Probe $CP$ violation in $H\to \gamma Z$ through forward-backward asymmetry

We suggest that the forward-backward asymmetry $(A_{FB})$ of the charged leptons in the $gg\to H\to \gamma Z\to \gamma {\ell }^{-}{\ell }^{+}$ process could be used to probe the $CP$-violating $H\gamma Z$ coupling when the interference from the $gg\to \gamma Z\to \gamma {\ell }^{-}{\ell }^{+}$ process is included. With $CP$ violation in $H\gamma Z$ coupling, the interference effect leads to a nonvanishing $A_{FB}$, which is also sensitive to the strong phase differences. The resonant and nonresonant strong phases together make $A_{FB}(\widehat{s})$ change sign around Higgs mass $M_H$. For the phenomenology study, we suggest the integral over the one-side mass region below $M_H$ to magnify the $A_{FB}$ strength.

Figure 1

The Feynman diagram of the process $gg\to H\to \gamma Z\to \gamma {\ell }^{-}{\ell }^{+}$. The $c_g$ and $c,\tilde{c}$ factors represent the $Hgg$ and $H\gamma Z$ effective couplings, respectively.

Figure 2

The Feynman diagram of the process $gg\to \gamma Z\to \gamma {\ell }^{-}{\ell }^{+}$.

Figure 3

The kinematic angles for the $gg\to H\to \gamma Z\to \gamma {\ell }^{-}{\ell }^{+}$ process. $\theta$ is the polar angle of the $Z$ boson in the $H$ (or $gg$) rest frame. ${\theta }_1$ is the angle of ${\ell }^{-}$ in the $Z$ boson rest frame. The $z$ axis of the $Z$ boson rest frame is defined as the $Z$ boson production momentum direction in the $H$ rest frame. ${\varphi }_1$ is the angle between $Z$ boson production and decay planes. This image was reproduced with minor changes from the leftmost image of Fig. 1 in Anderson et al., Ref. [17].

Figure 4

$\mathrm{Im}[{\tilde{\sigma }}_{H,\mathrm{box}}^{2\to 2}{]}_{++}$ versus $\sqrt{\widehat{s}}$ for different $\psi$ values. $M_H=126\mathrm{GeV}$, and ${\mathrm{\Gamma }}_H=4.3\mathrm{MeV}$.

Figure 5

Left panel: The $M_{\gamma Z}$ differential cross section for the $\xi =0$ (blue histogram) and $\xi =\frac{\pi }{2}$ (red histogram with error bars) cases. Right panel: The $M_{\gamma Z}$ differential cross section of only the interference part ($\propto |{\mathcal{A}}_H+{\mathcal{A}}_{\mathrm{box}}{|}^2-|{\mathcal{A}}_H{|}^2-|{\mathcal{A}}_{\mathrm{box}}{|}^2$) integrated over $\cos {\theta }_1$ from 0 to 1. The blue histogram is scaled by $\times 0.2$.

Figure 6

$d{\sigma }_{\mathrm{int}}/d\cos {\theta }_1$ versus $\cos {\theta }_1$ when $\xi =\frac{\pi }{2}$ for the [124, 126] GeV integral region (red histogram with error bars) and [124, 128] GeV integral region (blue histogram).