Constraining the Higgs potential using multi-Higgs production

TL;DR

This paper reviews how next-to-leading-order electroweak corrections to double-Higgs production within effective field theories enhance sensitivity to Higgs self-couplings, aiding future collider measurements.

Contribution

It compares Standard Model and Higgs Effective Field Theory approaches to electroweak corrections, highlighting their impact on constraining Higgs self-interactions.

Findings

Both EFT approaches provide consistent constraints on Higgs self-couplings.

Electroweak corrections significantly improve sensitivity beyond leading order.

The study supports future collider efforts to probe Higgs potential.

Abstract

The Higgs self-couplings remain only weakly constrained by current Large Hadron Collider (LHC) measurements, leaving ample room for physics beyond the Standard Model that could modify the structure of the Higgs potential. Multi-Higgs production processes provide a particularly sensitive probe of deviations in both the Higgs trilinear and quartic self-couplings. In this note, we summarize the current status of next-to-leading-order electroweak (EW) corrections to double-Higgs production computed within the Standard Model Effective Field Theory and Higgs Effective Field Theory frameworks, emphasizing how these calculations introduce sensitivity to the Higgs self-couplings beyond what is accessible at leading order. We discuss the key conceptual and technical differences between the two effective field theory approaches, including their treatment of higher-dimensional operators, renormalization procedures, and the structure of EW~two-loop amplitudes. Despite these differences, both approaches yield broadly consistent constraints, illustrating the complementarity of double- and triple-Higgs measurements. With the high-luminosity LHC and future high-energy colliders on the horizon, these developments and further advances provide an essential foundation for extracting increasingly precise information on the dynamics of EW symmetry breaking.