Extremal Effective Field Theories

TL;DR

This paper investigates the constraints on effective field theory coefficients imposed by causality and unitarity, using scattering amplitudes and semi-definite programming to delineate the allowed parameter space.

Contribution

It introduces a method to bound EFT coefficients from both below and above, demonstrating that causality enforces dimensional analysis scaling and identifying extremal amplitudes that define the boundaries.

Findings

EFT coefficients are bounded both below and above by causality.

Dimensional analysis scaling emerges as a consequence of causality.

Constructed extremal amplitudes that span a large portion of allowed coefficient space.

Abstract

Effective field theories (EFT) parameterize the long-distance effects of short-distance dynamics whose details may or may not be known. It is known that EFT coefficients must obey certain positivity constraints if causality and unitarity are satisfied at all scales. We explore those constraints from the perspective of 2 to 2 scattering amplitudes of a light real scalar field, using semi-definite programming to carve out the space of allowed EFT coefficients for a given mass threshold M. We point out that all EFT parameters are bounded both below and above, effectively showing that dimensional analysis scaling is a consequence of causality. This includes the coefficients of four- and six-derivative interactions. We present simple extremal amplitudes which realize, or "rule in", kinks in coefficient space and whose convex hull span a large fraction of the allowed space.