Slope and curvature of the hadron vacuum polarization at vanishing   virtuality from lattice QCD
  We compute the slope and curvature, at vanishing four-momentum transfer squared, of the leading order hadron vacuum polarization function, using lattice QCD. Calculations are performed with 2+1+1 flavors of staggered fermions directly at the physical values of the quark masses and in volumes of linear extent larger than 6fm. The continuum limit is carried out using six different lattice spacings. All connected and disconnected contributions are calculated, up to and including those of the charm. 
Sz. Borsanyi, Z. Fodor, T. Kawanai, S. Krieg, L. Lellouch, R. Malak,   K. Miura, K.K. Szabo, C. Torrero, B. Toth
hep-lat hep-ph