Fully charmed tetraquark production at the LHC experiments

We develop the formalism for production of a fully heavy tetraquark and apply it to the calculation of $pp\to T_{4c}+X$ cross-sections. We demonstrate that the production cross-section of a fully heavy tetraquark, even if it is a diquark-antidiquark cluster, can be obtained in the meson-like basis, for which the spin-color projection technique is well established. Prompted by the recent LHCb, ATLAS and CMS data, we perform a pQCD calculation of ${\cal O}(\alpha_s^5)$ short-distance factors in the dominant channel of gluon fusion, and match these to the four-body $T_{4c}$ wave functions in order to obtain the unpolarized $T_{4c}(0^{++},1^{+-},2^{++})$ cross-sections. The novelty in comparison with the recently published article~\cite{Feng:2023agq} lies in the fact that we predict the absolute values as well as the $d\sigma/dp_T$ spectra in the kinematic ranges accessible at the ongoing LHC experiments. From the comparison with the signal yield at LHCb we derive the constraints on the $\Phi\cdot\text{Br}(J/\psi\,J/\psi)$ (reduced wave function times branching) product for the $T_{4c}$ candidates for $X(6900)$ and observe that $X(6900)$ is compatible with a $2^{++}(2S)$ state.