|Vector Correlators in Lattice QCD (Vol. 43 No. 1)|
Comparison of the vacuum polarisation calculated from e+e- annilhilation cross section with recent lattice simulations.
Vacuum polarisation, the modification of the photon propagator due to virtual electron-positron pairs, is one of the first quantum loop corrections encountered in field theory. In both QED and QCD it causes the running of the appropriate fine structure constant as the physical scale is varied, and also corrects the magnetic moments of electrons and muons from the value 2 predicted by the Dirac equation. For scales below a few GeV the QCD vacuum polarisation cannot be calculated perturbatively, but can be accessed via the optical theorem from the annihilation cross section of e+e- into hadrons, which is simply related to the spectral density ρ(s) in the vector isoscalar channel.. This paper opens a new direction by first assessing the current state-of-the-art in calculating the vacuum polarisation in lattice QCD, the most systematic non-perturbative approach, and then by setting out two different routes to improving on this, and identifying applications to strong interaction phenomenology.
Comparison with experimental data reveals that current results are badly finite-volume affected. The paper provides technical details enabling these distortions to be understood and ultimately extrapolated to the large volume limit. It also uses the same data to estimate the current-current correlator as a function of Euclidean time exposing the possibility that different ranges are amenable to different theoretical approaches; the dominant hadronic correction to (g-2) for the muon, about to be measured with unprecedented precision at Fermilab, comes from the range 0.5fm<ct<1.5fm. This reasoning is also suggests a new QCD reference scale, to help callibrate the lattice spacing using high-precision numerical estimates of the vector correlator.
Vector Correlators in Lattice QCD: Methods and Applications