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The recent light-by-light scattering cross section measurement made by theATLAS\ Collaboration is used to constrain nonlinear corrections to Maxwellelectrodynamics parametrized by the Lagrangian $L=F+4\alpha F^{2}+4\betaG^{2}+4\delta FG$. The ion's radiation is described using the equivalent photonapproximation, and the influence of four different nuclear charge distributionsis evaluated. Special attention is given to the interference term between theStandard Model and the nonlinear corrections amplitudes. By virtue of thequadratic dependence on $\alpha$, $\beta$ and $\delta$, the nonlinearcontribution to the Standard Model $\gamma \gamma $ cross section is able todelimit a finite region of the parameter's phase space. The upper values for$\alpha$, $\beta$ in this region are of order $10^{-10}$GeV, a constraint of atleast $12$ orders of magnitude more precise when compared to low-energyexperiments. An upper value of the same order for $\delta$ is obtained for thefirst time in the LHC energy regime. We also give our predictions for theStandard Model cross section measured at ATLAS for each distribution andanalyze the impact of the absorption factor. We finally give predictions forthe future measurements to be done with upgraded tracking acceptance$\left\vert \eta \right\vert <4$ by the ATLAS Collaboration.

Constraining nonlinear corrections to Maxwell electrodynamics using $\gamma\gamma$ scattering