Higgs production in association with a Z boson at high-energy lepton colliders

Abstract We study Higgs production in association with a Z boson via vector boson scattering (VBS Vh production) at future lepton colliders, whose cross section becomes larger than for $$l^-l^+\rightarrow Zh$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>l</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:msup> <mml:mi>l</mml:mi> <mml:mo>+</mml:mo> </mml:msup> <mml:mo>→</mml:mo> <mml:mi>Z</mml:mi> <mml:mi>h</mml:mi> </mml:mrow> </mml:math> at high energies. We classify the amplitudes into three main groups based on the topology of each Feynman diagram; VBS, $$l^-W^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>l</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> scattering, and $$W^-l^+$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>W</mml:mi> <mml:mo>-</mml:mo> </mml:msup> <mml:msup> <mml:mi>l</mml:mi> <mml:mo>+</mml:mo> </mml:msup> </mml:mrow> </mml:math> scattering, and study the interference patterns among the amplitudes. We show that gauge cancellation among the amplitudes at high energies in the unitary gauge is absent in the Feynman diagram gauge, and the physical distributions can be interpreted by the contributions from each subgroup.