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

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 $\Sigma \propto \sqrt{{\chi }^{\prime }(0)}$, where ${\chi }^{\prime }$ 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.

38 pages, 12 figures

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• Small-x Evolution of the Gluon Generalized Parton Distribution Eg of the Nucleon
• QED as a many-body theory of worldlines: I. General formalism and infrared structure
• Fractional topological charge in $SU(N)$ gauge theories without dynamical quarks
• QED as a many-body theory of worldlines: II. All-order S-matrix formalism
• Chirality distributions inside baryons in $\mathrm{QC}{\mathrm{D}}_2$