A Model with Simultaneous Dynamical Breaking of Supersymmetry and GUT Gauge Symmetry

We try to construct a model in which supersymmetry and grand unified gauge symmetry are dynamically broken at the same time. In this model SUSY breaking is mediated mainly by massive vector multiplet, and a new solution for the μ problem is proposed. e-mail: [email protected] e-mail: [email protected] e-mail: [email protected] If supersymmetry (SUSY) is a real solution for gauge hierarchy problem, we should understand how SUSY is broken and why the SUSY Higgs mass is around the SUSY breaking scale, which is much less than the grand unified scale or the Planck scale. One of the most interesting scenarios of understanding the SUSY breaking is gauge mediated SUSY breaking scenario [1]. In the last few years, using the recent development on SUSY gauge theories [2, 3], various dynamical SUSY breaking models are examined [1, 4, 5, 6, 7]. Unfortunately, in the gauge mediated SUSY breaking scenario, we have not understood well why the SUSY Higgs term is around the SUSY breaking scale, though various attempts are considered [1, 6, 8]. One possible solution for the μ problem is to introduce the singlet field which is coupled with the Higgs fields, and to realize that the vacuum expectation value (VEV) which becomes the SUSY Higgs mass, is determined by the SUSY breaking parameters [1]. However, it is dangerous because the radiative correction generally breaks the gauge hierarchy when the singlet field couples to the heavy fields [9]. On the point of SUSY grand unified theories (GUT) we should understand not only the mechanism of the doublet-triplet splitting [10] but the consistency between GUT formalism and the solution of the μ problem. For example, the singlet field introduced for the μ problem is also coupled with the colored Higgs, which breaks gauge hierarchy. In this paper, we examine a model in which SUSY and GUT gauge symmetry are simultaneously broken and the μ problem can be solved. To break SUSY and GUT gauge symmetry at the same time, it is natural that SUSY breaking is mediated by the massive vector multiplet (gauge messenger) [11]. The gauge messenger can work only when the F-term of the Higgs, which breaks a gauge symmetry, is non-zero, namely when the spectrum of the massive gauge multiplets deviates from the SUSY limit. Since the original gauge symmetry should include the standard gauge symmetry for inducing all needed soft SUSY breaking parameters, it is natural that GUT gauge symmetry is adopted as the original one. We examine a following model with the gauge symmetry SU(5)G×SU(3)H × SU(2)H × U(1)H in addition to the strong gauge group Sp(8) . The quantum numbers of introduced fields are The rank of Sp(2N) is N .