Implementation and performance of the ATLAS pixel clustering neural networks

The high particle densities produced at the Large Hadron Collider (LHC) mean that in the ATLAS pixel detector the clusters of deposited charge start to merge. A neural network-based approach is used to estimate the number of particles contributing to each cluster, and to accurately estimate the hit positions even in the presence of multiple particles. The algorithm and its implementation are thoroughly described and a set of benchmark measurements is presented. The problem is most acute in the core of high-momentum jets where the average separation between particles becomes comparable to the detector granularity. This is further complicated by the high number of interactions per bunch crossing. Both these issues will become more acute as the Run 3 and HL-LHC program require analysis of higher and higher $p_{\mathrm{T}}$ jets, while the interaction multiplicity rises. Future prospects in the context of LHC Run 3 and the upcoming ATLAS inner detector upgrade are also discussed.