Loops and trees in generic EFTs

TL;DR

This paper analyzes the structure and behavior of operators in a generic 4d EFT of massless particles, focusing on tree and one-loop amplitudes, operator classifications, and the effects of non-renormalization theorems up to dimension 8.

Contribution

It extends the classification of operators and their loop contributions in EFTs up to dimension 8, revealing new helicity selection rules and vanishing contributions at one-loop.

Findings

Many dimension 6 contributions to helicity amplitudes vanish at one-loop.

Non-renormalization theorems influence operator contributions at dimension 8.

Helicity selection rules extend beyond one loop in non-supersymmetric EFTs.

Abstract

We consider aspects of tree and one-loop behavior in a generic 4d EFT of massless scalars, fermions, and vectors, with a particular eye to the high-energy limit of the Standard Model EFT at operator dimensions 6 and 8. First, we classify the possible Lorentz structures of operators and the subset of these that can arise at tree-level in a weakly coupled UV completion, extending the tree/loop classification through dimension 8 using functional methods. Second, we investigate how operators contribute to tree and one-loop helicity amplitudes, exploring the impact of non-renormalization theorems through dimension 8. We further observe that many dimension 6 contributions to helicity amplitudes, including rational parts, vanish exactly at one-loop level. This suggests the impact of helicity selection rules extends beyond one loop in non-supersymmetric EFTs.