Jet tagging algorithm of graph network with Haar pooling message passing

Abstract

Recently, methods of graph neural networks (GNNs) have been applied to solving the problems in high-energy physics (HEP) and have shown its great potential for quark-gluon tagging with graph representation of jet events. In this paper, we introduce an approach of GNNs combined with a Haar pooling operation to analyze the events, called Haar pooling message passing neural network (HMPNet). In HMPNet, Haar pooling not only extracts the features of graph, but embeds additional information obtained by clustering of $k$ means of different particle features. We construct Haar pooling from five different features: absolute energy $\mathrm{log}E$, transverse momentum $\mathrm{log}{p}_{T}$, relative coordinates $(\mathrm{\ensuremath{\Delta}}\ensuremath{\eta},\mathrm{\ensuremath{\Delta}}\ensuremath{\phi})$, the mixed ones $(\mathrm{log}E,\mathrm{log}{p}_{T})$, and $(\mathrm{log}E,\mathrm{log}{p}_{T},\mathrm{\ensuremath{\Delta}}\ensuremath{\eta},\mathrm{\ensuremath{\Delta}}\ensuremath{\phi})$. The results show that an appropriate selection of information for Haar pooling enhances the accuracy of quark-gluon tagging, as adding extra information of $\mathrm{log}{P}_{T}$ to the HMPNet outperforms all the others, whereas adding relative coordinates information $(\mathrm{\ensuremath{\Delta}}\ensuremath{\eta},\mathrm{\ensuremath{\Delta}}\ensuremath{\phi})$ is not very effective. This implies that, by adding effective particle features from Haar pooling, one can achieve much better results than that which a solely pure message passing neutral network can do, which demonstrates significant improvement of feature extraction via the pooling process. Finally, we compare the HMPNet study, ordering by ${p}_{T}$, with other studies and prove that the HMPNet is also a good choice of GNN algorithms for jet tagging.