Tetraquark mass relations in quark and diquark models

TL;DR

This paper derives new linear mass relations for S-wave tetraquarks in quark and diquark models, which can help identify their internal structure and discriminate among theoretical models through comparison with experimental data.

Contribution

It introduces new mass relations for tetraquarks sensitive to internal degrees of freedom and explores their validity across different models, linking diquark and quark model frameworks.

Findings

Mass relations are accurate at the MeV level.

Relations can distinguish internal tetraquark structures.

Diquark models are special cases of quark models.

Abstract

We present new linear relations among the masses of S-wave tetraquarks with either one flavour ($QQ \bar Q \bar Q$) or two ($QQ\bar q \bar q$). Because the relations are sensitive to the hidden-colour, spin, and spatial degrees of freedom, comparison to experimental data can help to reveal the internal structure of tetraquarks, and discriminate among different theoretical models. Depending on the model, the relations are either exact, or valid in perturbation theory, and a thorough comparison with existing literature confirms their validity at the MeV level. Additionally, we explore the connections among tetraquark models, and show how those with effective (quark or diquark) masses are related to dynamical potential models. We also show how the spectrum of diquark models is effectively a limiting case of (more general) quark models, and in particular, that the diquark concept is most relevant in the particular combination $QQ\bar q \bar q$, where $Q$ is much heavier than $\bar q$.