One-loop analysis of the electroweak breaking in supersymmetric models and the fine-tuning problem

Abstract We examine the electroweak breaking mechanism in the minimal supersymmetric standard model (MSSM) using the complete one-loop effective potential V1. First, we study what is the region of the whole MSSM parameter space (i.e. M 1 2 , m0, μ, …) that leads to a successful SU(2) × U(1) breaking with an acceptable top-quark mass. In doing this it is observed that all the one-loop corrections to V1 (even the apparently small ones) must be taken into account in order to obtain reliable results. We find that the allowed region of parameters is considerably enhanced with respect to former “improved” tree-level results. Next, we study the fine-tuning problem associated with the high sensitivity of Mz to ht (the top Yukawa coupling). Again, we find that this fine-tuning, once the one-loop effects are considered, is appreciably smaller than in previous tree-level calculations. Finally, we explore the ambiguities and limitations of the ordinary criterion to estimate the degree of fine-tuning. As a result of all this, the upper bounds on the MSSM parameters, and hence on the supersymmetric masses, are substantially raised, thus increasing the consistency between supersymmetry and observation.