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This is an extremely important paper, I will explain why in the thread below
As you probably are aware, the "standard model" physics theory used to describe elementary particles inside atoms is really good at describing things. It is also clear that it is what physicists call an effective theory, meaning it will not work at all energies
Other examples of successful effective theories are for example Newtons gravitational laws and Einstein's general theory of relativity. Both describe gravity, both are correct, but Newtons only works for small objects that do not move very fast.
The standard model is in a similar position as Newtonian gravity: it works great. But it can not be the entire picture, in extreme cases it stops working. This is why particle physicists look for new particles, that belong to the extra theory beyond the standard model
Now there are multiple ways to look for new particles. You can search for them directly. This is what is done in about ~50% of results that come from the LHC. There are a LOT of different searches for different particles as the expansions to the SM have very diverse predictions
But you can also search *indirectly* by picking parts of the standard model that are sensitive to new particles and measure if the standard model predicts these behaviours correctly. (This is what a large part of the rest of the LHC results does)
And one of the most sensitive predictions that has a sensitivity to new physics beyond the standard model is the so-called muonic magnetic moment; how the spin and magnetic behaviour of a muon are affected when a muon is immersed in a magnetic field.
The muon magnetic moment can be calculated ridiculously precisely by the standard model, this is what these authors have done, and to over 7 decimals precision! And it's off. The chance that the prediction is consistent with the measurement is less than 99.98%!
And soon, a very precise new experiment at @Fermilab has will this property even more accurately.
by the way, for those of you that think theorists are working alone in a room: this new calculation was a collaboration of over one hundred theoretical physicists (this also gives some appreciation of how difficult that calculation is, btw)
some exciting conclusions to this thread:

- these inconsistent results make it really convincing that the standard model is not the whole picture

- very soon a more precise measurement of the muon magnetic moment will be released (no pressure at all!!! Muon g-2 experiment)
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