Coulomb flux tube on the lattice

Abstract

In Coulomb gauge a longitudinal electric field is generated instantaneously with the creation of a static quarkantiquark pair. The field due to the quarks is a sum of two contributions, one from the quark and one from the antiquark, and there is no obvious reason that this sum should fall off exponentially with distance from the sources. We show here, however, from numerical simulations in pure SU(2) lattice gauge theory, that the color Coulomb electric field does in fact fall off exponentially with transverse distance away from a line joining static quark-antiquark sources, indicating the existence of a color Coulomb flux tube, and the absence of long-range Coulomb dipole fields.

Coulomb flux tube revisited

“…We followed the fitting procedure from Ref. [30] and deviated from it only for R = 6, 7, 8, for which fit intervals are [2,7] compared to [1,7] in Ref. [30].…”

“…(25) and (26) of Ref. [30], i.e. it is oriented in xt-plane and placed at position p = R 2ê x + yê y , for even R ,…”

“…From Q(R, y), in Ref. [30], the energy distribution in the Coulomb state was obtained. The generalization given by Eq.…”

“…As an illustration of how a choice of the fitting interval affects the quality of the fit, for the exponential model Q CG we followed the fit procedure of Ref. [30]. Specifically, we used the same intervals as in [30] for small R, up to R = 5.…”

“…The red, solid line is the best exponential (CG) fit to the data, performed following the procedure of Ref. [30] for R 5. The green, dashed line is the best PL fit.…”