The Z2 Two Higgs Doublet Model and the hierarchy problem

The hierarchy problem is investigated in the $\mathbb{Z}_2$ Two Higgs Doublet extension of the Standard Model. From the quadratic divergences of the Higgs field propagators fine-tuning constraints are extracted and solved. This leads to the mass relation $m_{h^0}^2 < 2 m_t^2 < m_{H^0}^2$, where $h^0$ is the analogue of the SM Higgs boson and $H^0$ a heavier neutral scalar. The constraint leads to an admissible condition on the Higgs boson mass, in contrast to a similar treatment for the Standard Model. Based on this analysis it is argued that there may not be a little hierarchy problem for the $\mathbb{Z}_2$ model, as it is the low energy counterpart of the MSSM.