Search for noncommutative interactions in $$\gamma \gamma \rightarrow \gamma \gamma $$ γ γ → γ γ process at the LHC

Abstract 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 $$\gamma \gamma \rightarrow \gamma \gamma $$ γ γ → γ γ 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 $$\Lambda _{\mathrm {NC}} = 1.64(1.35)$$ Λ NC = 1.64 ( 1.35 ) TeV can be probed in the $$pp\rightarrow p(\gamma \gamma )p \rightarrow p'(\gamma \gamma )p'$$ p p → p ( γ γ ) p → p ′ ( γ γ ) p ′ 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.