Gauge ambiguity of the quark spectrum in the Color Glass Condensate

摘要

In the Color Glass Condensate, the inclusive spectrum of produced quarks in a heavy ion collision is obtained as the Fourier transform of a 2-fermion correlation function. Due to its non-locality, the two points of this function must be linked by a Wilson line in order to have a gauge invariant result, but when the quark spectrum is evaluated in a background that has a non-zero chromo-magnetic field, this procedure suffers from an ambiguity related to the choice of the contour defining the Wilson line. In this paper, we use an analytically tractable toy model of the background field in order to study this contour dependence. We show that for a straight contour, unphysical contributions to the spectrum in p(perpendicular to)(-2) and p(perpendicular to)(-3) cancel, leading to a spectrum with a tail in p(perpendicular to)(-4). If the contour defining the Wilson line deviates from a straight line, the path dependence is at most of order p(perpendicular to)(-5) if its curvature is bounded, and of order p(perpendicular to)(-4) otherwise. When the contour is forced to go through a fixed point, the path dependence is even larger, of order p(perpendicular to)(-2). (C) 2019 Elsevier B.V. All rights reserved.