ABSTRACT
Beyond the Desert 1999: Accelerator, Non-Accelerator and Space Approaches into the Next Millennium 3
Department of Physics, Northeastern University, Boston, MA, 02115-5000, USA
1. INTRODUCTION
In SUSY theories with a softly broken scale Ms radiative breaking of the electro-weak symmetry gives Mz "" Ms[l]. As Ms moves up the Mz '" Ms relation creates a naturalness problem[2, 3, 4, 6, 7, 8]. A second aspect of naturalness problem is that softly broken SUSY theories contain new sources of CP violation since the soft SUSY parameters are in general complex, The natural size of these CP violating phases is 0(1) and phases of this size give the neutron and the electron electric dipole moments already in excess of experiment[9], These problems arise in a wide class of models, e,g" in models with gravity mediated breaking of supersymmetry and with gauge mediated breaking of supersymmetry. In this paper we discuss these naturalness problems and their implications for dark matter and for CP violating effects. In Sec,2 we discuss weak scale supersymmetry. In Sec.3 we discuss the quantitative measure of fine tuning. In Sec.4 we discuss the question of how high the scale of weak scale SUSY can be within a fixed fine tuning criterion. In, Sec.5 we discuss the implications of naturalness for the direct detection of dark matter. In Sec.6 we discuss the implications of naturalness for the indirect detection of dark matter. In Sec,7 we discuss naturalness and the EDM constraints and their effects on the direct detection of dark matter. Conclusions are given in See8,
For the sake of concreteness we shall assume in this paper the scenario where supersymmetry is broken in a hidden sector and the breaking of supersymmetry is communicated to the visible sector via gravitational interactions[10, 1]. The breaking of supersymmetry in the hidden sector is governed by the Kahler potential and in the simplest model of this potential is assumed to be flat. In this case integration over the hidden sector and the heavy fields in the theory give a low energy supersymmetry breakinf potential which is of the following form at the GUT scale: VSB = moz; z; + Ao W(3) + Bo W(2). Here mo is the universal scalar mass for the scalar fields z;, W(3) is the cubic part of the superpotential and Ao is the universal trilinear coupling, and W(2) is the quadratic part of the superpotential and Bo is the universal bilinear coupling. For the minimal supersymmetric standard model (MSSM) the quadratic part of the superpotential W(2) is parametrized by W(2) = J.10HIH2 where H2 gives mass to the up quark and HI gives mass to the down quark and the lepton, and J.1o is the Higgs mixing parameter at the GUT scale. In addition, one has the universal gaugino mass term ~m!'\A in the theory.
