Vacuum correlators at short distances from lattice QCD

We propose a method to help control cutoff effects in the short-distance contribution to integrated correlation functions, such as the hadronic vacuum polarization (HVP), using the corresponding screening correlators computed at finite temperature. The strategy is investigated with Wilson fermions at leading order, which reveals a logarithmically-enhanced lattice artifact in the short-distance contribution, whose coefficient is determined at this order. We then perform a numerical study with $N_{\mathrm{f}}=2$ O($a$)-improved Wilson fermions and a temperature $T\approx 250\mathrm{M}\mathrm{e}\mathrm{V}$, with lattice spacings down to $a\approx 0.03\mathrm{f}\mathrm{m}$, which suggests good control can be achieved on the short-distance contribution to the HVP and the Adler function at large virtuality. Finally, we put forward a scheme to compute the complete HVP function at arbitrarily large virtualities using a step-scaling in the temperature.