Two–Loop Radiative Corrections to the Lightest Higgs Boson Mass in the Minimal Supersymmetric Model

In the minimal supersymmetric model (MSSM), the upper limit of the lightest Higgs boson mass, mh0 , depends strongly on the top quark mass, mt. We have computed the dominant twoloop radiative corrections to this upper limit of mh0 in order to eliminate large uncertainties due to QCD and mt corrections. It is shown that the QCD corrections significantly reduce the one-loop corrections. As a result, the SUSY parameter space accessible to LEP experiments is significantly increased. In recent years supersymmetric theories have become maybe the most popular alternatives to the standard model (SM) of elementary particle physics. In the minimal supersymmetric extension of the SM (MSSM) 1 the Higgs sector contains only the two doublets, H1 and H2, required to give masses to up and down type fermions with all the quartic couplings related to the gauge couplings. This leads to various restrictions among the Higgs masses and couplings 2 . The most important consequence is the existence of a well defined tree-level upper limit for the mass of the lightest Higgs boson mh0 ≤ m |cos 2β| ≤ mz , with m ≡ min{mz, mA0} . (1) However, it has been shown recently that radiative corrections can significantly alter this prediction 3 . In particular, the experiments at LEP200 may not be able to detect h0 or rule out the MSSM. The region in the SUSY parameter space, than can be ruled out at LEP experiments depends crucially on the top quark mass, mt. However, there is a significant uncertainty in mt due to large QCD corrections (e.g. the running mass differs from the pole mass by O(7%)). Eliminating this uncertainty by defining mt as the pole mass at the one-loop level requires an explicit two-loop calculation of mh0 . The case tanβ → ∞ is particularly interesting because here the tree-level constraint mh0 ≤ mz is saturated as long as mA0 > ∼ mz and thus we expect this case to yield the maximum Higgs mass. Note that mh0 has another maximum in the limit tanβ = 0 (i.e., v2 = 0). However, the constraint that the Yukawa couplings do not develop a Landau-pole at high energies, together with the experimental lower bound on mt > 113 GeV (95% CL) 5 require that tanβ > ∼ 0.5 6 . On the other hand, β ≈ π/2 is theoretically very favorable since it would explain the large ratio of mt/mb (e.g. grand unified theories based on SO(10) predict tanβ = mt/mb). The numerical analysis of the one-loop corrections 3;7;8 shows that the dominant contributions to mh0 come from the top-stop sector due to an g 2 tm 2 t dependence (gt is the top Yukawa coupling). Thus we expect the dominant two-loop corrections to be the contributions proportional to g4 tm 2 t and g 2 t g 2 sm 2 t (gs is the QCD gauge coupling). These terms can be obtained most