Memory effect in Yang-Mills theory

TL;DR

The paper investigates memory effects in Yang-Mills theory, contrasting the classical electrodynamics memory with non-Abelian memory realized in Color Glass Condensate. It shows that the YM memory signal appears as a transverse momentum kick only after fixing the gauge and averaging over an ensemble of classical processes in the quantum theory, with the kick magnitude linked to the saturation scale $Q_s$. The analysis uses Wong equations for colored particles and CGC averaging to derive a memory signal that scales as $p_T^2 \,\sim\, Q_s^2$, connecting to observables such as the color dipole cross-section. It also discusses the limitations of YM memory as an analogue to gravitational memory and points to potential experimental probes in high-energy nuclear collisions and future Electron-Ion Colliders.

Abstract

We study the empirical realisation of the memory effect in Yang-Mills theory, especially in view of the classical vs. quantum nature of the theory. Gauge invariant analysis of memory in classical U(1) electrodynamics and its observation by total change of transverse momentum of a charge is reviewed. Gauge fixing leads to a determination of a gauge transformation at infinity. An example of Yang-Mills memory then is obtained by reinterpreting known results on interactions of a quark and a large high energy nucleus in the theory of Color Glass Condensate. The memory signal is again a kick in transverse momentum, but it is only obtained in quantum theory after fixing the gauge, after summing over an ensemble of classical processes.

Figures (2)

• Figure 1: Memory effect in electrodynamics. A radiator at $r=0$ sends a pulse of radiation to null infinity ${\cal I}^+$ during the time interval $u_i<u<u_f$. The time integrated pulse of transverse electric field gives a total momentum kick in (\ref{['memory']}) to a test charge at null infinity.
• Figure 2: Interaction of a nuclear Yang-Mills field and a test quark. The nucleus $N$ is represented by a color current $J^+=\rho(x^-,x^i)$ and associated classical YM field $A^+$. There is no dependence on the LC time $x^+$. The field extends over the range $0<x^-<\epsilon$ and $\epsilon\to0$ with increasing energy. In the transverse gauge $A^\mu=(0,0,A^i=i/g U\partial_i U^\dagger \theta(x^-))$, fields in $0<x^-<\epsilon$ are given in blaizot. The collision with the test quark at rest accelerates the quark to transverse momentum $p^i$; this is the YM memory. Transverse coordinates are not shown in the figure.