Memory effect in Yang-Mills theory with an axion

We study the empirical realization of the memory effect in Yang-Mills theory with an axionlike particle, especially in view of the classical vs quantum nature of the theory. We solve for the coupled equations of motion iteratively in the axionic contributions and explicitly display the gauge-invariant effects in terms of field strengths. We apply our results in the context of heavy-ion collisions, in the thin nuclear sheet limit, and point out that a probe particle traversing radiation train acquires a longitudinal null memory kick in addition to the usual transverse kick.