Classifying Standard Model Extensions Effectively with Precision Observables

TL;DR

This paper demonstrates that analyzing which effective operators are induced by specific Standard Model extensions enables more precise identification of the underlying high-scale theories using low-energy observables.

Contribution

It introduces a method to distinguish Standard Model extensions by their characteristic effective operators and applies it to 15 scalar field models, improving model identification.

Findings

Most models can be phenomenologically distinguished based on their operator signatures.

Few models remain indistinguishable after analysis.

The approach helps determine the effective field theory truncation level.

Abstract

Effective theories are well established theoretical frameworks to describe the effect of energetically widely separated UV models on observables at lower energy scales. Due to the complexity of the effective theory when taking all the Standard Model symmetries and degrees of freedoms into account, tensioning the entire system in a completely agnostic way against experimental measurements results in constraints on the Wilson Coefficients of the effective operators that either bears little information or challenge intrinsic assumptions imposed on the effective field theory framework. In general, a specific high-scale extension of the Standard Model only induces a subset of all possible operators. Thus, by investigating which operators are induced by different classes of the Standard Model extensions and comparing to which precision observables they contribute, we show that it is possible to obtain an improved understanding of which UV model is realised in nature. We consider 15 UV models which are single scalar field extensions of the Standard Model and compute their dimension-6 operators after integrating out the heavy scalars up to 1-loop level. Only very few of these scenarios remain indistinguishable, while most of the models can be phenomenologically separated from one another. Most of these scenarios possess their own characteristic operator signature. Following the approach outlined here, a comparative analysis of a wide range of models will allow to assess at what level the effective field theory series can be truncated and which experimental measurements to prioritise.