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The gradient-flow operator product expansion for QCD current correlators including operators up to mass dimension four is calculated through NNLO. This paves an alternative way for efficient lattice evaluations of hadronic vacuum polarization functions. In addition, flow-time evolution equations for flowed composite operators are derived. Their explicit form for the non-trivial dimension-four operators of QCD is given through order $alpha_s^3$.
We propose a method to compute the hadronic vacuum polarization function on the lattice at continuous values of photon momenta bridging between the spacelike and timelike regions. We provide two independent demonstrations to show that this method lea
In order to reduce the current hadronic uncertainties in the theory prediction for the anomalous magnetic moment of the muon, lattice calculations need to reach sub-percent accuracy on the hadronic-vacuum-polarization contribution. This requires the
We present two examples of applications of the analytic continuation method for computing the hadronic vacuum polarization function in space- and time-like momentum regions. These examples are the Adler function and the leading order hadronic contrib
There are emerging tensions for theory results of the hadronic vacuum polarization contribution to the muon anomalous magnetic moment both within recent lattice QCD calculations and between some lattice QCD calculations and R-ratio results. In this p
We construct a physically motivated model for the isospin-one non-strange vacuum polarization function Pi(Q^2) based on a spectral function given by vector-channel OPAL data from hadronic tau decays for energies below the tau mass and a successful pa