The current consensus between experimental measurements and theoretical predictions of particle collisions is extraordinary, imposing stringent limits on exotic phenomena beyond the Standard Model. Despite this remarkable agreement, many open questions remain. This talk will address a subset of these questions, intricately linked to the mechanism of electro-weak symmetry breaking and the scalar sector of our theory. In particular, I will focus on a potential generation mechanism for the observed matter-antimatter asymmetry in the universe, catalyzed by additional scalar fields - an idea known as "electro-weak baryogenesis". I will discuss the signatures of such scalar fields at present and future collider experiments, and outline the possible next steps following their discovery, with an emphasis on multi-scalar production processes. Venturing beyond baryogenesis, I will explore the additional information that can be extracted through the challenging triple-scalar production process, shedding light on the deeper aspects of our understanding of the scalar sector.
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