The Muon $g-2$ in Progress

Two next generation muon $g-2$ experiments at Fermilab in the US and at J-PARC in Japan have been designed to reach a four times better precision from 0.54 ppm to 0.14 ppm and the challenge for the theory side is to keep up in precision as far as possible. This has triggered a lot of new research activities. The main motivation is the persisting 3 to 4 $\sigma$ deviation between standard theory and experiment. As Standard Model predictions almost without exception match perfectly all other experimental information, the deviation in one of the most precisely measured quantities in particle physics remains a mystery and inspires the imagination of model builders. Plenty of speculations are aiming to explain what beyond the Standard Model effects could fill what seems to be missing. Here very high precision experiments are competing with searches for new physics at the high energy frontier lead by the Large Hadron Collider at CERN. Actually, the tension is increasing steadily as no new states are found which could accommodate the $g_\mu-2$ discrepancy. With the new muon $g-2$ experiments this discrepancy would go up at least to 6 $\sigma$, in case the central values do not move, up to 10 $\sigma$ could be reached if the present theory error could be reduced by a factor of two. Interestingly, the new $\alpha$ from Berkeley by R. H. Parker et al. Science 360, 191 (2018): $\alpha^{-1}({\rm Cs18})=137.035999046(27)$ gives an $a_e$ prediction $a_e=0.00115965218157(23)$ such that $a_e^{\rm exp}-a_e^{\rm the}=(-84\pm36)\times 10^{-14}$ shows a $- 2.3~ \sigma$ deviation now