Enhancing Primary Vertex Association with Machine Learning at the LHCb Experiment

The correct association of the $B$ meson is of great importance for accurate lifetime measurements and measurements with missing energy. During Run 1 and Run 2, an average of one visible $p p$-collision, defined as primary vertex, was observed per bunch crossing. Starting in Run 3, after Upgrade 1, the number of visible $p p$-collisions increased to an average of five. Looking ahead to Run 5, after Upgrade 2, an average of 50 visible $p p$-collisions per bunch crossing is expected. Since the PV misassociation is highly correlated with the number of visible $p p$-collisions, the misassociation rate has been studied under Run 3 conditions. Therefore, Run 3 Monte Carlo samples for semi-leptonic decays with varying numbers of neutrinos in the final state have been employed. Utilizing a traditional approach in which a $B$ meson is assigned to the primary vertex with minimum impact parameter for a given event, a primary vertex misassociation rate up to parameter in an event, a PV-misassociation rate of up to $5.5\%$ was observed.\\ To improve the PV-misassociation rate, machine learning approaches have been explored. A simple Neural Network on PV-B binary classification resulted in an improvement of up to $1.3\%$ in the decay channel the Neural Network is trained on and is able to generalize to the other decay channels of interest. As a second approach, a heterogeneous Graph Neural Network was implemented, as it can be applied on a global event level. The heterogenous Graph Neural Network outperformed the simple Neural Network on the decay mode used for training, however, it does not generalize to the other decay channels. Since the heterogeneous Graph Neural Network is still a work in progress, significant improvements are expected after further investigation.