Spatial Wilson loops in the classical field of high-energy heavy-ion collisions

Abstract

It has been previously shown numerically that the expectation value of the magnetic Wilson loop at the initial time of a heavy-ion collision exhibits area law scaling. This was obtained for a classical non-Abelian gauge field in the forward light cone and for loops of area $A\gtrsim 2/Q_s^2$. Here, we present an analytic calculation of the spatial Wilson loop in the classical field of a collision within perturbation theory. It corresponds to a diagram with two sources, for both projectile and target, whose field is evaluated at second order in the gauge potential. The leading non-trivial contribution to the magnetic loop in perturbation theory is proportional to the square of its area.