Two-loop Results for the Masses of the Neutral Cp-even Higgs Bosons in the Mssm

Diagrammatic two-loop results are presented for the leading QCD corrections to the masses of the neutral CP-even Higgs bosons in the Minimal Supersymmetric Standard Model (MSSM). The results are valid for arbitrary values of the parameters of the Higgs and scalar top sector of the MSSM. Their impact on a precise prediction for the mass of the lightest Higgs boson is briefly discussed. The MSSM offers a theoretically very appealing extension of the Standard Model (SM) of the electroweak and strong interactions. While for the predicted superpartners of the SM particles present-day accelerators can cover only a very limited part of the MSSM parameter space, the Higgs sector of the model provides the opportunity for a stringent direct test in requiring the existence of a light neutral Higgs boson. At tree level its mass, mh, is predicted to be lower than the one of the Z boson. However, the one-loop corrections are known to be huge [1, 2] and shift the upper bound to about 150 GeV. Beyond one-loop order renormalization group methods have been applied in order to include higher-order leading and next-to-leading logarithmic contributions [3, 4, 5]. A diagrammatic calculation is available for the dominant two-loop contributions in the limiting case of vanishing t̃-mixing and infinitely largeMA and tanβ [6]. These results indicate that the two-loop corrections considerably reduce the predicted value ofmh. A precise prediction formh in terms of the relevant SUSY parameters is crucial in order to determine the discovery and exclusion potential of LEP2 and the upgraded Tevatron and also for physics at the LHC, where eventually a highprecision measurement ofmh might be possible. Diagrammatic two-loop results which take into account virtual particle effects without restrictions of their masses and mixing are therefore very desirable. We have performed a Feynman diagrammatic calculation of the leading two-loop QCD corrections to the masses of the neutral CP-even Higgs bosons in the MSSM [7]. The calculation has been performed in the on-shell scheme. The results are valid for arbitrary values of the parameters of the Higgs and scalar top sector of the MSSM. The Higgs sector of the MSSM contains two Higgs doublets,