Search for noncommutative interactions in $\gamma \gamma \to \gamma \gamma $ process at the LHC

The noncommutative QED (NCQED) has a non-Abelian nature due to the presence of 3- and 4-photon vertices in the lagrangian. Thus, NCQED predicts a new physics contribution to the $\gamma \gamma \to \gamma \gamma $ scattering already at the tree level. We have examined NCQED by studying the light-by-light process at the 14 TeV LHC with intact protons. Our results show that the NC scale up to ${\Lambda }_{\mathrm{NC}}=1.64\left(1.35\right)$ TeV can be probed in the $pp\to p\left(\gamma \gamma \right)p\to {p}^{\prime }\left(\gamma \gamma \right){p}^{\prime }$ collision for the time-space (space-space) NC parameters. These bounds are stronger than the limits that can be obtained in the light-by-light scattering at high energy linear colliders.