Higgs Boson Mass in Supersymmetry to Three Loops

Within the minimal supersymmetric extension of the standard model, the mass of the light $CP$-even Higgs boson is computed to three-loop accuracy, taking into account the next-to-next-to-leading order effects from supersymmetric quantum chromodynamics. We consider two different scenarios for the mass hierarchies of the supersymmetric spectrum. Our numerical results amount to corrections of about 500 MeV, which is of the same order as the experimental accuracy expected at the CERN Large Hadron Collider.

Figure 1

$\Delta M_h$ as a function of $M_{\mathrm{SUSY}}$ at one-, two-, and three-loop level. The renormalization scale is set to $\mu =M_t$.

Figure 2

$\Delta M_h$ as a function of the renormalization scale $\mu$ at two- and three-loop level, where $M_{\mathrm{SUSY}}=1\mathrm{TeV}$ has been chosen.