The Higgs boson plays a pivotal role in our understanding of the fundamental forces of nature and is unique as the only known scalar boson in the Standard Model (SM) of particle physics. The Higgs field is responsible for the spontaneous breaking of electroweak symmetry, giving masses to the gauge bosons. A key element of this mechanism is the Higgs potential—assumed in the SM to have a Mexican-hat shape, but introduced ad hoc and not derived from first principles. Probing the shape of this potential experimentally is therefore of fundamental importance.

Double Higgs (HH) production provides a unique window into the Higgs potential, offering insight into the stability of the electroweak vacuum and possibly the origins of the matter–antimatter asymmetry in our universe. However, the HH production rate is extremely small, about 34 fb in proton–proton collisions at vs = 13.6 TeV.

In this talk, I will describe the challenges of observing this rare process and the innovative methods used by the CMS experiment at the LHC to search for it. I will also discuss how emerging detector technologies—such as next-generation silicon sensors with 4D (space and time) tracking—will dramatically enhance our ability to reconstruct complex final states, improving the sensitivity to HH production. Finally, I will outline the prospects for observing HH production and constraining the Higgs potential at future particle colliders.