Towards 6D Tracking: A Study Of Using Fast-Timing For Measuring Track Position, Time, And Angles
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 tilted particle tracks traversing multiple pixels exhibit systematic timing variations of hundreds of picoseconds between adjacent pixels. We derive an analytical linear model relating inter-pixel timing differences to incident track angles, enabling single-layer angular reconstruction with a precision of a few degrees for tracks which traverse at least three pixels. Stochastic energy loss fluctuations (Landau fluctuations) impose a fundamental limit 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 angular resolution.