Energy Growth in $V_L{V}_L\to V_L{V}_L,V_L{V}_{L}h$ Scattering to Probe Higgs Cubic and HEFT Interactions

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.

Comments: 28 pages, 3 tables, 7 figures, 5 appendices. v2: Journal version; added references, corrected equations, and minor text changes