Supersimple analysis of $e^{-}{e}^{+}\to ZH$ at high energy

We study the process $e^{-}{e}^{+}\to ZH$ where $H$ represents the standard model (SM) Higgs particle $H_{\mathrm{SM}}$, or the minimal supersymmetric standard model (MSSM) ones $h^0$ and $H^0$. In each case, we compute the one-loop effects and establish very simple expressions, called supersimple (sim), for the helicity-conserving (dominant) and the helicity-violating (suppressed) amplitudes. Such expressions are then used to construct various cross sections and asymmetries, involving polarized or unpolarized beams and Z-polarization measurements. We examine the adequacy of such expressions to distinguish SM from MSSM effects or from other types of beyond the standard model contributions.

Figure 1

Energy dependence of the six Born helicity amplitudes at $\theta ={60}^{\circ }$, for the SM processes $e^{-}{e}^{+}\to ZH$ (upper left panel), and the MSSM processes $e^{-}{e}^{+}\to Z{h}^0$, $Z{H}^0$ (upper right and the lower panels, respectively). For the SUSY cases we use the S1 MSSM benchmark of [21].

Figure 2

The six $e^{-}{e}^{+}\to ZH$ SM amplitudes at $\theta =60°$, in the Born, one-loop and sim approximations, together with amplitudes containing “eff” BSM contributions. The upper row gives the HC amplitudes, while the HV ones are shown in the lower ones.

Figure 3

The six MSSM $e^{-}{e}^{+}\to Z{h}^0$ amplitudes at $\theta =60°$, for the S1 benchmark of [21], in the Born, one-loop and sim approximations. The upper row gives the HC amplitudes, while the HV ones are shown in the lower ones.

Figure 4

The unpolarized differential cross sections in SM (left panels) and the S1 MSSM benchmark [21] (right panels). The upper row describes energy dependence at $\theta =60°$; the middle (lowest) panels give the angular distributions at $\sqrt{s}=1\mathrm{TeV}$ ($\sqrt{s}=5\mathrm{TeV}$).

Figure 5

The $A_{LR}$ asymmetries for unpolarized $Z$, as defined in (27). See caption in Fig. 4.

Figure 6

The $A_{LR}$ asymmetries defined in (28), for a final $Z$ of helicity $\tau =0$. See caption in Fig. 4.

Figure 7

The $A_{LR}$ asymmetries defined in (28), for a final $Z$ of helicity $\tau =-1$. See caption in Fig. 4.

Figure 8

The $A_{LR}$ asymmetries defined in (28), for a final $Z$ of helicity $\tau =1$. See caption in Fig. 4.

Figure 9

$A^{\text{pol}Z}$ asymmetries defined in (30), for unpolarized ($e^{-}$, $e^{+}$) beams. See caption in Fig. 4.

Figure 10

$A^{\text{pol}Z}(\lambda )$ asymmetries defined in (31) for $e^{-}$ beams with definite helicity $\lambda =L$, $R$. See caption in Fig. 4.