Precise interpretations of traditional fine-tuning measures

TL;DR

This paper provides two rigorous interpretations of traditional electroweak fine-tuning measures, framing them as a statistical plausibility change and an information-theoretic measure, enhancing understanding and application in particle physics.

Contribution

It introduces two precise interpretations of fine-tuning measures, connecting them to statistical and information theory, and applies these to weak scale supersymmetry.

Findings

New interpretations clarify the meaning of fine-tuning measures.

Mathematical derivations underpin the interpretations.

Examples from supersymmetry illustrate the concepts.

Abstract

We uncover two precise interpretations of traditional electroweak fine-tuning (FT) measures that were historically missed. (i) a statistical interpretation: the traditional FT measure shows the change in plausibility of a model in which a parameter was exchanged for the $Z$ boson mass relative to an untuned model in light of the $Z$ boson mass measurement. (ii) an information-theoretic interpretation: the traditional FT measure shows the exponential of the extra information, measured in nats, relative to an untuned model that you must supply about a parameter in order to fit the $Z$ mass. We derive the mathematical results underlying these interpretations, and explain them using examples from weak scale supersymmetry. These new interpretations allow us to rigorously define FT in particle physics and beyond; shed fresh light on the status of extensions to the Standard Model; and lastly, allow us to precisely reinterpret historical and recent studies using traditional FT measures.