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arXiv · 2406.03533

Precise interpretations of traditional fine-tuning measures

Andrew Fowlie·Gonzalo Herrera
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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.

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Andrew Fowlie, Gonzalo Herrera. 2024-06-05. Precise interpretations of traditional fine-tuning measures. https://doi.org/10.1103/physrevd.111.015020

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