The spectra of $bc\bar{b}\bar{c}$ tetraquark states from a diquark-antidiquark perspective

TL;DR

This paper predicts the mass spectra of fully heavy $bcar{b}ar{c}$ tetraquarks using a diquark-antidiquark model and Bethe-Salpeter equations, indicating these states are likely broad and above decay thresholds.

Contribution

It introduces a Bethe-Salpeter formalism for fully heavy tetraquarks within the diquark-antidiquark framework, providing numerical mass spectra predictions.

Findings

All $S$-wave tetraquark states are above decay thresholds.

Ground states are expected to be broad.

Mass spectra are obtained using covariant instantaneous approximation.

Abstract

Within the diquark-antidiquark framework, this study investigates the masses of ground-state tetraquarks composed of heavy charm ($c$) and bottom ($b$) quarks and antiquarks, using the Bethe-Salpeter formalism. We establish the Bethe-Salpeter equations for the fully heavy $bc\bar{b}\bar{c}$ tetraquarks to the leading order in $1/m_Q$ expansion. These equations are subsequently solved numerically under the covariant instantaneous approximation with kernels containing scalar confinement and one-gluon exchange terms. Our results show that the spectra of all possible $S$-wave tetraquark states are above the corresponding two lowest meson decay thresholds via the quark rearrangement. This implies that the ground $bc\bar{b}\bar{c}$ tetraquark states should be broad.