Does the Ritus-Narozhny scaling survive in realistic finite-duration fields?
In plain words
The predicted breakdown was derived for an idealized field that never switches off, while real laser pulses last a finite time. Calculations for finite pulses find much milder growth of the corrections, so it is unclear whether any real field shows the breakdown.
Precise statement
The $(\alpha \chi^{2/3})^n$ loop scaling (Ritus-Narozhny conjecture) holds in an infinite constant crossed field; for finite plane-wave pulses at fixed intensity parameter $a0 = e E/(m c \omega)$ and growing particle energy, loop corrections to observables grow only logarithmically (Podszus and Di Piazza 2019; Ilderton 2019), with the constant-field behavior recovered only under a condition of the form $\chi$ $<< a0^{3}$ (approximate). Determine the region in the space of $a0, \chi$ and pulse phase duration in which n-loop corrections to physical observables (photon emission probability, pair yield, electron mass shift) scale as $(\alpha \chi^{2/3})^n$, and decide whether that region overlaps $\alpha \chi^{2/3} >\sim 1$ for any physically realizable background, including non-plane-wave fields such as colliding beams.
What would settle it
Explicit higher-loop calculations of observables in finite pulses and in beam-beam field configurations, mapping where the power-law scaling holds.
Status in the literature
Edwards and Ilderton (Phys. Rev. D, 2021) found, for inclusive observables with background-collinear degeneracies resummed to all orders in $\alpha$, an exponential rather than the conjectured power-law intensity dependence, while Di Piazza and Lopez-Lopez (2020) found vertex-correction asymptotics consistent with the conjecture.
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