Validity of the effective potential and the precision of Higgs field self-couplings

The global picture of the Higgs potential in the bottom-up approach is still unknown. A large deviation as big as O(1) fluctuations of the Higgs self-couplings is still a viable option for the new physics. An interesting new physics scenario that can be linked to a large Higgs self-coupling is the baryogenesis based on the strong first order phase transition. We revisit the strong first order phase transition in two classes of beyond the Standard Models, namely the Higgs portal with the singlet scalar under the Standard Model gauge group with Z2 symmetry and the effective field theory approach with higher-dimensional operators. We numerically investigate a few important issues in the validity of the effective potential, caused by the breakdown of the high-temperature approximation, and in the criteria for the strong first order phase transition. We illustrate that these issues can lead to O(1) uncertainties in the precision of the Higgs self-couplings, which are relevant when discussing sensitivity limits of different future colliders. We also find that the quartic coupling of the above two classes of scenarios compatible with the strong first order electroweak phase transition where the cubic coupling is not negligible can achieve a 2σ sensitivity at the 100 TeV pp collider. From this novel observation, we show that the correlation between the Higgs cubic coupling and the quartic coupling will be useful for differentiating various underlying new physics scenarios and discuss its prospect for the future colliders. Throughout our numerical investigation, the contribution from the Goldstone boson is not included.