Role of the chiral anomaly in polarized deeply inelastic scattering. II. Topological screening and transitions from emergent axionlike dynamics

In [A. Tarasov and R. Venugopalan, Phys. Rev. D 102, 114022 (2020)], we demonstrated that the structure function g1(xB; Q2) measured in polarized deeply inelastic scattering (DIS) is dominated by the triangle anomaly in both Bjorken (Q2 -+ 0) and Regge (xB -+ 0) asymptotics. 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 eta over bar arises in this framework. We demonstrate the fundamental role played by this contribution both in topological mass generation of the eta' and in the cancellation of the off-forward pole arising from the triangle anomaly in the proton's helicity sigma(Q2). We recover the striking result by Shore and Veneziano that sigma proportional to chi'(0), where chi' is the slope of the QCD topological susceptibility in the forward limit. We construct an axionlike effective action for g1 at small xB that describes the interplay between gluon saturation and the topology of the QCD vacuum. In articular, we outline the role of "over-the-barrier" sphaleronlike transitions in spin diffusion at small xB. Such topological transitions can be measured in polarized DIS at a future Electron-Ion Collider.