Naturalness and GUT scale Yukawa coupling ratios in the constrained MSSM

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 fb(-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 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 grand unification 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.