SISSA 62/2011/EP Naturalness and GUT Scale Yukawa Coupling Ratios in the CMSSM

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−1 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 2σ constraint for (g − 2)µ and fine-tuning less than 30 yields an allowed range of yτ/yb = [1.31, 1.70], which points towards the alternative GUT prediction yτ/yb = 3/2. Relaxing the (g − 2)µ constraint to 5σ extends the possible region to [1.02,1.70], allowing for approximate b − τ Yukawa coupling unification