New constraints on extended scalar sectors from the trilinear Higgs coupling

The trilinear Higgs coupling ${\lambda }_{hhh}$ is a crucial tool to probe the structure of the Higgs potential and to search for possible effects of physics beyond the Standard Model (SM). Focusing on the Two-Higgs-Doublet Model as a concrete example, we identify parameter regions in which ${\lambda }_{hhh}$ is significantly enhanced with respect to its SM prediction. Taking into account all relevant corrections up to the two-loop level, we show that current experimental bounds on ${\lambda }_{hhh}$ already rule out significant parts of the otherwise unconstrained parameter space. We illustrate the interpretation of the current results and future measurement prospects on ${\lambda }_{hhh}$ for a benchmark scenario. Recent results from direct searches for BSM scalars in the $A\to ZH$ channel and their implications will also be discussed in this context.