Slope and curvature of the hadronic vacuum polarization at vanishing virtuality from lattice QCD

We compute the slope and curvature, at vanishing four-momentum transfer squared, of the leading order hadronic vacuum polarization function, using lattice quantum chromodynamics. 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 6 fm. 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.