Reconciling the two-loop diagrammatic and effective field theory computations of the mass of the lightest CP-even Higgs boson in the MSM

The mass of the lightest CP-even Higgs boson of the minimal supersymmetric extension of the standard model (MSSM) has previously been computed including O(alpha alpha(s)) two-loop contributions by an on-shell diagrammatic method, while approximate analytic results have also been obtained via renormalization-group-improved effective potential and effective field theory techniques. Initial comparisons of the corresponding two-loop results revealed an apparent discrepancy between terms that depend logarithmically on the supersymmetry-breaking scale, and different dependences of the nonlogarithmic terms on the squark mixing parameter, XI, In this paper, we determine the origin of these differences as a consequence of different renormalization schemes in which both calculations are performed. By reexpressing the on-shell result in terms of MS parameters, the logarithmic two-loop contributions obtained by the different approaches are shown to coincide. The remaining difference, arising from genuine nonlogarithmic two-loop contributions, is identified, and its effect on the maximal value of the lightest CP-even Higgs boson mass is discussed. Finally, we show that in a simple analytic approximation to the Higgs mass, the leading two-loop radiative corrections can be absorbed to a large extent into an effective one-loop expression by evaluating the running top quark mass at appropriately chosen energy scales. (C) 2000 Elsevier Science B.V. All rights reserved.