High Energy Vector Boson Scattering in Four-Body Final States to Probe Higgs Cubic, Quartic, and HEFT interactions

TL;DR

This paper analyzes high-energy vector boson scattering in four-body final states to explore modifications in Higgs self-couplings and effective interactions, highlighting the potential of 2→4 processes for future collider experiments.

Contribution

It provides a detailed comparison of unitarity violation scales and cross sections for 2→3 and 2→4 vector boson scattering processes in various Higgs interaction scenarios.

Findings

2→4 processes show lower unitarity violation scales in modified Higgs potentials.

Cross sections for 2→4 processes increase with energy, offering more high-energy events.

2→4 processes are less beneficial for probing derivative interactions in HEFT.

Abstract

We compute the energy scales of perturbative unitarity violation in various $2 \to 4$ vector boson scattering (VBS) processes and compare them to lower multiplicity processes. The final states include $h^4$, $V_L V_L h h$, and $V_L^4$, where $V_L$ represents the longitudinal mode of $Z$ or $W$ boson, and $h$ the Higgs boson. We consider scenarios with modified cubic and quartic Higgs self-couplings, including those derived from the Standard Model Effective Field Theory (SMEFT), as well as scenarios involving derivative operators from Higgs Effective Field Theory (HEFT). Modified Higgs self-couplings typically lead to perturbative unitarity violation in at least the $2\to 3$ VBS; however, the corresponding energy scales of unitarity violation are often very high. Our analysis reveals that, in the case of modified Higgs potentials, $2\to4$ processes exhibit significantly lower energy scales of unitarity violation compared to $2 \to 3$ processes. This, combined with the fact that the cross sections of $2 \to 4$ processes increase with energy, suggests they generate more signal events at high energies, $\sqrt{\hat{s}} \gtrsim 2$ TeV, which could be achieved in future colliders. In contrast, for HEFT derivative interactions, higher multiplicity offers diminished benefits, as $2 \to 4$ cross sections are often smaller than those of related $2 \to 3$ processes within the valid energy range. This study shows that $2 \to 4$ VBS processes are particularly compelling for probing Higgs potential modification, including the cubic and quartic couplings, but are less advantageous when derivative interactions dominate.