Precise interpretations of traditional fine-tuning measures

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.

10 pages, 4 figures, matches version accepted for publication in Phys. Rev. D

References in corpus (42)

• String Axiverse
• SOFTSUSY: a program for calculating supersymmetric spectra
• The NANOGrav 15-year Data Set: Search for Signals from New Physics
• Multi-TeV Scalars are Natural in Minimal Supergravity
• Focus Points and Naturalness in Supersymmetry
• Neutralino Dark Matter in Focus Point Supersymmetry
• Naturalness and the Status of Supersymmetry
• Natural Dark Matter from an Unnatural Higgs Boson and New Colored Particles at the TeV Scale
• Focus Point Supersymmetry Redux
• SUSY models under siege: LHC constraints and electroweak fine-tuning
• Naturalness Priors and Fits to the Constrained Minimal Supersymmetric Standard Model
• Post-LHC7 fine-tuning in the mSUGRA/CMSSM model with a 125 GeV Higgs boson
• The Last Vestiges of Naturalness
• Natural Priors, CMSSM Fits and LHC Weather Forecasts
• Implications for New Physics from Fine-Tuning Arguments: I. Application to SUSY and Seesaw Cases
• Bayesian approach and Naturalness in MSSM analyses for the LHC
• Upper bounds on sparticle masses from naturalness or how to disprove weak scale supersymmetry
• Multiple universes, cosmic coincidences, and other dark matters
• The Degree of Fine-Tuning in our Universe -- and Others
• Anthropic Reasons for Non-Zero Flatness and Lambda
• Quantified naturalness from Bayesian statistics
• Should we still believe in constrained supersymmetry?
• Screams for Explanation: Finetuning and Naturalness in the Foundations of Physics
• A New Measure of Fine Tuning
• Bayesian evidence for the tensor-to-scalar ratio $r$ and neutrino masses $m_{\nu }$: Effects of uniform vs logarithmic priors
• The fine-tuning price of the early LHC
• CMSSM, naturalness and the "fine-tuning price" of the Very Large Hadron Collider
• Bayes factor functions for reporting outcomes of hypothesis tests
• Naturalness of the relaxion mechanism
• The current status of fine-tuning in supersymmetry
• Is the CNMSSM more credible than the CMSSM?
• Bayesian analysis and naturalness of (Next-to-)Minimal Supersymmetric Models
• Non-parametric uncertainties in the dark matter velocity distribution
• Cosmologically safe QCD axion without fine-tuning
• Dark Matter and Naturalness
• Halo-independence with quantified maximum entropy at DAMA/LIBRA
• Assessing Bayes factor surfaces using interactive visualization and computer surrogate modeling
• The Bayes factor surface for searches for new physics
• Naturalness made easy: two-loop naturalness bounds on minimal SM extensions
• Bayesian naturalness, simplicity, and testability applied to the $B-L$ MSSM GUT
• Evidential Calibration of Confidence Intervals
• Finetuned Cancellations and Improbable Theories

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