bounds can dominate convexity bounds in certain EFT regimes.

Semiarcs provide a new dispersive tool for analyzing scattering amplitudes.

Abstract

We study the impact of full unitarity on the moment structure of forward scattering amplitudes. We introduce the semiarcs, calculable quantities in the EFT dispersively related to both real and imaginary parts of the UV amplitude for a fixed number of subtractions. It is observed that large hierarchies between consecutive moments are forbidden by unitarity. Bounds from full unitarity compete with the ones stemming from convexity, and become more important in EFTs where the loop expansion is more important than the derivative expansion.