The masses of the neutral ${\cal CP}$ -even Higgs bosons in the MSSM: Accurate analysis at the two-loop level

Abstract

We present detailed results of a diagrammatic calculation of the leading two-loop QCD corrections to the masses of the neutral ${\cal CP}$ -even Higgs bosons in the Minimal Supersymmetric Standard Model (MSSM). The two-loop corrections are incorporated into the full diagrammatic one-loop result and supplemented with refinement terms that take into account leading electroweak two-loop and higher-order QCD contributions. The dependence of the results for the Higgs-boson masses on the various MSSM parameters is analyzed in detail, with a particular focus on the part of the parameter space accessible at LEP2 and the upgraded Tevatron. For the mass of the lightest Higgs boson, $m_h$ , a parameter scan has been performed, yielding an upper limit on $m_h$ which depends only on $\tan \beta$ . The results for the Higgs-boson masses are compared with results obtained by renormalization group methods. Good agreement is found in the case of vanishing mixing in the scalar quark sector, while sizable deviations occur if squark mixing is taken into account.