[maho]

The main interesting thing about a high-precision measurement of the proton's magnetic moment is to compare the result to the magnetic moment of the antiproton. Depending on your string theory of choice, you should be able to see a difference between those two values. So far, they are identical within the measurement uncertainty.

The proton team (Mooser et al in Mainz) and antiproton team (Ulmer et al at CERN) are collaberating very closely, so any improvement in one apparatus leads to an improvement in the other.

The same groups are closely related to a group (Sturm et al in Mainz/Heidelberg) that measures the magnetic moment of the electron near a nucleus. The measurement precision is even higher, and QED gives predictions of similar precision, so these measurements are used as tests of QED.