Multidimensional analysis of particles

This paper analyses several features of fundamental and composite particles using a computational approach. Different distances are used to unravel the connections among particles emerging from their characteristics. Two clustering and visualization techniques are adopted, namely hierarchical clustering (HC) and multidimensional scaling (MDS), for comparing the particles’ attributes and portraying the results in a smaller number of dimensions. In the first phase, 31 fundamental particles are assessed under the light of 6 characteristics. The Canberra and Lorentzian distances adapt well to the data set producing graphical representations consistent with the present-day knowledge. In the second phase, 88 composite particles including 21 tetraquark and 7 pentaquark candidates, described by 10 characteristics, are considered. The different cases are represented and visualized using maps created by the HC and MDS techniques. The MDS exhibits superior performance for representing the pentaquark states. Additionally, the two computational tools are tested when representing (1) normalized numerical real-valued data, and (2) categorical data. The MDS reveals that the categories’ strategy captures better the main characteristics of the data set. The numerical measures allow assessing a few unmeasured spin-parity quantum numbers J P for 5 tetraquark candidates, namely the X (4020), X (4050), X (4055), X (4100), and X (4250). Therefore, algorithmic modeling proves to be a powerful tool for exploring numerical data sets with complex information.