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They say the zero point energy in vacuume is infinite! But ask how we measure such, they say we actually measure the energy differences, ie potential energy. Such infinity-infinity=the answere they were looking for, which they call 'renormalization', is obviously nonsense. So they introduce another technique called 'regularization'. Here, we introduce a cuttof (this is where Planck's Length comes from). So we are realy not summing upto infinity. We must replace our equation with another one which surpresses the energy due to frequencies below Planck's length. This is because, so they say, at Planck's Length, we might need new physics (quantum gravity) to describe how the frequency is related to energy.
However, this new equation that dumps the vebrations below Planck's Length is nolonger the one predicted by any quantum equations (eg Schrodinger equation). They pulled it from thin air! Furthermore, this equation contradict QM as the demand that the zero point energy is strictly given by hf comes from uncertainty principle.
Also this shows that SM is wrong!! There is no way we could test Newt's law if in our calculations, we neaded to add in the interactions between an object with ever tiny air molecules and then at some point, we say hell, perhaps there is a new physics for subatomic interactions (QM)! We would only sum a few and regard Newt's Theory as falsified, should it not agree with experiments!
You see the problem? In Newt's law, the smaller the object, the lesser it contributes to the 'force', and so we could neglect the quantum effects, hence we could test Newt's law without having in mind a 'cut off' due to possibility of new physics for small objects (in this case quantum mechanics or QM ). However, in SM (Standard Model), the smaller the domain, the larger its contribution. This is due to the equation E=hf. (The larger the frequency the smaller the wavelength ). So the unknown physics at Planck's Length contributes the largest!! So there is no way we can test SM!
If we replace our equation for E=hf so that the higher frequencies contributes lesser, and completely dumps them at Planck's Frequency, as they do in regularization, then we contradict QM as strict zero-point energy as E=1/2hf comes from Heisenberg's Uncertainty Principle.
Such is how these goons do math to calculate g-factor! They 'swap the hat and pull out the rabbit'!
I had not known of the recent muon g-factor measurement. But your link did not contain anything. There is an error.
If you follow more on this, you will find that the supposed experiment does not challenge quantum theory (actually the standard model) in its domain. They are seeking for deviations in 5th or so decimal places.
Quantum guys normally boasts that standard model predict g-factor correct to 12 decimal places. But they use dubious maths that involves nonsensical use of zeroes and infinities, a technique they call 'renormalization' and 'regurlarization'. You can even see in this case of muon. Some are saying that they calculated and found a different solution! In other words they don't even know how to solve the equations! But they still call it 'prediction of standard model'. That is to say fitting calculations into data is still called a 'prediction'!!
Standard model invent new rules at every addition of new decimal place! For instance Feynman introduces 'propagators', 'quasi-particles', summing infinite waves (regardless the fact that it makes no mathematical sense), renormalization Feynman Diagrams etc. These rules were not there in previous quantum theory. So the 'prediction' of g-factor is actually its first prediction! If they introduce new rules in obtaining even farther decimal places, then the theory is actually worthless. This is the case! If you draw different Feynman Diagrams, you get different answers!