Probing Symmetry-Breaking Pattern Using Sfermion Masses

We study the mass spectrum of superparticles within supersymmetric grand unified models. For gaugino masses, it is pointed out that the GUT-relation in the SU(5) model is applicable to a more general case where a grand-unified gauge group breaks down to the standard model gauge group by several steps. We also show that the mass spectrum of squarks and sleptons carries the information on the breaking pattern of the gauge symmetry. It is demonstrated in some SO(10) models how the scalar mass spectrum distinguishes various SO(10) breaking patterns from each other. ∗Present address: Theoretical Physics Group, Lawrence Berkeley Laboratory, University of California, CA 94720. The Grand Unified Theory (GUT) has been attractive as a promising framework to explain the law of nature since its proposal [1]. The huge difference between the GUT scale and the weak scale gives rise to the famous gauge hierarchy problem. The prime motivation of introducing supersymmetry (SUSY) in a GUT [2] is that it will give a partial solution to this problem: SUSY can stabilize the hierarchy between the GUT scale and the weak scale against radiative corrections [3]. This wonderful theoretical framework, the SUSY-GUT, is consistent with the precise measurement of the weak-scale gauge coupling constants at LEP [4] for the minimal particle content of SUSY standard model [5]. Furthermore, the present non-observation of the nucleon decay is shown to be still consistent with the minimal version of the SUSY-GUT [6]. It is, however, not clear from the LEP data alone whether the minimal version of the SUSYGUT is the whole story. For example, the solar neutrino experiments [7] suggest the neutrino oscillation à la Mikheyev–Smirnov–Wolfenstein [8], and it is naturally incorporated into the SO(10) grand unification with seesaw mechanism [9]. While the direct breaking of the SO(10) group into the standard model group GSM = SU(3)C × SU(2)L ×U(1)Y is obviously consistent with the LEP data, there are possibilities that there is an intermediate scale with chain symmetry breaking. An important virtue of the SUSY-models is that the soft SUSY-breaking mass parameters can be novel probes of physics at very high energies. In this letter we point out that the gaugino mass spectrum generally satisfies the GUT-relation as far as the standard model gauge group is embedded into a simple group, irrespective of the symmetry breaking pattern. On the other hand, the squark and slepton mass spectrum will be shown to carry the information on the breaking pattern of the gauge symmetry. Therefore, the gaugino and the scalar mass spectrum will play a complementary role to select among the models of SUSY-GUT experimentally. We will demonstrate how the scalar mass spectrum distinguishes various SO(10) breaking patterns from each other. We first consider the gaugino mass spectrum. We expect that the gaugino mass parameters are common at the unification scaleMU . Though it is known that the vacuum expectation values of the fields responsible for the GUT symmetry breaking would give a non-universal contribution to the gaugino ∗An explicit example was first given in Ref. [15] from different motivation.