Meson properties and symmetry emergence based on the deep neural network

As a key property of hadrons, the total width is quite difficult to obtain in theory due to the extreme complexity of the strong and electroweak interactions. In this work, a deep neural network model with the Transformer architecture is built to precisely predict meson widths in the range of 10^-14 ∼ 625 MeV based on meson quantum numbers and masses. The relative errors of the predictions are 0.12%, 2.0%, and 0.54% in the training set, the test set, and all the data, respectively. We present the predicted meson width spectra for the currently discovered states and some theoretically predicted ones. The model is also used as a probe to study the quantum numbers and inner structures for some undetermined states including the exotic states. Notably, this data-driven model is investigated to spontaneously exhibit good charge conjugation symmetry and approximate isospin symmetry consistent with physical principles. The results indicate that the deep neural network can serve as an independent complementary research paradigm to describe and explore the hadron structures and the complicated interactions in particle physics alongside the traditional experimental measurements, theoretical calculations, and lattice simulations.