| Abstract | We present the latest lattice results for the hadronic vacuum polarization from lattice QCD. In order to isolate the different origin of systematic errors in lattice computations, the observable is decomposed into several windows. The latest discrepancy between the data-driven theory prediction of the intermediate and long distance window of the hadronic vacuum polarization using the experimental input of e+e- to hadrons cross-section and the lattice predictions have sparked several new physics scenarios. We elaborate on the Mainz results for the intermediate and long distance windows and discuss the implications of the discrepancy. The anomalous magnetic moment of the muon (aµ) provides a stringent test of the Standard Model and Beyond, that too, interestingly on two independent fronts: the “aµ-test” and the “HVP-test”.We discuss a generic, light (∼ 100 MeV-1 GeV) Z′’s impact on both these tests in multiple ways making this arena an excellent probe of such models. |