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

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