Determine the quantum numbers of $X(6900)$ from photon-photon fusion in ultra-peripheral heavy ion collisions

Abstract: We study the production of the $X(6900)$ through the $J/\psi J/\psi$ decay channel in the ultra-peripheral heavy ion collisions at the LHC energy region. The potential quantum numbers of $X(6900)$ would be $0^{\pm +}$ and $2^{\pm+}$. We find that the transverse momentum and the polar angle distributions of $X(6900)$ can be used to distinguish these four potential quantum numbers. These typical distributions stem from the linearly polarized photon from the fast-moving nuclei and can be measured with the LHC experiments in further.