A review of the experiment, and the theory behind this, is sufficiently covered in APS Physics, and you do get free access to the actually paper itself in PRX. But after all the brouhaha, this is the conclusion we get:
The differing conclusions in these papers serve as a call to improve the quantum theory for radiation reaction. But it must be emphasized that the new data are too statistically weak to claim evidence of quantum radiation reaction, let alone to decide that one existing model is better than the others. Progress on both fronts will come from collecting more collision events and attaining a more stable electron bunch from laser-wakefield acceleration. Additional information could come from pursuing complementary experimental approaches to observing radiation reaction (for example, Ref. ), which may be possible with the next generation of high-intensity laser systems . In the meantime, experiments like those from the Mangles and Zepf teams are ushering in a new era in which the interaction between matter and ultraintense laser light is being used to investigate fundamental phenomena, some of which have never before been studied in the lab.
I know that they need very high-energy electron beam, but the laser wakefield technique that they used seem to be providing a larger spread in energy than what they can resolve:
Both experiments obtained only a small number of such successful events, mainly because it was difficult to achieve a good spatiotemporal overlap between the laser pulse and the electron bunch, each of which has a duration of only a few tens of femtoseconds and is just a few micrometers in width. A further complication was that the average energy of the laser-wakefield-accelerated electrons fluctuated by an amount comparable to the energy loss from radiation reaction.
I suppose this is the first step in trying to sort this out, and I have no doubt that there will be an improvement in such an experiment soon.