Supersymmetric Grand Unification

Abstract

One of the original motivations for the application of supersymmetry to particle physics was to solve the gauge hierarchy problem that arises in the grand unification program. As has been emphasized in Chapter 5, the tree level parameters must be fine tuned to an accuracy of 10^-26 or so, to generate the mass ratio M _x /m _w ≃ 10¹² in the SU(5) model. In other models, due to the presence to intermediate mass scales, the problem of fine tuning is not as severe but a lesser degree of fine tuning is always required. Since a nonsupersymmetric theory with scalar bosons is plagued with quadratic divergences, such tree level fine tunings are upset in higher orders. This need not happen in supersymmetric theories due to the nonrenormalization theorem of Grisaru, Rocek, and Siegel described in Chapter 10. According to this theorem, the parameters of the superpotentials do not only receive infinite renormalization but they also do not receive finite renormalization in higher orders. Supersymmetry can, therefore, be used to solve one aspect of the gauge hierarchy problem, i.e., once we fine tune parameters at the tree level the radiative corrections do not disturb the hierarchy. This point was utilized by Dimopoulos and Georgi [1] and Sakai [2] to construct supersymmetric SU(5) models with partial solutions to the gauge hierarchy problem. We illustrate their procedure with a simple but realistic supersymmetric SU(5) model.