Masses of the $QQ\bar Q\bar Q$ tetraquarks in the relativistic diquark--antidiquark picture

TL;DR

This paper calculates the masses of heavy $QQ\bar Q\bar Q$ tetraquarks using a relativistic diquark-antidiquark model, predicting broad decay structures that could match recent LHCb observations.

Contribution

It introduces a relativistic quark model with non-point-like diquarks to compute tetraquark masses, considering internal diquark structure and decay thresholds.

Findings

All tetraquarks are above decay thresholds to heavy quarkonia.

Predicted broad structures decay mainly to quarkonia.

Possible identification of a $2^{++}$-state tetraquark near di-$J/\psi$ threshold.

Abstract

Masses of the ground-state teraquarks composed from heavy $c$ and $b$ quarks and antiquarks are calculated in the diquark-antidiquark picture in the framework of the relativistic quark model based on the quasipotential approach. The quasipotentials of the quark-quark and diquark-antidiquark interactions are constructed similarly to the previous consideration of mesons and baryons. It is assumed that the diquark and antidiquark interact in the tetraquark as a whole and the internal structure of the diquarks is taken into account. All such tetraquarks are found above the thresholds of decays to two heavy quarkonia. This is a result of the consideration of the diquark not to be a point-like object. Therefore such tetraquarks can be observed as broad structures decaying dominantly to quarkonia. The broad structure next to the di-$J/\psi$ mass threshold, recently observed by the LHCb Collaboration, can correspond to the ground $2^{++}$-state tetraquark consisting of four charm quarks.