Troubles with the Minimal SU(5) Supergravity Model

Abstract

We show that within the framework of the minimal $SU(5)$ supergravity model, radiatively-induced electroweak symmetry breaking and presently available experimental lower bounds on nucleon decay, impose severe constraints on the available parameter space of the model which correspond to fine-tuning of the model parameters of over two orders of magnitude. Furthermore, a straightforward calculation of the cosmic relic density of neutralinos ($\chi$) gives ${\Omega }_{\chi }{h}^2\gg 1$ for most of the allowed parameter space in this model, although small regions may still be cosmologically acceptable. We finally discuss how the {\it no-scale flipped $SU(5)$ supergravity model} avoids naturally the above troubles and thus constitutes a good candidate for the low-energy effective supergravity model.

12 pages plus 3 figures (not included); CERN-TH.6554/92, CTP-TAMU-49/92

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