Measures of fine tuning

TL;DR

The work tackles the problem of quantifying naturalness in SUSY theories by showing that the traditional Barbieri-Giudice sensitivity measure $c(M_Z^2;a)$ can misinterpret ordinary sensitivity as fine tuning. It introduces a probabilistic framework with a prior distribution $f(a)$ for high-energy parameters, derives a density $\rho(X)$ per unit observable, and defines a normalized fine-tuning measure $\gamma$ that equals $c/\bar{c}$, thereby distinguishing genuine tuning from typical sensitivity. Through two illustrative examples and a detailed MSSM analysis with radiative EWSB, the authors demonstrate that $\gamma$ is robust to the choice of prior and typically indicates less tuning than $c$, allowing a higher scale of SUSY breaking than older criteria would permit. The methodology provides a more faithful basis for setting upper bounds on superpartner masses and clarifies the implicit theoretical prejudices in naturalness assessments. Overall, the paper offers a principled, normalization-aware approach to naturalness with practical implications for SUSY phenomenology.

Abstract

Fine-tuning criteria are frequently used to place upper limits on the masses of superpartners in supersymmetric extensions of the standard model. However, commonly used prescriptions for quantifying naturalness have some important shortcomings. Motivated by this, we propose new criteria for quantifying fine tuning that can be used to place upper limits on superpartner masses with greater fidelity. In addition, our analysis attempts to make explicit the assumptions implicit in quantifications of naturalness. We apply our criteria to the minimal supersymmetric extension of the standard model, and we find that the scale of supersymmetry breaking can be larger than previous methods indicate.