Hadronic vacuum polarization contributions to the muon $g$-2 in the space-like region

We present simple analytic expressions to compute the hadronic vacuum polarization contribution to the muon $g$-2 in the space-like region up to next-to-next-to-leading order. These results can be employed in lattice QCD calculations of this contribution as well as in space-like determinations based on scattering data, like that expected from the proposed MUonE experiment at CERN.Comment: 14 pages, 6 figures. v2: NNLO results presented. v3: minor change