CP-violating ZZh Coupling at e+e- Linear Colliders

TL;DR

The work addresses CP violation in the Higgs–gauge sector by parameterizing the $ZZh$ vertex with CP-even and CP-odd form factors, notably the CP-odd coefficient $\tilde{b}$. It analyzes two production channels at e+e- colliders, $Zh$ production and $ZZ$ fusion, and constructs four CP asymmetries using polarized beams to access the real and imaginary parts of $\tilde{b}$, finding complementary sensitivity across channels. Simple polar-angle observables primarily probe $\mathcal{I}m(\tilde{b})$, while lepton-orientation variables access $\mathcal{R}e(\tilde{b})$, enabling robust coverage of the CP-odd coupling. Quantitatively, at $\sqrt{s}=500$ GeV$ with $\mathcal{L}=1000$ fb$^{-1}$ and realistic beams, the 95% CL limits reach $\mathcal{I}m(\tilde{b}) \approx 2\times10^{-3}$ and $\mathcal{R}e(\tilde{b}) \approx 1.7\times10^{-2}$, with higher energy and the $ZZ$ fusion channel enhancing sensitivity; overall, the results demonstrate the potential of future linear colliders to probe CP-violating Higgs–gauge couplings via asymmetry measurements.

Abstract

We study the general Higgs-weak boson coupling with CP-violation via the process e+e- -> f \bar f h. We categorize the signal channels by sub-processes Zh production and ZZ fusion and construct four CP asymmetries by exploiting polarized e+e- beams. We find complementarity among the sub-processes and the asymmetries to probe the real and imaginary parts of the CP-violating form factor. Certain asymmetries with unpolarized beams can retain significant sensitivity to the coupling. We conclude that at a linear collider with high luminosity, the CP-odd ZZh coupling may be sensitively probed via measurements of the asymmetries.

Figures (10)

• Figure 1: Vertex function for $ZZh$ coupling.
• Figure 2: Normalized mass distributions for $e^+e^- \to e^+e^- h$ at $\sqrt s=500\ \rm GeV$ with $m_h^{}=120\ \rm GeV$. The dashed curve is for the recoil mass in Eq. (\ref{['rec']}), and the solid is for the invariant mass $m_{ee}$.
• Figure 3: Total cross sections for $e^+e^- \to e^+e^- h$ in fb (a) versus $\sqrt s$ for representative values of $m_h^{}$, and (b) versus $m_h^{}$ for representative values of $\sqrt s$. The dashed curves are for $e^+e^- \to Zh \to e^+e^- h$ only. No kinematical cuts are imposed.
• Figure 4: Normalized polar angle distributions for $\sigma_{-+}$ at $\sqrt s=500\ \rm GeV$ with $m_h^{}=120\ \rm GeV$ for (a) $e^+e^- \to Z h$ with $Z\to f\bar{f}$, and (b) $e^+e^- \to e^+e^- h$ via $ZZ$ fusion. The solid curves are for the SM interaction ($a=1$), the dashed for the CP-odd (${\cal I}\!m(\tilde{b})=1$), and the dotted for CP violation with $a={\cal I}\!m(\tilde{b})=1$. $100\%$ longitudinal polarization of $e^-_L e^+_R$ has been used.
• Figure 5: Forward-backward asymmetries for $\sigma_{-+}$ versus ${\cal I}\!m(\tilde{b})$ at $\sqrt s=500\ \rm GeV$ with $m_h^{}=120\ \rm GeV$ for (a) $Zh\to f\bar{f} h$: asymmetry in fb, (b) $Zh\to f\bar{f} h$: percentage asymmetry, (c) $ZZ$ fusion: asymmetry in fb, and (d) $ZZ$ fusion: percentage asymmetry. The dashed curves are for $100\%$ longitudinal polarization $e_L^-e_R^+$, the solid for a realistic polarization $(e_L^-,e_R^+)=(80\%,60\%)$, and the dotted for unpolarized beams. The error bars are statistical uncertainties obtained with a luminosity of $1000\ \rm fb^{-1}$.