The masses of the Higgs bosons in the next-to-minimal supersymmetric model

We find that the lightest scalar Higgs boson in the next-to-minimal supersymmetric standard model (NMSSM) may have a small mass for reasonable values of the relevant parameters, which does not contradict the present experimental data. We analyze numerically the renormalization group equations for the soft parameters A(lambda) and A(k) of the NMSSM, assuming that they are related at the scale. The analysis suggests, with certain boundary conditions at the scale, that tan beta greater than or equal to 3. Using the present LEP data on the Higgs search, we establish the allowed ranges for the masses of the scalar Higgs bosons in the NMSSM. In particular, the mass of the lightest scalar Higgs boson may be as small as between 27.3 and 38.5 GeV for tan beta = 6 if the discovery limit of the LEP is 1 pb.