Naturalness and GUT scale Yukawa coupling ratios in the constrained MSSM

Abstract

We analyze the fine-tuning in the constrained minimal supersymmetric standard model in the light of the present and expected ATLAS and CMS searches for supersymmetry. Even with $10\text{ }\text{ }{\mathrm{fb}}^{\ensuremath{-}1}$ of data and no discovery of supersymmetry valid regions might remain with fine-tuning less than 20. Moreover we investigate the fine-tuning price of grand unification scale Yukawa coupling relations. Considering a $2\ensuremath{\sigma}$ constraint for $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ and fine-tuning less than 30 yields an allowed range of ${y}_{\ensuremath{\tau}}/{y}_{b}=[1.31,1.70]$, which points towards the alternative grand unification prediction ${y}_{\ensuremath{\tau}}/{y}_{b}=3/2$. Relaxing the $(g\ensuremath{-}2{)}_{\ensuremath{\mu}}$ constraint to $5\ensuremath{\sigma}$ extends the possible region to [1.02, 1.70], allowing for approximate $b\ensuremath{-}\ensuremath{\tau}$ Yukawa coupling unification.