Vacuum correlators at short distances from lattice QCD

Understand

Non-perturbatively computing the hadronic vacuum polarization at large photon virtualities and making contact with perturbation theory enables a precision determination of the electromagnetic coupling at the $Z$ pole, which enters global electroweak fits.

• In order to achieve this goal ab initio using lattice QCD, one faces the challenge that, at the short distances which dominate the observable, discretization errors are hard to control.
• Here we address challenges of this type with the help of static screening correlators in the high-temperature phase of QCD, yet without incurring any bias.
• The idea is motivated by the observations that (a) the cost of high-temperature simulations is typically much lower than their vacuum counterpart, and (b) at distances $x_3$ far below the inverse temperature $1/T$, the operator-product expansion guarantees the thermal correlator of two local currents to deviate from the vacuum correlator by a relative amount that is power-suppressed in $(x_3\:T)$.