The hadronic contributions to muon g-2 from lattice QCD

Fermilab announced a new experimental result for muon g-2 on August 10, 2023. The statistical uncertainty of the new result is smaller than the previous experiments by a factor of two and the central value is consistent. A result with even more statistics from Fermilab is expected in the coming years. For the Standard Model prediction, the two hadronic contributions, HVP (hadronic vacuum polarization) and HLbL (hadronic light-by-light) are the dominant sources of uncertainty. Currently, there is a tension between the lattice QCD calculations and the dispersion-relation based data-driven approach in the determination of the HVP contribution. We are trying to resolve this tension and reach a consensus on the theoretical determination of muon g-2. I will report the efforts from the lattice side, and also the progress of improving the overall precision of the theoretical prediction of muon g-2 from lattice.