Precise interpretations of traditional fine-tuning measures
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866915118807252992 |
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| author | Fowlie, Andrew Herrera, Gonzalo |
| author_facet | Fowlie, Andrew Herrera, Gonzalo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_03533 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Precise interpretations of traditional fine-tuning measures Fowlie, Andrew Herrera, Gonzalo High Energy Physics - Phenomenology High Energy Physics - Theory Data Analysis, Statistics and Probability 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. |
| title | Precise interpretations of traditional fine-tuning measures |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory Data Analysis, Statistics and Probability |
| url | https://arxiv.org/abs/2406.03533 |