Abstract
Using pNRQCD and known results for the field strength correlator, we calculate the ultrasoft contribution to the QCD static energy of a quark-antiquark pair at short distances at NNNNLO in alpha_s. At the same order, this provides the logarithmic terms of the singlet static potential in pNRQCD and the log alpha_s terms of the static energy.
Highlights
The ground state energy, E0(r), of a static quark and a static antiquark separated by a distance r is a key object for the understanding of the QCD dynamics
A convenient method to calculate the logarithmic contributions to Eq (1), which steam from the dynamics at the ultrasoft scale E0(r), consists in integrating out from static QCD degrees of freedom at the soft energy scale 1/r and working within the effective field theory framework of pNRQCD [18,19](see [20] for a review)
We have calculated the ultrasoft contribution to the QCD static energy of a quark-antiquark pair at order αs5
Summary
The ground state energy, E0(r), of a static quark and a static antiquark separated by a distance r is a key object for the understanding of the QCD dynamics. It is a basic ingredient of the Schrodinger-like formulation of heavy quarkonium systems [1]. When calculated in perturbation theory, infrared divergences are found starting at three loops [3,4] These are due to the virtual emission of ultrasoft gluons with energy of the order E0(r), which turn a color singlet quark-antiquark pair into
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