Heavy tetraquarks in the diquark–antidiquark picture

Abstract

The homogeneous Lippmann–Schwinger integral equation is solved in momentum space to calculate the masses of heavy tetraquarks with hidden charm and bottom. The tetraquark bound states are studied in the diquark–antidiquark picture as a two-body problem. A regularized form of the diquark–antidiquark potential is used to overcome the singularity of the confining potential at large distances or small momenta. Our numerical results indicate that the relativistic effect leads to a small reduction in the mass of heavy tetraquarks, which is less than 2% for charm and less than 0.2% for bottom tetraquarks. The calculated masses of heavy tetraquarks for 1s, 1p, 2s, 1d and 2p states are in good agreement with other theoretical calculations and experimental data. Our numerical analysis predict the masses of heavy tetraquarks for 3s, 2d and 3p states for the first time, and we are not aware of any other theoretical results or experimental data for these states.