On the non-minimal character of the SMEFT

TL;DR

This paper investigates the minimal possible operator content in the SMEFT when integrating out new physics, showing that generating only one dimension-six operator at tree level is highly restrictive and typically leads to multiple operators.

Contribution

It demonstrates that achieving a single dimension-six operator from a new physics sector requires unrealistic conditions, and dynamical scales generally induce multiple operators in the SMEFT.

Findings

Single operator generation requires restrictive UV conditions.

Dynamical scales induce multiple operators.

Global SMEFT analyses should consider multiple operators.

Abstract

When integrating out unknown new physics sectors, what is the minimal character of the Standard Model Effective Field Theory (SMEFT) that can result? In this paper we focus on a particular aspect of this question: "How can one obtain only one dimension six operator in the SMEFT from a consistent tree level matching onto an unknown new physics sector?" We show why this requires conditions on the ultraviolet field content that do not indicate a stand alone ultraviolet complete scenario. Further, we demonstrate how a dynamical origin of the ultraviolet scales assumed to exist in order to generate the masses of the heavy states integrated out generically induces more operators. Therefore, our analysis indicates that the infrared limit captured from a new sector in consistent matchings induces multiple operators in the SMEFT quite generically. Global data analyses in the SMEFT can and should accommodate this fact.