One-Loop Analysis of the Electroweak Breaking in Supersymmetric Models and the Fine-Tuning Problems

TL;DR

The paper investigates electroweak symmetry breaking in the MSSM using the full one-loop effective potential $V_1$, rather than the renormalization-improved tree-level potential. It shows that including all one-loop corrections expands the viable MSSM parameter space and reduces the sensitivity of $M_Z$ to the top Yukawa coupling $h_t$, thereby softening fine-tuning. The study also examines ambiguities in the standard fine-tuning criterion and recommends a conservative relaxation of the bound, which raises upper limits on soft SUSY-breaking parameters and sparticle masses. Overall, the results align SUSY with observations more readily and suggest a heavier but still accessible superpartner spectrum for future colliders.

Abstract

We examine the electroweak breaking mechanism in the minimal supersymmetric standard model (MSSM) using the {\em complete} one-loop effective potential $V_1$. First, we study what is the region of the whole MSSM parameter space (i.e. $M_{1/2},m_o,μ,...$) that leads to a succesful $SU(2)\times U(1)$ breaking with an acceptable top quark mass. In doing this it is observed that all the one-loop corrections to $V_1$ (even the apparently small ones) must be taken into account in order to get 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 $M_Z$ to $h_t$ (the top Yukawa coupling). Again, we find that this fine-tuning is appreciably smaller once the one-loop effects are considered 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.