Higgs production in association with a Z boson at TeV-scale lepton colliders

We study the $l^-l^+\to \nu\bar{\nu}Zh$ process for future lepton colliders, whose cross section becomes larger than that for $l^-l^+\to Zh$ in the energy region above a few TeV. We classify the amplitudes into three main groups based on the topology of each Feynman diagram; vector boson scattering, $l^-W^+$ scattering, and $W^-l^+$ scattering, and study the interference patterns among the amplitudes. We show that subtle gauge cancellation among the amplitudes at high energies in the unitary gauge is absent in the recently proposed Feynman-diagram gauge, and the physical distributions can be interpreted by the contributions from each subgroup. We also find that the interference patterns in kinematical distributions of the Z boson can be understood by those in the $l^-l^+\to \nu\bar{\nu}Z$ process.