Role of angular observables in probing non-standard $HZZ$ couplings at an electron-proton collider

In this study, we explore various lab-frame angular observables at Large Hadron-electron Collider (LHeC) to test their sensitivity on the most general structure of the Higgs ($H$) to neutral weak boson ($Z$) coupling ($HZZ$) via the process $e^- p \rightarrow e^- H j$ at the center of mass energy $\sqrt{s}~\approx$ 1.3 TeV. The most general Lorentz structure of the $HZZ$ coupling beyond the standard model is composed of two CP-even ($\lambda_{1Z}$ and $\lambda_{2Z}$) and one CP-odd (${\tilde \lambda_Z}$) components. In a previous study, we looked at the absolute value of azimuthal correlation ($|\Delta \phi|$) between the final state electron and the jet to derive constraints on the non-standard $HZZ$ couplings. This choice of observable is motivated by its potential to discriminate between CP-odd and CP-even couplings in the $e^- p \rightarrow \nu_e H j$ process. Since the process $e^- p \rightarrow e^- H j$ has an electron in the final state, one can construct more angular observables. In addition to $|\Delta \phi|$, we identify new angular observables: the sign-sensitive azimuthal correlation ($\Delta \phi$) and the polar angle of the final state electron ($\theta$), suitable for constraining non-standard $HZZ$ coupling. Our analysis shows that these new angles improve the constraints on $\lambda_{2Z}$ and ${\tilde \lambda}_Z$ in the range of 48-67\%. We also study the potential of the asymmetry in $\Delta \phi$ to constrain the parameters corresponding to the CP-odd coupling.