# Gauge ambiguity of the quark spectrum in the Color Glass Condensate

## TL;DR

This paper investigates the gauge ambiguity in the quark spectrum within the Color Glass Condensate, revealing how the choice of Wilson line contour affects the spectrum's behavior at high transverse momentum.

## Contribution

The study introduces an analytically solvable toy model to analyze how Wilson line contour choices influence the gauge invariance and spectral tail behavior in the quark spectrum.

## Key findings

- Straight contours lead to a $p_ot^{-4}$ tail in the spectrum.
- Deviations from straight contours introduce path dependence at order $p_ot^{-4}$ or $p_ot^{-5}.
- Path dependence becomes significant when the contour passes through a fixed point.

## Abstract

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 $p_\perp^{-2}$ and $p_\perp^{-3}$ cancel, leading to a spectrum with a tail in $p_\perp^{-4}$. If the contour defining the Wilson line deviates from a straight line, the path dependence is at most of order $p_\perp^{-5}$ if its curvature is bounded, and of order $p_\perp^{-4}$ otherwise. When the contour is forced to go through a fixed point, the path dependence is even larger, of order $p_\perp^{-2}$.