Quantified naturalness from Bayesian statistics

TL;DR

This paper introduces a Bayesian statistical framework for quantifying naturalness in physics, clarifying conceptual issues and providing a general sensitivity measure applicable to complex models, with practical application to supersymmetry.

Contribution

It formulates a Bayesian approach to naturalness, unifying and extending existing sensitivity measures, and applies it to supersymmetric models to analyze fine-tuning.

Findings

Unambiguous interpretation of naturalness via Jeffreys' scale.

General sensitivity formula for multiple observables.

Application to gauge hierarchy and dark matter in supersymmetry.

Abstract

We present a formulation of naturalness made in the framework of Bayesian statistics, which unravels the conceptual problems related to previous approaches. Among other things, the relative interpretation of the measure of naturalness turns out to be unambiguously established by Jeffreys' scale. Also, the usual sensitivity formulation (so-called Barbieri-Giudice measure) appears to be embedded in our formulation under an extended form. We derive the general sensitivity formula applicable to an arbitrary number of observables. Several consequences and developments are further discussed. As a final illustration, we work out the map of combined fine-tuning associated to the gauge hierarchy problem and neutralino dark matter in a classic supersymmetric model.