Structure of $cc \bar c \bar c$ tetraquarks and interpretation of LHC states

Motivated by recent experimental evidence for apparent $cc\bar c \bar c$ states at LHCb, CMS and ATLAS, we consider how the mass spectrum and decays of such states can be used to discriminate among their possible theoretical interpretations, with a particular focus on identifying whether quarks or diquarks are the most relevant degrees of freedom. Our preferred scenario is that $X(6600)$ and its apparent partner state $X(6400)$ are the tensor $(2^{++})$ and scalar $(0^{++})$ states of an S-wave multiplet of $cc\bar c \bar c$ states. Using tetraquark mass relations which are independent of (or only weakly dependent on) model parameters, we give predictions for the masses of additional partner states with axial and scalar quantum numbers. Additionally, we give predictions for relations among decay branching fractions to $J/\psi J/\psi$, $J/\psi \eta_c$, $\eta_c\eta_c$ and $D^{(*)} \bar{D}^{(*)}$ channels. The scenario we consider is consistent with existing experimental data on $J/\psi J/\psi$, and our predictions for partner states and their decays can be confronted with future experimental data, to discriminate between quark and diquark models.