Studying the Higgs Potential via $e^+e^- \to Zhh$

The physics prospect at future linear $e^+e^-$ colliders for the study of the Higgs triple self-coupling via the process of $e^+e^-$ $\rightarrow Zhh$ is investigated. The measurement of this cross section leads us to the first non-trivial information on the Higgs potential. We found that the Standard Model and the model without the Higgs self-coupling can be distinguished at the level of one standard deviation for a rather light Higgs mass with 100 fb$^{-1}$ integrated luminosity. In the MSSM, the cross section is enhanced if the production of at least one of heavy Higgs bosons ($H$ or $A$) and its subsequent decay ($H \rightarrow hh$, $A \rightarrow Zh$) are kinematically allowed. When such processes are not allowed, the cross section in the region of small $m_A$ is significantly suppressed relative to the SM cross section.