Abstract
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 x3 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 (x3T). The method is first investigated in lattice perturbation theory, where we point out the appearance of an O(a2 log(1/a)) lattice artifact in the vacuum polarization with a prefactor that we calculate. It is then applied to non-perturbative lattice QCD data with two dynamical flavors of quarks. Our lattice spacings range down to 0.049 fm for the vacuum simulations and down to 0.033 fm for the simulations performed at a temperature of 250 MeV.
Highlights
Many cases, vacuum correlators represent crucial input for precision tests of the Standard Model
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 x3 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 (x3 T )
We note that in certain cases, there is a logarithmic enhancement of the cutoff effects on the short-distance contribution at leading order in perturbation theory, in contrast to the modification of cutoff effects by logarithms affecting on-shell correlators, which only appears beyond the free-field theory level [8]
Summary
The key observation is that with the multiplicative renormalization of the tensor current included, which in perturbation theory only contains logarithmic corrections in the lattice spacing, this correlator would have a continuum limit. For contrast it is instructive to consider briefly the |x0|3 moment of G(x0), which is a physical quantity, expressable through the vector spectral function In this case, the corresponding moment of h(x0) would not be finite by power counting; that moment is finite in the continuum due to chiral symmetry, buts its straightforward implementation in Wilson lattice QCD would not have the correct continuum limit. The improvement term makes an O(a2 log(1/a)) contribution to I(t) This is of the same order as the artifacts we find in the unimproved correlator. Anticipating the explicit perturbative calculation, we find the latter to be consistent with the conclusions of this subsection, since no O(a) effects are found in I(t) computed with unimproved vector currents, even though the improvement coefficient cV for the conserved current is already non-vanishing at tree-level
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
