Coulomb confinement in the Hamiltonian limit

The Gribov-Zwanziger scenario attributes the phenomenon of confinement to the instantaneous interaction term in the QCD Hamiltonian in the Coulomb gauge. For a static quark-antiquark pair, it leads to a potential energy that increases linearly with the distance between them. Lattice studies of the SU(2) Yang-Mills theory determined the corresponding (Coulomb) string tension for sources in the fundamental representation, <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:msub><a:mi>σ</a:mi><a:mi>C</a:mi></a:msub></a:math>, to be about 3 times larger than the Wilson loop string tension, <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:msub><c:mi>σ</c:mi><c:mi>F</c:mi></c:msub></c:math>. It is far above the Zwanziger variational bound, <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>σ</e:mi><e:mi>C</e:mi></e:msub><e:mo>≥</e:mo><e:msub><e:mi>σ</e:mi><e:mi>F</e:mi></e:msub></e:math>. We argue that the value often reported in the literature is artificially inflated. We examine the lattice definition of the instantaneous potential, find the source of the string tension’s enhancement, and perform its improved determination in SU(2) lattice gauge theory. We report our conservative estimate for the value of the Coulomb string tension as <g:math xmlns:g="http://www.w3.org/1998/Math/MathML" display="inline"><g:msub><g:mi>σ</g:mi><g:mi>C</g:mi></g:msub><g:mo>/</g:mo><g:msub><g:mi>σ</g:mi><g:mi>F</g:mi></g:msub><g:mo>=</g:mo><g:mn>2.0</g:mn><g:mo>±</g:mo><g:mn>0.4</g:mn></g:math> and discuss its phenomenological implications. Published by the American Physical Society 2024