Two-photon decay of X(6900) from light-by-light scattering at the LHC

Abstract

The LHCb Collaboration has recently discovered a structure around 6.9 GeV in the double-$J/\ensuremath{\psi}$ mass distribution, possibly a first fully charmed tetraquark state $X(6900)$. Based on vector-meson dominance (VMD) such a state should have a significant branching ratio for decaying into two photons. We show that the recorded LHC data for the light-by-light scattering may indeed accommodate for such a state, with a $\ensuremath{\gamma}\ensuremath{\gamma}$ branching ratio of order of ${10}^{\ensuremath{-}4}$, which is larger even than the value inferred by the VMD. The spin-parity assignment ${0}^{\ensuremath{-}+}$ is in better agreement with the VMD prediction than ${0}^{++}$, albeit not significantly at the current precision. Further light-by-light scattering data in this region, clarifying the nature of this state, should be obtained in the Run 3 and probably in the high-luminosity phase of the LHC (Run 4 etc.).