The proposed Large Hadron electron Collider (LHeC), with a center-of-mass energy of $\sqrt{s}\approx 1.3\mathrm{TeV}$, provides a clean and sensitive environment to probe the top quark’s neutral current interactions with the $Z$ boson via $e^{-}p\to e^{-}t\overline{t}$. We investigate the precision with which the Standard Model (SM) $t\overline{t}Z$ couplings—the vector and axial-vector components ($\mathrm{\Delta }{C}_{1V},\mathrm{\Delta }{C}_{1A}$) can be measured, along with possible new physics effects parametrized by higher-dimensional operators inducing weak electric and magnetic dipolelike interactions ($C_{2V},C_{2A}$). Focusing on the semileptonic decay channel, where either the top quark decays leptonically to a positively charged lepton (${\ell }^{+}=e^{+},{\mu }^{+}$) and the antitop hadronically, or vice versa, we utilize the azimuthal angle difference $\mathrm{\Delta }{\varphi }_{e^{-}{\ell }^{\pm }}$ between the scattered electron and the charged lepton ${\ell }^{\pm }$ as the key observable to derive projected constraints. Using a one-parameter multibin ${\chi }^2$ analysis of the differential $\mathrm{\Delta }{\varphi }_{e^{-}{\ell }^{\pm }}$ distribution, the constraints on $\mathrm{\Delta }{C}_{1A}$ improve from $\mathcal{O}({10}^{-1})$ at $50{\mathrm{fb}}^{-1}$ to $\mathcal{O}({10}^{-2})$ at $1000{\mathrm{fb}}^{-1}$, while the improvement for $\mathrm{\Delta }{C}_{1V}$ remains within the same order of magnitude, $\mathcal{O}({10}^{-1})$. These results correspond to average relative precisions of approximately 8% and 68%, respectively, with respect to their SM values. The anomalous tensor couplings $C_{2V}$ and $C_{2A}$ are constrained at the $\mathcal{O}({10}^{-1})$ level even at low luminosity and improve moderately with increasing luminosity. While the two-parameter analysis broadens the allowed regions due to parameter correlations, it maintains competitive sensitivity, particularly for the SM-like couplings. Throughout, we assume a systematic uncertainty of ${\delta }_s=5\%$ in all analyses, and all results are quoted at the 95% confidence level. These results demonstrate the LHeC’s potential to provide complementary and competitive sensitivity to top-$Z$ couplings compared to current and future hadron and lepton collider capabilities.

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• W & Z bosons
• Top quark
• Lepton-hadron colliders