The role of the chiral anomaly in polarized deeply inelastic scattering III: Wess-Zumino-Witten contributions and chiral Ward identities for finite quark mass

TL;DR

This paper investigates the effects of finite quark mass on the axial anomaly in polarized deep inelastic scattering, revealing how chiral dynamics and topological effects influence observable quantities like the proton's helicity and the structure function g_1.

Contribution

It extends previous worldline anomaly calculations to include finite quark mass effects and clarifies the role of the Wess-Zumino-Witten coupling and chiral Ward identities in QCD.

Findings

Finite quark mass corrections to the proton's helicity are a few percent.

The anomaly pole is shifted to the physical η' mass due to chiral dynamics.

The quark mass effects do not alter the predicted quenching of g_1 at small x.

Abstract

We extend our prior results on the worldline computation of the axial vector-vector-vector (AVV) triangle anomaly in polarized deeply inelastic scattering (DIS) to the finite mass case by computing in addition the pseudoscalar-vector-vector (PVV) triangle graph. For the well-studied QED case, we show explicitly how the off-forward AVV pole exactly cancels an identical PVV pole. We then demonstrate the dramatic difference in QCD due to the chiral condensate, which qualitatively modifies anomalous Ward identities. As in the massless case, the anomaly pole in QCD is canceled by the dynamics of a primordial isosinglet pseudoscalar $\bar \eta$-meson, whose Wess-Zumino-Witten coupling to the topological charge density shifts the pole to the physical $\eta^\prime$ mass, with the finite quark mass contribution differing by $O(10\%)$ from the Witten-Veneziano formula. We obtain a compact analytic expression for the finite mass corrections to Shore and Veneziano's result that the proton's net quark helicity $\Delta \Sigma\propto \sqrt{\chi_{\rm QCD}' |_{m=0}(0)}$, the forward slope of the topological susceptibility in the chiral limit, and show they are of the order of a few percent. Our prior prediction that the polarized DIS structure function $g_1$ is quenched by sphaleron-like topological transitions at small $x$ is unaffected by quark mass effects. Our results illustrate how worldline computations of anomalous processes, in synergy with lattice computations and nonet chiral perturbation theory, can uncover novel nonperturbative features of QCD at the Electron-Ion collider.