Haggling over the fine-tuning price of LEP Original Research Article

We amplify previous discussions of the fine-tuning price to be paid by supersymmetric models in the light of LEP data. The whole range of tan β is discussed, including large values. In the minimal supergravity model with universal gaugino and scalar masses, a small fine-tuning price is possible only for intermediate values of tan β and for a small range of superpartner masses. Moreover, the fine-tuning price in this region is significantly higher if we require β-τ Yukawacoupling unification. We interpret the significant increase after LEP of the fine-tuning price in the minimal supergravity model as a message for theory and not for the experiment. For possible choices of low-energy parameters in the MSSM consistent with present experimental constraints and, optionally, with some other theoretical assumptions such as ifb-τ Yukawa-coupling unification, a measure of the amount of fine tuning becomes an interesting criterion for the naturalness of various theoretical models for mass terms in the MSSM Lagrangian. In particular, we emphasize that the fine-tuning price will depend on the actual solution to the μ problem. We illustrate the relevance of this fact by considering a simple ansatz of linear dependence of μ on M12 or A0, showing that big price reductions are obtained in such cases. Significant price reductions are also obtained for large tan β if non-universal soft Higgs mass parameters are allowed. We also study input relations between MSSM parameters suggested in some interpretations of string theory: the price may depend significantly on these inputs, potentially providing guidance for building string models. However, in the available models the fine-tuning price may not be reduced significantly.