A Light Higgs Scalar and a Heavy Gravitino

Abstract

A radiative electroweak symmetry breaking in the minimal supergravity model is discussed, with assumptions of an 0(10 TeV) gravitino and the Nambu-Goldstone Higgs bosons. The electroweak symmetry is broken if a fine tuning of initial parameters for the renormalization group equations is made. This model predicts one light (::;; 0(10 GeV)) neutral Higgs boson. 23 Supergravity theories necessarily involve a massive spin 3/2 particle, the gravitino, and the mass of a gravitino is expected to be 0(100 GeV) in many models/} in order to relate the supersymmetry (SUSY) breaking to the electroweak gauge symmetry breaking. However, the garvitino with a mass between 0(1 ke V) and 0(10 TeV) is forbidden in the standard big bang cosmology/} since such a gravitino has a lifetime longer than the cosmic time at the primordial nucleosynthesis, and disastrously alter the abundances of light elements. Although some works in antici­ pation of solving this problem (the gravitino problem) by changing the cosmological scenario (inflation, for example) exist,3} a satisfactory solution is not obtained yet. If the gravitino is assumed to be sufficiently heavy, one may expect that all sparticles and Higgs bosons are very heavy and such a model is not phenome­ nologically appealing at all. However if an assumption that Higgs scalars are (pseudo-) Nambu-Goldstone bosons of a certain broken global symmetry4} is added, one might hope the existence of some light Higgs bosons. In this paper, we analyze a possibility of the electroweak symmetry breaking under the two assumptions, namely, the gravitino mass m3/2=0(10 TeV) and the Nambu-Goldstone hypothesis. We find that the electroweak symmetry can be broken successfully by renormalization effects if a fine tuning of some parameters is allowed, and there exists indeed one light Higgs scalar while other scalar paticles, namely, squarks, sleptons and other Higgs bosons are quite heavy. The model used in our calculation is the minimal supersymmetric 5U(3) X 5U(2) X U(l) gauge model with soft and explicit SUSY breaking terms which are obtained from a spontaneous local SUSY breaking in a hidden sector as usua1. 5