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

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 $\alpha$ and $\beta$ in this region are of order ${10}^{-10}{\mathrm{GeV}}^{-4}$, 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 $|\eta |<4$ by the ATLAS Collaboration.

Figure 1

Ultraperipheral collision of lead ions. Charged particles scattering with impact parameter greater than the sum of their radii. Quasivirtual photons emitted by the ions scatter produce a new pair of photons.

Figure 2

Plot of normalized nuclear charge distributions given in Table 1.

Figure 3

Leading-order diagram for the Standard Model $\gamma \gamma$ scattering. Leptons, quarks, and bosons $W^{\pm }$ are the main particles composing the loop.

Figure 4

Interaction vertex due to nonlinear correction terms $F^2$, $G^2$, and $FG$.

Figure 5

Phase space accessible to the parameters $\alpha$ and $\beta$ derived from (26) when $\delta =0$. The more restrictive blue region is obtained with a Yukawa distribution. The broader yellow region is obtained with all three distributions: Fermi with two parameters, Gaussian, and homogeneously charged sphere. The green line $\beta =\alpha$ are the values accessible to Born-Infeld–like theories.

Figure 6

Phase space accessible to the parameters $\alpha$ and $\delta$ derived from (26) for the special case when $\beta =0$. Due to symmetry of the inequation, this phase space also corresponds to $\alpha =0$.

Figure 7

Phase space accessible to the parameters $\alpha$ and $\delta$ derived from (26) when $\alpha =\beta$.