> This paper is saying that the discrepancy has been solved by using a more fancy set of computations
That's underselling an important point I think. Here's my understanding of it:
There have been two methods to provide the theoretical value, one based on calculating loop corrections, the so-called data-driven approach, and one based on lattice QCD.
From what I can gather, the point in the paper is rather that they stopped using the data-driven prediction, and relied solely on the lattice QCD prediction. This is unlike the previous paper where they combined the two predictions into one.
The former method requires a bunch of measured data as inputs, like how frequently many different interactions happens in nature (their cross-section). It requires more theoretical work, figuring out the loop correction formulas, and all those measurements, but once you have that you can relatively quickly compute the result.
What happened was that one very important cross-section was measured significantly better, but it disagreed with all former measurements. This despite very thorough cross-checking of the experiment. So when those new results were plugged in, the data-driven method gave a much worse prediction.
Meanwhile, the latter method is more brute-force, and relies on simulating QCD on a lattice[1]. A much more complex version of those water simulations used in movies and such. Due to how the physics is, it's very expensive to simulate, and thus the simulations haven't been quite good enough. Recent improvements to the method has changed that, making its predictions in line with the measured value.
The authors states fixing the data-driven method is of high importance, so hopefully this will be fully resolved in the future.
At least that's my armchair understanding.
[1]: https://en.wikipedia.org/wiki/Lattice_QCD