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

Abstract

We study the $l^-l^+\to ν\barνZh$ 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 $l^-l^+\to ν\barνZ$ process.

Figures (13)

• Figure 1: Total cross sections of $e^{-}\mu^{+}\to\nu_e\bar{\nu}_\mu Z$ and $e^{-}\mu^{+}\to \nu_e\bar{\nu}_\mu Zh$ as a function of the collision energy. The helicity-dependent cross sections for $\lambda=0$ and $\pm1$ are also shown by red-dashed and blue-dotted lines, respectively, where $\lambda$ is the helicity of the Z boson in the $l^-l^+$ collision c.m. frame. Total cross sections of $e^{-}e^{+}\to Zh$ are also shown as a reference.
• Figure 2: Feynman diagrams for $e^-\mu^+\to \nu_{e}\bar{\nu}_{\mu}Z$.
• Figure 3: Total cross section of $e^{-}\mu^{+}\to \nu\bar{\nu}Z_{\lambda}$ for $\lambda=0$ as a function of the collision energy, where $\lambda$ is the helicity of the Z boson in the $e^-\mu^+$ collision c.m. frame. The solid line denotes the total cross section, while dashed (dotted) lines show contributions from the absolute value squared of each amplitude, as defined in Fig. \ref{['fig:vvz']}, in the FD (U) gauge.
• Figure 4: Rapidity distribution of the Z boson for $e^{-}\mu^{+}\to \nu\bar{\nu}Z_{\lambda}$ with $\lambda=0$ at $\sqrt{s}=1$ TeV, where $\lambda$ is the helicity of the Z boson in the $e^-\mu^+$ collision c.m. frame. The solid line denotes the observable distribution, while dashed (dotted) lines show contributions from the absolute value squared of each amplitude, as defined in Fig. \ref{['fig:vvz']}, in the FD (U) gauge.
• Figure 5: Rapidity distribution of the $Z$ boson for $e^{-}\mu^{+}\to \nu\bar{\nu}Z_{\lambda}$ with $\lambda=0$ at $\sqrt{s}=30\ \text{TeV}$. In both panels the solid lines denote the observable distribution. In the left panel the five individual contributions in the FD gauge are shown, while in the right panel contributions from the absolute value squared of the sum of the two or three amplitudes are shown.