Volume 135, number 1,2,3 PHYSICS LETTERS 2 February 1984 ELECTROWEAK BREAKING IN SUGRA MODELS S.K. JONES Department of TheoreticalPhysics, University of Oxford, 1 Keble Road, Oxford, OX1 3NP, UK and G.G. ROSS Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, UK and Pembroke College, University of Oxford, Oxford, UK Received 27 September 1983 We discuss electroweak breaking in SUGRA models both at the tree level and in radiative order. In the latter case we find new solutions for which electroweak breaking occurs even for a light top quark. These may either have the electro- weak scale rented to the supersymmetry breaking in the light sector, or via dimensional transmutation, related to the PNnck scale and larger than the light sector supermultiplet splitting. Supersymmetric GUTs may solve the hierarchy problem allowing the grand unified scale M x to co- exist with the electroweak scale M w. Realistic models have been constructed based on the structure G ® [N = 1 global supersymmetry], where G is the grand unified group, in which the hierarchy is stable against radiative corrections [1]. An unattractive feature of these models is the need to introduce a gauge singlet sector to break the supersymJnetry together with ad- ditional Yukawa couplings to transmit this breaking into the gauge non-singlet sector. It is possible to sim- plify this scheme if the SUSY breaking scale MSUSY is large ~O(1010 GeV), for then gravitational correc- tions alone communicate the SUSY breaking from the gauge singlet (hidden) sector to the gauge non- singlet sector. One can do without the additional Yukawa couplings, giving a model which has fewer parameters, is more constrained and more predictive. A pleasing feature of this scenario is that the low energy structure is uniquely given in terms of an [SU(3) X SU(2)X U(1)] ® IN= 1 global supersym- metry] model plus soft SUSY breaking terms arising from the gravitational corrections. The form of the soft breaking terms and their dependence upon the hidden sector has been calculated, and is simply 0.370-2693/84/$ 03.00 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division) parameterised [2-4]. Since SUSY has been introduced to solve the hier- archy problem, it is desirable to try to explain the various mass scales in as few fundamental scales as possible. In a SUSY GUT one automatically starts with the Planck scale Mp. M x is typically larger in SUSY GUTs than in minimal SU(5), and plausibly connected to Mp by some coupling constant, i.e. it is not a new fundamental scale. In addition supersym- metry must be broken at an intermediate scale, M~USY ~ 1010 GeV, giving a gravitino mass m 3/2 = M~Usy/M = O(102 GeV). (Here we choose M = Mp-lanck/~/8n = 1.2 X 1018 GeV for notational sim- plicity). It is possib!e to construct models [5] in which MsusY ~ M(Mx/M)n so that MsusY need not be a new fundamental scale either. Finally it is attractive to identify the scale M w at which SU(2) X U(1) breaks to U(1)E M with m3/2. Models breaking SU(2) X U(1) at tree level with M w = O(m3/2) have been constructed [3,6]. However, in these models with no further mass parameter the desired minimum of the potential is a local, not global, minimum [7]. A more promising and economical approach is to follow the idea in global SUSY models in which the electroweak breaking is induced through radiative 69