Investigation on the stabilities of doubly heavy tetraquark states

TL;DR

This study uses a nonrelativistic quark model to explore the stability of various doubly heavy tetraquark states, identifying some configurations as deeply bound and highlighting differences based on quark composition.

Contribution

The paper extends previous work by systematically analyzing the stability of doubly heavy tetraquarks with a complete harmonic oscillator basis, revealing specific configurations with significant binding energies.

Findings

The $ar{u}ar{s}cb$ tetraquark is deeply bound.

The $ar{u}ar{d}cb$ tetraquark is less bound due to isospin effects.

Complete harmonic oscillator bases are essential for accurate stability analysis.

Abstract

In our recent work\cite{Noh:2023zoq}, the mass and binding energy of $T_{cc}$ are found to be $3873$ MeV and $-2$ MeV, respectively, which align with the observations reported at LHCb\cite{LHCb:2021vvq}. Based on our latest quark model approach, we extend our search for other potentially stable configurations of doubly heavy tetraquarks using our nonrelativistic quark model described in Ref.~\cite{Noh:2023zoq}. Our numerical calculations indicate that the $\bar{u}\bar{s}cb$ configuration is deeply bound. However, the $\bar{u}\bar{d}cb$ configuration with the isospin symmetry in the light quark sector is relatively less bound. In this study, we emphasize a compulsory aspect for requiring a complete set of three dimensional harmonic oscillator bases through the discussion of the $\bar{u}\bar{s}cb$ configuration and investigate the essential differences between the $\bar{u}\bar{s}cb$ and $\bar{u}\bar{d}cb$ configurations.