Loop counting matters in SMEFT

TL;DR

This paper emphasizes the importance of counting both canonical dimensions and loop orders in SMEFT to establish a consistent hierarchy of operators, improving the accuracy and focus of high-energy physics analyses.

Contribution

It introduces the necessity of loop order counting alongside canonical dimensions for proper SMEFT power counting, which was previously overlooked.

Findings

Loop counting is essential for consistent SMEFT power counting.

Considering both dimensions and loops refines the hierarchy of operators.

This approach helps identify dominant effects in high-energy processes.

Abstract

We show that, in addition to the counting of canonical dimensions, a counting of loop orders is necessary to fully specify the power counting of Standard Model Effective Field Theory (SMEFT). Using concrete examples, we demonstrate that considering the canonical dimensions of operators alone may lead to inconsistent results. The counting of both, canonical dimensions and loop orders, establishes a clear hierarchy of the terms in SMEFT. In practice, this serves to identify, and focus on, the potentially dominating effects in any given high-energy process in a meaningful way. Additionally, this will lead to a consistent limitation of free parameters in SMEFT applications.