Energy Growth in $V_LV_L\to V_LV_L,\ V_LV_Lh$ Scattering to Probe Higgs Cubic and HEFT Interactions

TL;DR

This paper analyzes the energy scales at which perturbative unitarity breaks down in vector boson and Higgs scattering processes within HEFT, to identify the most sensitive channels for probing Higgs sector modifications at high energies.

Contribution

It compares unitarity violation scales in different scattering processes within HEFT, highlighting the potential of $V_L V_L h$ final states for collider studies.

Findings

Unitarity violation scales are similar for $V_L V_L o V_L V_L h$ and $V_L V_L o hhh$ processes.

$V_L V_L h$ final states are more experimentally feasible due to higher branching ratios.

Unitarity violation occurs in both $V_L V_L$ and $hh$ channels, with comparable or lower energy scales in $V_L V_L$ processes.

Abstract

We compute the energy scales of perturbative unitarity violation in $V_L V_L \to V_L V_L h$ processes and compare them to $V_L V_L \to hhh$ process, where $V_L$ refers to a longitudinal mode of $Z$ or $W$ boson, and $h$ the Higgs boson. Using these energy scales, we determine which process is more sensitive to potential modifications in the Higgs sector at high-energy colliders. Within the Higgs Effective Field Theory (HEFT), we consider the Higgs cubic coupling and other interactions with and without derivatives. Any HEFT interactions predict the perturbative unitarity violation at a finite scale, and in a generic case, the minimalistic process is $2\to 3$ scattering. Our analysis reveals that the energy scales for unitarity violation in $V_L V_L \to V_L V_L h$ and $V_L V_L \to hhh$ processes are similar across all scenarios considered. If the backgrounds are similar, $V_L V_L h$ final states are more feasible because $V_L V_L h$ has higher branching ratios in cleaner decay modes than $hhh$. We also investigate HEFT derivative interactions derived from various UV models. In these cases, both $V_L V_L \to V_L V_L$ and $V_L V_L \to hh$ processes exhibit unitarity violating behavior. We demonstrate that the energy scales for unitarity violation in $V_L V_L$ final states are comparable to or even lower than those in the $hh$ final state.