2010/06/04 by Y. Burnier, M. Laine, J. Langelage +1
Physics and Astronomy · #Asymptotic expansion #Euclidean geometry #Frequency domain #High-Energy Particle Collisions Research #Lattice (music) #Normalization (sociology) #Quantum Chromodynamics and Particle Interactions #Quantum and Classical Electrodynamics #Renormalization #Resummation #Spectral function #Spectral method #hep-lat #hep-ph
paper · pdf · doi:10.1007/jhep08(2010)094
published as JHEP 1008:094,2010 · 38 pages
arxiv created 2010/06/04 · openalex publication_date 2010/08/01 · arxiv updated 2014/11/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The spectral function related to the correlator of two colour-electric fields along a Polyakov loop determines the momentum diffusion coefficient of a heavy quark near rest with respect to a heat bath. We compute this spectral function at next-to-leading order, O(alphas2), in the weak-coupling expansion. The high-frequency part of our result (omega >> T), which is shown to be temperature-independent, is accurately determined thanks to asymptotic freedom; the low-frequency part of our result (omega << T), in which Hard Thermal Loop resummation is needed in order to cure infrared divergences, agrees with a previously determined expression. Our result may help to calibrate the overall normalization of a lattice-extracted spectral function in a perturbative frequency domain T << omega << 1/a, paving the way for a non-perturbative estimate of the momentum diffusion coefficient at omega -> 0. We also evaluate the colour-electric Euclidean correlator, which could be directly compared with lattice simulations. As an aside we determine the Euclidean correlator in the lattice strong-coupling expansion, showing that through a limiting procedure it can in principle be defined also in the confined phase of pure Yang-Mills theory, even if a practical measurement could be very noisy there.