Quantified naturalness from Bayesian statistics

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.

28 pages, 1 figure, v3: to be published in PRD

References in corpus (13)

• Observation of a new particle in the search for the Standard Model Higgs boson with the ATLAS detector at the LHC
• Observation of a new boson at a mass of 125 GeV with the CMS experiment at the LHC
• Five-Year Wilkinson Microwave Anisotropy Probe (WMAP) Observations: Cosmological Interpretation
• Bayes in the sky: Bayesian inference and model selection in cosmology
• The formal definition of reference priors
• TASI Lectures on the Cosmological Constant
• The Cosmological Constant and the String Landscape
• Natural Priors, CMSSM Fits and LHC Weather Forecasts
• Should we still believe in constrained supersymmetry?
• A New Measure of Fine Tuning
• The fine-tuning price of the early LHC
• The Fine-Tuning Price of Neutralino Dark Matter in Models with Non-Universal Higgs Masses
• Determination of Dark Matter Properties at High-Energy Colliders

Cited by in corpus (34)

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• How conventional measures overestimate electroweak fine-tuning in supersymmetric theory
• Current and future constraints on Higgs couplings in the nonlinear Effective Theory
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• Should we still believe in constrained supersymmetry?
• The fine-tuning cost of the likelihood in SUSY models
• Bayesian naturalness of the CMSSM and CNMSSM
• CMSSM, naturalness and the "fine-tuning price" of the Very Large Hadron Collider
• Supergravity gauge theories strike back: There is no crisis for SUSY but a new collider may be required for discovery
• Fine Tuning in the Constrained Exceptional Supersymmetric Standard Model
• Naturalness of the relaxion mechanism
• The current status of fine-tuning in supersymmetry
• Naturalness of MSSM dark matter
• Naturalness, b to s gamma, and SUSY Heavy Higgses
• Z' mass limits and the naturalness of supersymmetry
• Is the CNMSSM more credible than the CMSSM?
• Fixing the EW scale in supersymmetric models after the Higgs discovery
• Bayesian analysis and naturalness of (Next-to-)Minimal Supersymmetric Models
• On new physics searches with multidimensional differential shapes
• Naturalness of scale-invariant NMSSMs with and without extra matter
• Naturalness, Extra-Empirical Theory Assessments, and the Implications of Skepticism
• Gauging Fine-Tuning
• Bayesian Model comparison of Higgs couplings
• $R$-parity Violating Decays of Bino Neutralino LSPs at the LHC
• Bayesian naturalness, simplicity, and testability applied to the $B-L$ MSSM GUT
• Low-mass neutralino dark matter in supergravity scenarios: phenomenology and naturalness
• Finetuned Cancellations and Improbable Theories
• SUSY naturalness without prejudice
• The Hierarchy Problem: From the Fundamentals to the Frontiers
• Probing the scale of New Physics at the LHC: the example of Higgs data
• Precise interpretations of traditional fine-tuning measures
• Lectures on Naturalness, String Landscape and Multiverse
• Toy models for hierarchy studies
• Higgs, supersymmetry and dark matter after Run I of the LHC