Tetraquark mass relations in quark and diquark 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 $\bar q$.