# 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, which leads to a potential energy that increases linearly with the distance between a static quark-antiquark pair. Previous lattice studies of the $SU(2)$ Yang-Mills theory determined the corresponding (Coulomb) string tension, $\sigma_{C}$, to be about three times larger than the Wilson loop string tension, $\sigma_F$, far above Zwanziger's variational bound, $\sigma_C \geq \sigma_F$. This work, carried out by Sebastian Dawid (UW), Wyatt Smith (GWU, ExoHad postdoc), Arkaitz Rodas (ODU & JLab, co-PI), Robert Perry (Barcelona U.) , Cesar Fernandez-Ramirez (UNED), Eric Swanson (Pitt, co-PI), and Adam Szczepaniak (Indiana U. & JLab, PI), examines the lattice definition of the instantaneous potential and the extraction of the Coulomb and Wilson string tensions in the $SU(2)$ Yang-Mills theory. It performs an improved determination of the ratio $\sigma_C/\sigma_F$, which is conservatively estimated as $2.0 \pm 0.4$, reducing substantially the tension with Zwanziger's bound.