Towards 6D Tracking: A Study Of Using Fast-Timing For Measuring Track Position, Time, And Angles

Current and next-generation particle tracking detectors will incorporate precision timing capabilities with resolutions approaching tens of picoseconds. Using Technology Computer-Aided Design (TCAD) simulations of Low-Gain Avalanche Diode (LGAD) detectors, we demonstrate that oblique particle incidence induces systematic timing variations of hundreds of picoseconds across multiple pixels. We derive an analytical linear model relating inter-pixel timing differences to incident track angles, enabling single-layer angular reconstruction with few-degree precision. Stochastic energy loss fluctuations (Landau fluctuations) impose fundamental limits on both angular resolution and reconstruction efficiency. Comparison with neural network approaches demonstrates that the linear model achieves near-optimal angular resolution, indicating that the physics of charge collection geometry, rather than algorithmic sophistication, dominates the achievable performance.