Lower limits on soft supersymmetry-breaking scalar masses

Working in the context of the CMSSM, we argue that phenomenological constraints now require the universal soft supersymmetry-breaking scalar mass m₀ be non-zero at the input GUT scale. This conclusion is primarily imposed by the LEP lower limit on the Higgs mass and the requirement that the lightest supersymmetric particle not be charged. We find that m₀> for all tan β if μ <0, m₀= 0 and may be allowed for μ> 0 only when tan β ∼ 8 and one allows an uncertainty of 3+ GeV in the theoretical calculation of the Higgs mass. Upper limits on flavour-changing neutral interactions in the MSSM squark sector allow substantial violations of non-universality in the m₀ values, even if their magnitudes are comparable to the lower limit we find in the CMSSM. Also, we show that our lower limit on m₀ at the GUT scale in the CMSSM is compatible with the no-scale boundary condition m₀ = 0 at the Planck scale.