On metastability in supersymmetric models

We make a critical reappraisal of 'unbounded-from-below' (UFB) constraints in the MSSM and R-parity violating models. We explain why the 'traditional' UFB bounds are neither necessary nor sufficient and propose, instead, a sufficient condition which ensures that there are no focal minima along the Aat directions. This conservative (but meaningful) condition divides the parameter space into regions which are allowed, regardless of cosmology, and regions in which cosmology is expected to play a major role. We study both conditions at low tan beta and obtain analytic approximations to the UFB bounds far all low tan beta (< 15). Finally we show that R-parity violation just below current experimental limits avoids UFB problems by lifting the dangerous flat directions. (C) 1998 Elsevier Science B.V.