# Anomalous magnetic moment [closed]

I have the two values of the anomalous magnetic moments:

$$a_{\mu}^{SM}=(1 165 917 760 \pm 662)\cdot 10^{-12} \\ a_{\mu}^{exp}=(1 165 920 910 \pm 630) \cdot 10^{-12}$$

Where the first is the theoretical and the latter the measured value.

I now have to tell how many standard deviations the theoretical value deviates from the measured value. Assuming both values are Gaussian.

Now to my question, how do i get the standard deviation $$\sigma$$ from the expectation value $$a_{\mu}^{exp}$$ and the knowledge that it is Gaussian?

There is also a second part to that question. I have to tell what the probability is whether this deviation is just a statistical fluctuation.

My problem with that second part is that i do not really understand what a statistical fluctuation is in that context and thus do not know which probability i have to calculate. My idea is that every value outside the first standard deviation is a statistical fluctuation, but i am not sure and couldn't find a fitting definition for this.

• forgot in the beginning to add the second part to the question. i now added it. – Elskrt Nov 1 '19 at 12:23

The number that comes after the "$$\pm$$" sign, is the uncertainty in the value (commonly the standard deviation for Gaussian distributions, for other distributions other measures are usually given, Lorentzian distributions for example, have undefined standard deviation and usually use the full width at half maximum).
The difference between the values (means) is $$\Delta a = 3150 \times 10^{-12}$$. If we take the SD from your experiment $$\sigma _{exp} = 630 \times 10^{-12}$$, then its clear that $$\Delta a \sim 5 \times \sigma_{exp}$$.