Modular invariance, soft breaking, μ and tanβ in superstring models

We go beyond parameterizations of soft terms in superstring models and investigate the dynamical assumptions that lead to the relative strength of the dilaton vs. the moduli contributions in the soft breaking. Specifically, we discuss in some simple heterotic orbifold models sufficient conditions to achieve dilaton dominance. Assuming self-dual points to be minima we find multiple solutions to the trilinear and bilinear soft parameters A0 and B0. We discuss the constraints on μ and tanβ in superstring models in the context of radiative breaking of the electroweak symmetry. We show that string models prefer a small to a moderate value of tanβ, i.e., tanβ⩽10, and a value much larger than this requires a high degree of fine tuning. Further, we show that for large tanβ the radiative electroweak symmetry breaking constraint leads to a value αstring=gstring2/4π which is typically an order of magnitude smaller than implied by the LEP data and the heterotic superstring relation gstring=kigi, where gi is the gauge coupling constant for the gauge group Gi and ki is the corresponding Kac–Moody level in the class of models considered. This situation can be overcome by another fine-tuned cancellation between the dilaton and the moduli contributions in the soft parameters.