Practical naturalness and its implications for weak scale supersymmetry
Howard Baer, V. Barger, D. Martinez, Shadman Salam
Abstract
We revisit the various measures of practical naturalness for models of weak-scale supersymmetry (SUSY) including: 1. electroweak (EW) naturalness; 2. naturalness via sensitivity to high-scale (HS) parameters [Ellis-Enquist-Nanopoulos-Zwirner/Barbieri-Giudice (EENZ/BG)]; 3. sensitivity of Higgs soft terms due to high-scale radiative corrections; and 4. stringy naturalness (SN) from the landscape. The EW measure is most conservative and seems unavoidable. We debut a new numerical routine for calculating the EENZ/BG measure from any SUSY Les Houches Accord file. We implement a careful analysis and comparison of these measures in the mSUGRA/CMSSM and NUHMi model parameter spaces and via parameter-space scans. We demonstrate the reasoning behind why---and the extent to which---the EENZ/BG and HS measures overestimate the degree of fine-tuning. We find the overestimation can range up to a factor of over 1000. While EENZ/BG and HS have ambiguities when applied to models such as anomaly- and mirage-mediation, the EW measure has no such ambiguity and so we display the natural parameter space regions of these models. SN depends on the landscape distribution of soft terms, but is closely related to EW naturalness via the atomic principle.