High-intensity scaling in UV-modified QED

QED perturbation theory in a background field has been conjectured to break down for sufficiently high field intensity. The high-intensity behavior of a field theory is however intertwined with its high-energy (UV) behavior. Here we show that a UV modification of QED changes the high-intensity behavior of observables. Specifically we study nonlinear Compton scattering in a constant crossed field in QED with an additional Pauli term. In the UV modified theory the cross section exhibits a faster power-law scaling with intensity than in ordinary QED.

Figure 1

The upper contour choice for the integration in (39), to be complemented by its mirror image below the real axis. The mark on the imaginary axis indicates a pole of the integrand.

Figure 2

Asymptotic scalings with $\chi$ of integrals $J={\int }_0^{1}fds$ of the form (32) or (34), cf. subcaptions. Each dot represents one numerical integration. Lines indicate power law scaling, including asymptotic constants. In panels (b) and (f), the vertical axis shows $\mathrm{arcsisin}h(J/c)$ for a scale $c$; this interpolates symmetrically around 0 between a linear scale for values $\ll c$ and a logarithmic scale for values $\gg c$, allowing us to show both positive and negative values over a wide range of magnitudes. The steepness of the smaller-$\lambda$ curves as the integral changes sign is an artefact of using the same scale $c$ for all curves; see Fig. 5. Note that different $\lambda$ lead to very similar curves; this is explained by rescaling $t\mapsto t/|\lambda {|}^3$ in (38) and (39); see Appendix pp2 for details.

Figure 3

The integral $J={\int }_0^{1}s\chi z^{3/2}Ai(z+\lambda /\sqrt{z})ds$ scales as $\log \chi$ for $\lambda \le 0$; naive power counting would suggest ${\chi }^0$.

Figure 4

For any $\lambda \ne 0$, the argument of $\mathcal{A}(z+\lambda /\sqrt{z})$ bends away from the straight line for small $z$, making the $\lambda \ne 0$ case qualitatively different from the $\lambda =0$ case in integrals like (32).

Figure 5

The data from Figs. 2 and 2, normalized to the asymptotic constant value $J_{\infty }$ for each $\lambda$.