Which experiments show that QED (and more generally the standard model) is correct? It is often stated that QED makes predictions correct up to many decimal places.
What are the experiments that show this? And all have to provide measurements up to 12 decimal places?
To my understanding you need at least two experiments with that precision, because first you need to determine the fine-structure constant and only then you can plug it in into the formula for predictions?
And technically, it would only show consistency between those two experiments with QED, but does not exclude that measuring another property is not predicted by QED?
 A: Some famous experiments that supported QFT are

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*Lamb–Retherford experiment: In 1947 this experiment showed physics beyond the relativistic quantum mechanics (RQM) founded by Dirac. In that same year, Hans Bethe explained this phenomenon using some new techniques. Interestingly Weisskopf derived it before Bethe but because of his insecurity about his mathematical abilities, he did not publish his results (which turned out to be correct). What's even more interesting is that when these people derived it QED was not yet known. Inspired by these techniques Tomonaga, Schwinger, Feynman, and Dyson later formulated QED. Lamb shift can be used to measure the fine-structure constant.

*Electron g-factor: It is exactly $-2$ in Diracs RQM. But QED predicts to a very great precision the experimental value which is $−2.00231930436256(35)\pm 1.7×10^{−13}$.

*Existence of Higgs boson: Because naively including mass in a gauge theory violates the gauge invariance, Anderson, Brout, Englert, Guralnik, Hagen, Higgs, Kibble, and 't Hooft have found an intelligent way (called Higgs mechanism) to give masses to gauge bosons using spontaneous symmetry breaking. This prediction was verified in 2012.

These are the most famous experiments. You can read the Precision tests of QED etc for less popular ones.

It is often stated that QFT makes predictions correct up to many decimal places.

This is not always true. In fact in the cosmological constant problem the prediction of $\Lambda$ is "the largest discrepancy between theory and experiment in all of science" and "the worst theoretical prediction in the history of physics". Depending on the Planck energy cutoff and other factors, the discrepancy is as high as 120 orders of magnitude.
