No abstract

Higgs scalars may be (pseudo-) Goldstone particles related to a spontaneous breakdown of a global symmetry which contains grand unified gauge group as a subgroup. This hypothesis gives severe con· straint on possible form of Higgs mass terms in a framework of supersymmetric grand unified theories coupled to N = 1 supergravity.Remarkably, their tree level mass terms, both supersymmetric and soft-breaking, are definitely given by gravitino mass m3/2 and do not depend on a detailed structure of a superpotential of GUT sector. These mass terms are best desirable for the relatively light top quark (m,::S 50 Ge V) suggested at CERN to be active in the radiative 5U(2) x um breaking scenario. §1.Higgs scalars, in spite of their indispensable roles, have been mysterious and even troublesome existence throughout every stage of the progress of unified gauge theories. Although supersymmetry shed important light on them!) and successive attempts gave some valuable hints,2),3) we are still "far from the position to clarify their nature.In the last couple of years some attempts have been made to assign leptons and quarks (and Higgs scalars) to (pseudo-) Goldstone multiplets in the supersymmetric non-linear a-model in a context of composite models to get natural explanation of their lightness. 4 ) Even if we do not rush into composite models, this idea is appealing and suggestive enough within the standard scenario of grand unified theories (GUTs) when we recall the well-known problem of doublet-triplet Higgs mass splitting and related mess. Surely it will be most comfortable if we can attribute lightness of Higgs doublets to the Goldstone theorem supplemented by hon-renormalization theorem. That is, Higgs scalars are light because they are (p-) Goldstone bosons due to spontaneous breakdown of some global symmetry G which is large enough to contain GUT gauge group GGUT as a subgroup.Consider, for example, a theory possessing a global symmetry SU(6). The subgroup SU(5) is gauged. Suppose the vacuum of the theory breaks SU(6) down to SU (4)

413The full renormalization group equations in the minimal SU(3)x SU(2)x U(l) gauge model with softly broken supersymmetry, which are originally given in the paper [Prog. Theor. Phys. 68 (1982), 927] are re·examined and corrected.Supersymmetry has recently attracted much attention as it provides a viable principle to solve the hierarchy problem in grand unified theories.,),2) It is well known that a scheme with spontaneously broken supersymmetry at low energies (~0(100 GeV» is plagued with difficulties owing to the famous mass sum rule. 3) Thus the supersymmetry breaking terms in the effective low energy theory should be explicit and soft,2) though they may be messages from a hidden sector in which supersymmetry is spontaneously broken at a large mass scale (~0(10'O GeV»!)In a previous paper we have studied the renormalization of these soft breaking parameters in the supersymmetric SU(3)xSU (2)x U(l) gauge model with the minimal set of chi~al matter-Higgs multiplets. S) We obtained an important result that the weak gauge symmetry breaking can be induced by the renormalization effects on these soft breaking parameters, provic;led that the top quark. is sufficiently heavy.S) On the other hand, it has recently been recognized that the explicit and soft supersymmetry breaking terms in the effective lagrangian naturally appear in the spontaneously broken N = 1 supergravity theory.S),7) Furthermore it has also been pointed out that the light singlet, which is necessary inorder to break the weak gauge symmetry at the tree level, is dangerous because it destabilizes the light-heavy hierarchy. B) Thus there is growing interest in the set of renormalization group equations for the breaking parameters in the minimal mode1. 9 )"O) Unfortunately; the original results given in the previous paper contain several errors (i.e., equations for ms, "', m,o).S) There are already independent calculations for the breaking parameters which originate from the spontaneous breakdown of the N=l supergravity.'O) In this short note, we shall give corrected set of renormalization group equations for parameters defined in the previous paper for the sake of completeness, since our breaking parameters are somewhat more general than those obtained from the N = 1 supergravity.The minimalSU(3)xSU(2)x U(1) gauge model consists of vector multiplets V" V2 and V3, corresponding respectively to U(1), SU(2) and SU(3), three generations of quark-lepton chiral multiplets and two Higgs chiral multiplets. Their representation contents and component fields are shown in Tables I, II and III. We neglect Yukawa couplings except those for the third generation:where i and j( =1,2) are the SU(2) indices and p( =1,2,3) the SU(3) index. The Grassman integration measure and the component expansion of a left-chiral superfield ¢ are defined as Jd 2 88 2 =1 and ¢ =exp( -i1roap8 P )(A + !28¢ + 8 2 F). The supersymmetry breaking masses of matter scalars and of gauge fermions are shown in Table IV. For the Higgs multiplets, we consider the following gauge invariant mass ter...

No abstract

No abstract