Complete Two-loop Dominant Corrections to the Mass of the Lightest CP-even Higgs Boson in the Minimal Supersymmetric Standard Model

Abstract Using an effective potential approach, we compute two-loop radiative corrections to the MSSM lightest CP -even Higgs boson mass M h 0 to O (α t 2 ) for arbitrary left-right top-squark mixing and tan β . We find that these corrections can increase M h 0 by as much as 5 GeV; assuming a SUSY scale of 1 TeV, the upper bound on the Higgs boson mass is M h 0 ≈129±5 GeV for the top quark pole mass 175±5 GeV. We also derive an analytical approximation formula for M h 0 which approximates our numerical results to a precision of ≲0.5 GeV for most of the parameter space and suitable to be further improved by including renormalization group resummation of leading and next-to-leading order logarithmic terms. Our final compact formula admits a clear physical interpretation: radiative corrections up to the two-loop level can be well approximated by a one-loop expression with parameters evaluated at the appropriate scales, plus a smaller finite two-loop threshold correction term.