Higgs boson $ZZ$ couplings in Higgs-strahlung at the ILC

We derive the fully differential cross section of the Higgs-strahlung process $f\overline{f}\to Z\to Z(\to f_Z{\overline{f}}_Z)X(\to f_X{\overline{f}}_X)$, where $f$, $f_Z$, and $f_X$ are arbitrary fermions and $X$ is a spin-zero particle with arbitrary couplings to $Z$ bosons and fermions. This process with $f=e$ and $X=h$ ($h$ denotes the Higgs boson) is planned to be measured at the International Linear Collider to put constraints on the couplings $g_1$, $g_2$, $g_3$ of the Higgs boson to $Z$ bosons. Using the obtained fully differential cross section, we define the observables, measurement of which yields the tightest constraints on the couplings. Explicit dependences of these observables on $g_i$ are derived.

Figure 1

A Feynman diagram of the Higgs-strahlung.

Figure 2

Kinematics of process (1). The momenta of $f$, $\overline{f}$, $Z_1$, $X$, and $Z_2$ are shown in the $f\overline{f}$ rest frame; the momenta of $f_Z$ and ${\overline{f}}_Z$ are displayed in the $Z_2$ rest frame; and the momenta of $f_X$ and ${\overline{f}}_X$ are described in the $X$ rest frame. The $z$ axis is codirectional with the $X$ momentum while the $x$ and $y$ axes are arbitrary axes forming a right-handed system with the $z$ axis.

Figure 3

Plots of the observables $O_2,\dots ,O_6$ for $\frac{g_2}{g_1},\frac{g_3}{g_1}\in [-0.5,0.5]$.