Naturalness Constraints in Supersymmetric Theories with Non-Universal Soft Terms

In the absence of universality the naturalness upper limits on supersymmetric particle masses increase significantly. The superpartners of the two light generations can be much heavier than the weak scale without extreme fine-tunings; they can weigh up to about 900 GeV — or even up to 5 TeV, if SU(5) universality is invoked. This supresses sparticlemediated rare processes and consequently ameliorates the problem of supersymmetric flavor violations. On the other hand, even without universality, the gluino and stop remain below about 400 GeV while the charginos and neutralinos are likely to be accessible at LEP2. CERN-TH/95-188 July 1995 On leave of absence from Stanford University, Stanford, Ca. 94305, USA. On leave of absence from INFN, Sezione di Padova, Padua, Italy. The naturalness problem of the standard model with fundamental Higgs particles [1] provides la raison d’être for supersymmetry at low energies [2]. Indeed supersymmetry cures the problem if the soft-supersymmetry breaking scale, which behaves as a cutoff for quadratic divergences, lies below the TeV range [2, 3]. This concept has been put on more quantitative grounds by the studies presented in refs. [4, 5], where upper bounds on physical supersymmetric particle masses were obtained. In this letter we wish to revisit the analysis of ref. [5] and extend it to models with non-universal boundary conditions at the unification scale. We follow the procedure proposed in ref. [5] and quantify the naturalness criterion by requiring that