The precise measurement of the top-Higgs coupling is crucial in particle physics, offering insights into potential new physics Beyond the Standard Model (BSM) carrying \( \mathcal{CP} \) Violation (CPV) effects. In this paper, we explore the \( \mathcal{CP} \) properties of a Higgs boson coupling with a top quark pair, focusing on events where the Higgs state decays into a pair of b-quarks and the top-antitop system decays leptonically. The novelty of our analysis resides in the exploitation of two conditional Deep Learning (DL) networks: a Multi-Layer Perceptron (MLP) and a Graph Convolution Network (GCN). These models are trained for selected CPV phase values and then used to interpolate all possible values ranging from 0 to π/2. This enables a comprehensive assessment of sensitivity across all \( \mathcal{CP} \) phase values, thereby streamlining the process as the models are trained only once. Notably, the conditional GCN exhibits superior performance over the conditional MLP, owing to the nature of graph-based Neural Network (NN) structures. Specifically, for Higgs top coupling modifier set to 1, with \( \sqrt{s} \) = 13.6 TeV and integrated luminosity of 3 ab−1 GCN excludes the \( \mathcal{CP} \) phase larger than 5° at 95.4% Confidence Level (C.L). Our Machine Learning (ML) informed findings indicate that assessment of the \( \mathcal{CP} \) properties of the Higgs coupling to the \( t\overline{t} \) pair can be within reach of the High Luminosity Large Hadron Collider (HL-LHC), quantitatively surpassing the sensitivity of more traditional approaches.
