Naturalness and GUT Scale Yukawa Coupling Ratios in the CMSSM

Abstract

We analyse the fine-tuning in the Constrained Minimal Supersymmetric Standard Model (CMSSM) in the light of the present and expected ATLAS and CMS SUSY searches. Even with 10/fb of data and no discovery of SUSY valid regions might remain with fine-tuning less than 20. Moreover we investigate the fine-tuning price of GUT scale Yukawa coupling relations. Considering a 2$\sigma$ constraint for $(g-2{)}_{\mu }$ and fine-tuning less than 30 yields an allowed range of $y_{\tau }/y_b=[1.31,1.70]$, which points towards the alternative GUT prediction $y_{\tau }/y_b=3/2$. Relaxing the $(g-2{)}_{\mu }$ constraint to 5$\sigma$ extends the possible region to [1.02,1.70], allowing for approximate $b-\tau$ Yukawa coupling unification.

Comments: 13 pages, 3 figures; version published in PRD