Investigating timing opportunities in ATLAS beyond Run 4

For ATLAS in Run 4 an upgrade of the Inner Detector to a fully Silicon based Inner Tracker has already been approved together with a High Granularity Timing Detector in the forward region with $|\eta| \in [2.4, 4.0]$. Due to the extreme environment close to the interaction point, the two innermost layers of the tracker are expected to be replaced after some years of data-taking. Here arises the opportunity to study and motivate a 4D tracking detector in the barrel region. The focus of my project has been to determine the precision of which the vertex $t_0$ can be found, which could have profound consequences on the physics as well as mitigating pile-up effects. With a simple iterative $\textit{a posteriori}$ 1D clustering of track times, removing pile-up contamination, it was shown that a resolution of 6 ps is possible assuming an $\eta$-independent trackt $t$ resolution of 30 ps.