# Two Notions of Naturalness

## TL;DR

This paper distinguishes two different notions of naturalness in BSM physics—one based on scale autonomy and the other on statistical likelihood—and explores their conceptual and methodological implications.

## Contribution

It clarifies the conceptual distinction between two notions of naturalness and discusses their different motivations and implications in BSM model building.

## Key findings

- The autonomy of scales notion justifies certain BSM model constructions.
- The statistical likelihood notion offers a different perspective on parameter values.
- Recognizing the distinction influences methodological approaches in BSM physics.

## Abstract

My aim in this paper is twofold: (i) to distinguish two notions of naturalness employed in BSM physics and (ii) to argue that recognizing this distinction has methodological consequences. One notion of naturalness is an "autonomy of scales" requirement: it prohibits sensitive dependence of an effective field theory's low-energy observables on precise specification of the theory's description of cutoff-scale physics. I will argue that considerations from the general structure of effective field theory provide justification for the role this notion of naturalness has played in BSM model construction. A second, distinct notion construes naturalness as a statistical principle requiring that the values of the parameters in an effective field theory be "likely" given some appropriately chosen measure on some appropriately circumscribed space of models. I argue that these two notions are historically and conceptually related but are motivated by distinct theoretical considerations and admit of distinct kinds of solution.