Experimental searches for fully heavy flavored tetraquark states are actively pursued at the LHC. The LHCb, CMS, and ATLAS collaborations have investigated fully charmed $cc\overline{c}\overline{c}$, doubly charmed-bottom $bc\overline{b}\overline{c}$ and fully bottom $bb\overline{b}\overline{b}$ tetraquarks. Fully charmed states are probed as intermediate resonances in processes like $p+p\to J/\psi J/\psi$ and $p+p\to J/\psi {\mu }^{+}{\mu }^{-}$ at $\sqrt{s}=7,8$, and 13 TeV. Notably, narrow structures such as $X(6200)$, $X(6900)$, and $X(7300)$ observed in the di-$J/\psi$ mass spectrum have ignited theoretical interest. In this study, we use a nonrelativistic model to perform a detailed study of the mass spectra for the ground ($1S$) and excited ($1P$, $2S$, $1D$, $2P$, $3S$, and $4S$) states of fully heavy tetraquarks $Q_1{Q}_2{\overline{Q}}_1{\overline{Q}}_2$ $(Q_{1,2}\in \{b,c\})$ in the diquark-antiquark picture. Tetraquarks are modeled as color-singlet bound states build from an axial-vector diquark (${[Q_1{Q}_2]}_{s=1}$) and axial-vector antidiquark (${[{\overline{Q}}_1{\overline{Q}}_2]}_{s=1}$) in the $\overline{\mathbf{3}}$ and $\mathbf{3}$ color representations, respectively, bound together by color forces. With this setup, the Schrödinger equation is solved numerically for a modified version of the Cornell potential, using the three-point difference central method. The spin-dependent terms are dealt with nonperturbatively and are used to describe the splitting structure of the diquark. The tetraquark states are investigated for a wide range of $J^{PC}$ quantum numbers including $0^{++}$, $1^{+-}$, $2^{++}$ for $S$-waves, $0^{-+}$, $1^{-\pm }$, $2^{-\pm }$, $3^{--}$ for $P$-waves, and $0^{++}$, $1^{+\pm }$, $2^{+\pm }$, $3^{+\pm }$, $4^{++}$ for $D$-waves. Following the same line as many previous works, we attempt, through this study of tetraquark mass spectra, to provide their possible signatures in narrow structures recently discovered in the di-$J/\psi$ production spectrum by the LHCb, CMS, and ATLAS collaborations. Our results provide precise mass predictions, analyze stability against strong fall-apart decays, and are directly compared with recent LHC observations and other relevant theoretical models. Our findings supports the interpretation of these discovered exotic heavy resonances as the different excitations of the fully charmed tetraquark, offering a crucial guide for ongoing experimental identification.

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• Particle interactions