Minimal supersymmetric Higgs boson self-couplings: Two-loop $\mathcal{O}({\alpha }_t{\alpha }_s)$ corrections

We analyze the minimal supersymmetric Higgs self-couplings at $\mathcal{O}({\alpha }_t{\alpha }_s)$ within the effective potential approach. The two-loop corrections turn out to be of moderate size in the $\overline{\mathrm{DR}}$ scheme of dimensional reduction (DR) if the central scale is chosen as half the supersymmetry scale. The inclusion of the two-loop corrections reduces the renormalization scale dependence to the percent level. These results have a significant impact on measurements of the trilinear Higgs self-couplings at the LHC and a future $e^{+}{e}^{-}$ collider.

Figure 1

Scale dependence of the trilinear Higgs couplings ${\lambda }_{hhh}$ (a) and ${\lambda }_{Hhh}$ (b) at one- and two-loop order in the $m_h^{\mathrm{mod}+}$ scenario for $M_A=300\mathrm{GeV}$ and $\mathrm{tg}\beta =5$.

Figure 2

Trilinear Higgs couplings ${\lambda }_{hhh}$ (a) and ${\lambda }_{Hhh}$ (b) at tree level, one- and two-loop order in the $m_h^{\mathrm{mod}+}$ scenario for $\mathrm{tg}\beta =5$. The bands indicate the scale uncertainties within $1/3$ and 3 times the central scale $M_{\text{SUSY}}/2$.