Nuclear Physics B259 (1985) 503-532 © North-Holland Publishing Company LOW-ENERGY PREDICTIONS OF A TWO-LOOP FINITE SUPERSYMMETRIC SU s THEORY J.E. BJC)RKMAN and D.R.T. JONES* Department of Physics, Universi(y of Colorado, Boulder, CO 80309, USA S. RABY Theory Group, T-8 MSB-285, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Received 3 January 1985 (Revised 15 April 1985) We present a detailed discussion of a two-loop finite supersymmetric SU 5 theory, with particular emphasis on the new particle mass spectrum and its dependence on the input parame- ters. The model predicts sin20w = 0.237, mb/m ~ = 1.8 (at Mw) and Mx = 5.3 × 1015 GeV, which means that nucleon decay, if observable, will be to strange final states. We find in general mg> mc~> me, and that results consistent with a supersymmetric explanation of the CERN monojet and "top-quark" events are possible, in which case we predict light (0(20 GeV)) charged scalar leptons. 1. Introduction The recent demonstration [1-3] that any one-loop finite supersymmetric Yang- Mills theory (SYM) is two-loop finite has raised the possibility that the set of ultraviolet finite four-dimensional field theories may be larger than the known [4] N = 4 and N = 2 examples. A classification of groups and representations compati- ble with the finiteness conditions has been presented [5], and the most promising candidate for a grand unified theory, an SU 5 model, has been discussed [6, 7]. In this paper we present a critical and detailed analysis of the SU 5 model, emphasizing the low-energy predictions for new particle masses. We introduce a set of supersymme- try-breaking masses and interactions compatible with finiteness [1, 8] and show that, with these interactions, we have gauge symmetry breaking to SU 3 x SU 2 x U 1 at the tree level and to SU 3 x U 1 via radiative corrections. The mechanism for radiative SU 2 × U 1 breaking we employ has been explored in some detail (for a review and references see [9]); the essential new feature of our work is the restricted form of the *Address from February 1st 1985: Department of Applied Mathematics and Theoretical Physics, University of Liverpool, PO Box 147. Liverpool L69 3BX, England. 503