  Lattice QCD (LQCD) studies for the hadron vacuum polarization (HVP) and its
contribution to the muon anomalous magnetic moment (muon g-2) are reviewed.
There currently exists more than 3-sigma deviations in the muon g-2 between the
BNL experiment with 0.5 ppm precision and the Standard Model (SM) predictions,
where the latter relies on the QCD dispersion relation for the HVP. The LQCD
provides an independent crosscheck of the dispersive approaches and important
indications for assessing the SM prediction with measurements at
ongoing/forthcoming experiments at Fermilab/J-PARC (0.14/0.1 ppm precision).
The LQCD has made significant progress, in particular, in the long distance and
finite volume control, continuum extrapolations, and QED and strong isospin
breaking (SIB) corrections. In the recently published papers, two LQCD
estimates for the HVP muon g-2 are consistent with No New Physics while the
other three are not. The tension solely originates to the light-quark connected
contributions and indicates some under-estimated systematics in the large
distance control. The strange and charm connected contributions as well as the
disconnected contributions are consistent among all LQCD groups and determined
precisely. The total error is at a few percent level. It is still premature by
the LQCD to confirm or infirm the deviation between the experiments and the SM
predictions. If the LQCD is combined with the dispersive method, the HVP muon
g-2 is predicted with 0.4% uncertainty, which is close upon the target
precision required by the Fermilab/J-PARC experiments. Continuous and
considerable improvements are work in progress, and there are good prospects
that the target precision will get achieved within the next few years.
