Heavy Tetraquarks in the Diquark-Antidiquark Picture

TL;DR

This paper calculates the masses of heavy tetraquarks with hidden charm and bottom using a momentum-space integral equation, incorporating relativistic effects and a regularized potential, and predicts new states.

Contribution

It introduces a regularized diquark-antidiquark potential and provides the first theoretical mass predictions for higher excited heavy tetraquark states.

Findings

Masses agree with existing theories and data

Relativistic effects cause less than 2% mass reduction

New predictions for 3s, 2d, and 3p states

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.