Higgs as (Pseudo-) Goldstone Particles

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)

Holographic grand unification

“…The lightness of the Higgs doublets can be understood group theoretically if we identify these states as pseudo-Goldstone bosons of a broken global symmetry [6]. Suppose that the G sector possesses a global SU(6) symmetry, of which an SU(5) (× U(1)) subgroup is gauged and identified as the unified gauge symmetry.…”

“…These couplings, however, disappear at low energies after integrating out all the heavy modes, because the strong G dynamics respects SU(6) and the Higgs doublets are the Goldstone bosons associated with the dynamical breaking of SU (6). Now, suppose that the theory also has several elementary fields that transform as 5 * and 10 under SU (5).…”

“…If this breaking is caused by the Higgs mechanism, then in the corresponding 4D description the fundamental gauge symmetry of the theory is SU(6), which is spontaneously broken to SU(5) × U(1) at a very high energy E M U . In this case, we must introduce matter fields in representations of SU (6), so that the standard SU(5) embedding of matter fields [23] should be modified/extended. On the other hand, if SU(6) → SU(5) × U(1) on the UV brane is caused by boundary conditions, then in the corresponding 4D description only the SU(5)×U(1) subgroup of the global SU(6) symmetry is explicitly gauged (see figure 1), so that we can employ the standard SU(5) embedding for matter fields.…”

“…(3.5) is a part of a continuum of vacua, which can easily be seen by studying the excitations. Under the unbroken SU(3) 6) where the numbers in parentheses represent the quantum numbers under SU(3…”

“…arises as a result of the dynamics of G, the third generation superparticles (presumably only the ones coming from the 10 representation of SU (5)) can have different masses than the lighter generation superparticles, which receive universal masses from the gauginos through loop corrections [33]. 6 These are consequences of our way of generating hierarchies in fermion masses and mixings.…”