Abstract: The recent muon g-2 measurement at Fermilab confirms the previous BNL result, hence emphasizing the longstanding discrepancy between the experimental value and the Standard Model (SM) prediction based on the use of e+e- → hadrons data to evaluate the leading hadronic vacuum polarization (HVP). This is what I call the “old” muon g-2 puzzle. On the other hand, a recent lattice result by the BMW collaboration shows a tension with the above mentioned SM prediction (this constitutes the “new” g-2 puzzle).
In this talk I plan to summarize the overall situation concerning the two muon g-2 puzzles and, in particular, I discuss the possibility that new physics may contribute to the e+e- → hadrons cross-section to solve or at least alleviate the new g-2 puzzle.