Resonance $X(7300)$: excited $2S$ tetraquark or hadronic molecule $\chi_{c1}\chi_{c1}$?

We explore the first radial excitation $X_{\mathrm{4c}}^{\ast}$ of the fully charmed diquark-antidiquark state $X_{\mathrm{4c}}=cc\overline{c}\overline{c}$ built of axial-vector components, and the hadronic molecule $\mathcal{M} =\chi_{c1}\chi_{c1}$. The masses and current couplings of these scalar states are calculated in the context of the QCD two-point sum rule approach. The full widths of $X_{\mathrm{4c}}^{\ast}$ and $\mathcal{M}$ are evaluated by taking into account their kinematically allowed decay channels. We find partial widths of these processes using the strong couplings $g_i^{\ast}$ and $G_i^{(\ast)}$ at the $X_{\mathrm{4c}}^{\ast}$($\mathcal{M}$ )-conventional mesons vertices computed by means of the QCD three-point sum rule method. The predictions obtained for the parameters $m=(7235 \pm 75)~ \mathrm{MeV}$, $\Gamma=(144 \pm 18)~\mathrm{MeV}$ and $\widetilde{m}=(7180 \pm 120)~\mathrm{MeV}$, $\widetilde{\Gamma}=(169 \pm 21)~\mathrm{MeV}$ of these structures, are compared with the experimental data of the CMS and ATLAS Collaborations. In accordance to these results, within existing errors of measurements and uncertainties of the theoretical calculations, both the excited tetraquark and hadronic molecule may be considered as candidates to the resonance $X(7300)$. Detailed analysis, however, demonstrates that the preferable model for $X(7300)$ is an admixture of the molecule $\mathcal{M}$ and sizeable part of $X_{\mathrm{4c}}^{\ast}$.