The role of the chiral anomaly in polarized deeply inelastic scattering II: Topological screening and transitions from emergent axion-like dynamics

TL;DR

This paper explores how the chiral anomaly influences polarized deep inelastic scattering, emphasizing topological effects, axion-like dynamics, and sphaleron transitions, with implications for future experimental measurements.

Contribution

It introduces a topological framework connecting the chiral anomaly to polarized DIS, including an axion-like effective action and the role of sphaleron transitions in spin dynamics.

Findings

Triangle anomaly dominates the structure function g_1 in DIS.

Topological mass generation of the η' is fundamental.

Sphaleron-like transitions influence spin diffusion at small x_B.

Abstract

In [1], we demonstrated that the structure function $g_1(x_B,Q^2)$ measured in polarized deeply inelastic scattering (DIS) is dominated by the triangle anomaly in both the Bjorken limit of large $Q^2$ and the Regge limit of small $x_B$. In the worldline formulation of quantum field theory, the triangle anomaly arises from the imaginary part of the worldline effective action. We show explicitly how a Wess-Zumino-Witten term coupling the topological charge density to a primordial isosinglet ${\bar \eta}$ arises in this framework. We demonstrate the fundamental role played by this contribution both in topological mass generation of the $\eta^\prime$ and in the cancellation of the off-forward pole arising from the triangle anomaly in the proton's helicity $\Sigma(Q^2)$. We recover the striking result by Shore and Veneziano that $\Sigma\propto \sqrt{\chi'(0)}$, where $\chi'$ is the slope of the QCD topological susceptibility in the forward limit. We construct an axion-like effective action for $g_1$ at small $x_B$ that describes the interplay between gluon saturation and the topology of the QCD vacuum. In particular, we outline the role of "over-the-barrier" sphaleron-like transitions in spin diffusion at small $x_B$. Such topological transitions can be measured in polarized DIS at a future Electron-Ion Collider.