Higgs Self-Coupling as a Probe of Electroweak Phase Transition

TL;DR

The paper addresses whether the order of the electroweak phase transition (EWPT) can be probed via the Higgs cubic self-coupling, proposing that a strongly first-order EWPT leaves a characteristic, observable imprint on $λ_3$. It employs a set of toy, renormalizable models to compute the finite-temperature effective potential $V_{ m eff}(h,T)$ and the transition strength parameter $ξ = v_T(T_c)/T_c$, exploring mechanisms from loop corrections to tree-level Higgs interactions and Higgs–singlet mixing. Across renormalizable unmixed-Higgs scenarios—single BSM scalar, single BSM fermion, scalar–fermion pairs, and multi-state spectra—the work demonstrates that a strong EWPT typically accompanies an order-one deviation in $λ_3$ relative to the SM, with the sign and size depending on the bosonic vs fermionic contributions and potential cancellations. The findings imply that precise measurements of the Higgs self-coupling at future colliders (e.g., HL-LHC, ILC) can serve as a powerful probe of EWPT dynamics, significantly constraining or supporting first-order EWPT scenarios and guiding interpretation of cosmological implications such as electroweak baryogenesis.

Abstract

We argue that, within a broad class of extensions of the Standard Model, there is a tight corellation between the dynamics of the electroweak phase transition and the cubic self-coupling of the Higgs boson: Models which exhibit a strong first-order EWPT predict a large deviation of the Higgs self-coupling from the Standard Model prediction, as long as no accidental cancellations occur. Order-one deviations are typical. This shift would be observable at the Large Hadron Collider if the proposed luminosity or energy upgrades are realized, as well as at a future electron-positron collider such as the proposed International Linear Collider. These measurements would provide a laboratory test of the dynamics of the electroweak phase transition.