Jet tagging algorithm of graph network with HaarPooling message passing

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 HaarPooling operation to analyze the events, called HaarPooling Message Passing neural network (HMPNet). In HMPNet, HaarPooling not only extracts the features of graph, but embeds additional information obtained by clustering of k-means of different particle features. We construct Haarpooling from five different features: absolute energy $\log E$, transverse momentum $\log p_T$, relative coordinates $(\Delta\eta,\Delta\phi)$, the mixed ones $(\log E, \log p_T)$ and $(\log E, \log p_T, \Delta\eta,\Delta\phi)$. The results show that an appropriate selection of information for HaarPooling enhances the accuracy of quark-gluon tagging, as adding extra information of $\log P_T$ to the HMPNet outperforms all the others, whereas adding relative coordinates information $(\Delta\eta,\Delta\phi)$ is not very effective. This implies that by adding effective particle features from HaarPooling can achieve much better results than solely pure message passing neutral network (MPNN) 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.