# High-energy behavior of strong-field QED in an intense plane wave

## TL;DR

This paper investigates the high-energy behavior of strong-field QED in intense plane waves, revealing that the previously predicted power-law scaling is specific to constant crossed fields, while general plane waves exhibit logarithmic energy dependence, with experimental tests feasible.

## Contribution

It demonstrates that the high-energy power-law scaling in strong-field QED is limited to constant crossed fields and clarifies the order of limits affecting the behavior in general plane waves.

## Key findings

- Power-law scaling applies only to constant crossed fields.
- High-energy corrections in general plane waves are logarithmic, like in vacuum.
- Experimental setups can test the power-law regime.

## Abstract

Analytical calculations of radiative corrections in strong-field QED have hinted that in the presence of an intense plane wave the effective coupling of the theory in the high-energy sector may increase as the $(2/3)$-power of the energy scale. These findings have raised the question of their compatibility with the corresponding logarithmic increase of radiative corrections in QED in vacuum. However, all these analytical results in strong-field QED have been obtained within the limiting case of a background constant crossed field. Starting from the polarization operator and the mass operator in a general plane wave, we show that the constant-crossed-field limit and the high-energy limit do not commute with each other and identify the physical parameter discriminating between the two alternative limits orders. As a result, we find that the power-law scaling at asymptotically large energy scales pertains strictly speaking only to the case of a constant crossed background field, whereas high-energy radiative corrections in a general plane wave depend logarithmically on the energy scale as in vacuum. However, we also confirm the possibility of testing the ``power-law'' regime experimentally by means of realistic setups involving, e.g., high-power lasers or high-density electron-positron bunches.