Abstract
The recent light-by-light scattering cross section measurement made by the ATLAS\ Collaboration is used to constrain nonlinear corrections to Maxwell electrodynamics parametrized by the Lagrangian $L=F+4\alpha F^{2}+4\beta G^{2}+4\delta FG$. The ion's radiation is described using the equivalent photon approximation, and the influence of four different nuclear charge distributions is evaluated. Special attention is given to the interference term between the Standard Model and the nonlinear corrections amplitudes. By virtue of the quadratic dependence on $\alpha$, $\beta$ and $\delta$, the nonlinear contribution to the Standard Model $\gamma \gamma $ cross section is able to delimit 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 at least $12$ orders of magnitude more precise when compared to low-energy experiments. An upper value of the same order for $\delta$ is obtained for the first time in the LHC energy regime. We also give our predictions for the Standard Model cross section measured at ATLAS for each distribution and analyze the impact of the absorption factor. We finally give predictions for the future measurements to be done with upgraded tracking acceptance $\left\vert \eta \right\vert <4$ by the ATLAS Collaboration.
Highlights
Maxwell electrodynamics is one of the most successful theories in physics
The efforts to quantize the theory of electrodynamics helped to lay the foundations of quantum field theory
We focus our study on nonlinear corrections to Maxwell electrodynamics, which includes nonlinear electrodynamics (NLED) in regimes where their Lagrangians can be correctly described by the first terms of their respective MacLaurin series
Summary
Maxwell electrodynamics is one of the most successful theories in physics. Since its publication in 1873, it has been the source of notable predictions, such as electromagnetic waves, and served as a keystone for the proposal of new theories, such as Einstein’s special relativity. Following a “bottom-up” approach, its Lagrangian can be derived imposing a Lorentz invariant gauge theory with Uð1Þ symmetry and second-order linear equations of motion for the potentials [2] In this way, generalizations of Maxwell electrodynamics can be obtained by breaking at least one of the restrictions mentioned above. Low-energy experiments, such as PVLAS [12] and BMV [13], are built to detect the presence of magnetic birefringence by measuring the ellipticity acquired by a linearly polarized beam after traversing a magnetic field While their current results are compatible with zero, they can be used to restrict a region of the parameter space constraining nonlinear corrections, such as was done in Ref. When compared to the free Lagrangian, these terms dominate at high-energy regimes where their effects become relevant For this reason, the light-by-light scattering cross section may be used to obtain today’s most precise constraints for nonlinear corrections to Maxwell electrodynamics.
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