Analyzing $t\bar{t}Z$-couplings at the future $e^-p$ collider

TL;DR

This work assesses how a future electron–proton collider (LHeC) can probe top quark neutral-current couplings to the Z boson via e^- p → e^- t t̄ in the semileptonic channel. By parameterizing deviations with ΔC_{1V}, ΔC_{1A}, C_{2V}, and C_{2A} and exploiting the azimuthal observable Δφ_{e^−ℓ}, the study demonstrates that differential, multi-bin χ^2 analyses significantly enhance sensitivity over inclusive rates. One-parameter fits show tightening bounds from the 10^-1 level at 50 fb^-1 to the 10^-2 level at 1000 fb^-1 for the vector/axial couplings, while tensor couplings remain at the 10^-1 level with modest gains at high luminosity. Correlations among couplings in two- and multi-parameter analyses broaden the allowed regions, with MCMC marginalization providing a realistic assessment of the parameter space and uncertainties. Overall, the LHeC offers complementary and competitive constraints on ttZ couplings relative to current LHC and future lepton colliders, highlighting the value of clean e^-p environments and differential observables in top-quark electroweak studies.

Abstract

The proposed Large Hadron Electron Collider (LHeC), with center-of-mass energy of $\sqrt{s}\approx 1.3$ TeV, provides a clean and sensitive environment to probe the top quark's neutral current interactions with the $Z$ boson via the process $e^- p \to e^- t \bar{t}$. We investigate the precision with which the Standard Model (SM) $t\bar{t}Z$ couplings-the vector and axial-vector components ($ΔC_{1V}$, $ΔC_{1A}$)-can be measured, along with possible new physics effects parameterized by higher-dimensional operators inducing weak electric and magnetic dipole-like interactions ($C_{2V}$, $C_{2A}$). Focusing on the semileptonic decay channel, where either the top quark or anti-top decays leptonically to a positively charged lepton ($\ell^+ = e^+, μ^+$), we utilize the azimuthal angle difference $Δφ$ between the scattered electron and the charged lepton as the key observable. Using a one-parameter multi-bin $χ^2$-analysis of this differential distribution, we find that constraints on $ΔC_{1V}$ and $ΔC_{1A}$ improve from order $10^{-1}$ at 50 fb$^{-1}$ to order $10^{-2}$ at 1000 fb$^{-1}$, corresponding to approximately 50% and 6% precision relative to their SM values. The anomalous tensor couplings $C_{2V}$ and $C_{2A}$ are constrained at the $10^{-1}$ level even at low luminosity and improve moderately with high luminosity. While the two-parameter analysis broadens the allowed regions due to parameter correlations, it retains competitive sensitivity, particularly for SM-like couplings. A systematic uncertainty of 5% is assumed throughout. These results highlight the LHeC's potential to provide complementary and competitive sensitivity to top-$Z$ couplings compared to current and future hadron and lepton collider capabilities.

Figures (9)

• Figure 1: Representative leading-order Feynman diagrams for the process $e^- p \to e^- t\bar{t}$: (a) the SM contributions mediated by $\gamma$ and $Z$ bosons, and (b) the new physics contribution probing the $t\bar{t}Z$ coupling, where the $t\bar{t}Z$ vertex is defined in Lagrangian \ref{['eq:ttZ-Lag']}.
• Figure 2: Total cross section for the process $e^{-} p \to e^{-} t \bar{t}$ in the semi-leptonic final state, shown as a function of each $t\bar{t}Z$ coupling parameter $C_i$, with all other couplings set to zero. The results are obtained for $\sqrt{s} \approx 1.3~\rm{TeV}$ at the LHeC.
• Figure 3: Normalized differential distributions of the azimuthal angle difference $\Delta \phi_{e^-\,\ell^\pm}$ between the final-state scattered electron $e^{-}$ and the charged lepton $\ell^\pm$, compared with the SM signal. The distributions are shown for benchmark BSM scenarios with coupling values $C_i$: (a) and (b) correspond to varying one coupling at a time ($C_i = 0.5$, others set to zero); (c) and (d) correspond to two couplings set simultaneously to $1.0$, with the remaining set to zero.
• Figure 4: The $\chi^2$ distributions obtained from the un-normalized $\Delta \phi_{e^-\,\ell^\pm}$ distribution, used as a sensitive observable for individual $t\bar{t}Z$ coupling parameters. The comparison is shown for the inclusive (web-blue) and differential (web-gray) cases, where the former corresponds to a single-bin (integrated) analysis and the latter to a multi-bin ($n$-bin) analysis. The results are presented for $\sqrt{s} \approx 1.3~\rm TeV$ and $\mathcal{L} = 50~\rm fb^{-1}$, using a threshold of $\chi^2 \approx 4$ to indicate the 95% confidence level, assuming $\delta_s = 5\%$.
• Figure 5: Projected 95% C.L. constraints on the individual BSM couplings as a function of the integrated luminosity, ranging from $10~\mathrm{fb}^{-1}$ to $1000~\mathrm{fb}^{-1}$, obtained from the one-parameter analysis using the inclusive-level (inclusive) and differential-level (multi-bin) approach, assuming $\delta_s = 5\%$. The results illustrate the improvement in sensitivity with increasing luminosity.