Depicting the Landscape of Generic Effective Field Theories

TL;DR

This paper introduces a comprehensive framework for mapping the space of Lorentz invariant effective field theories, enabling systematic construction and analysis of operators with various bases to understand their properties and origins.

Contribution

It presents a novel, systematic method to construct and analyze different operator bases within the landscape of effective field theories, linking them to their UV origins.

Findings

Systematic construction of operator bases using amplitude-operator correspondence

Transformation matrices encode model-independent properties of operators

Application to dimension 9 operators relevant for neutron-antineutron oscillation

Abstract

We describe a general framework to depict the space of Lorentz invariant effective field theories, which we call the landscape, given any kind of gauge symmetry and field content. Various operator bases in the landscape can be systematically constructed, with the help of amplitude-operator correspondence, to emphasize different aspects: operator independence (y-basis), flavor relation (p-basis) and conserved quantum number (j-basis). The transformation matrices among the bases encode model-independent properties of the operators, such as implications on their UV origin. We illustrate this salient feature in examining the dimension 9 operators relevant for neutron-antineutron oscillation.