Probing the quartic Higgs boson self-interaction

The Higgs self-interactions play a crucial role in exploring the underlying mechanisms of electroweak symmetry breaking and the nature of the phase transition involved. In this article, we propose to probe the quartic Higgs self-interaction at lepton and hadron colliders, via the di-Higgs productions. We analyze the contributions of the quartic Higgs coupling, including the renormalization of the cubic Higgs coupling and the modification of the VVhh form factor, to the vector boson-fusion and the vector boson-associated di- Higgs productions at one-loop level. Such an effect is independent of the choice of gauge fixing, if the quartic Higgs coupling is decoupled from other couplings in the contexts considered. Notably, a combination of these two di-Higgs productions is important for optimizing the collider sensitivities to probe the quartic Higgs coupling. With this guideline, we explore the International Linear Collider and Compact Linear Collider sensitivities, and find that the International Linear Collider has the potential to measure the quartic Higgs coupling, normalized by its standard model value, with a precision of similar to +/- 25 (500 GeV, 4 ab(-1 )+ 1 TeV, 2.5 ab(-1)) and similar to +/- 20 (500 GeV, 4 ab(-1 )+ 1 TeV, 8 ab(-1)), at 1 sigma C.L., after marginalizing the cubic Higgs coupling in the chi(2) analysis. The dependence on the renormalization scheme of the cubic Higgs coupling is discussed.