Anomalies in String-inspired Non-local Extensions of QED
Fayez Abu-Ajamieh, Pratik Chattopadhyay, Anish Ghoshal, Nobuchika Okada
TL;DR
This work analyzes anomalies in a string-inspired non-local QED framework, where gauge-invariant exponential form factors render the theory finite and non-locality is governed by a scale $\Lambda$. Using triangle and bubble diagrams, it shows the vector anomaly vanishes and the Ward identity is preserved, while the chiral anomaly vanishes at leading order for massless fermions but persists when fermion mass is included, with the non-local result approaching the local anomaly in the correct regulator regime. The authors derive explicit non-local Noether currents that encode higher-order gauge insertions and demonstrate how the local limit is recovered as $\Lambda\to\infty$. They illustrate the formalism by computing non-local corrections to $\pi^{0}\to\gamma\gamma$ decay, deriving a bound $\Lambda \gtrsim 57$ GeV from PrimEx-II data, and comparing with stronger collider bounds. Overall, the results validate gauge-invariance-based expectations in a non-local EFT, clarify the mass dependence of the chiral anomaly, and connect non-locality to observable processes.
Abstract
We investigate anomalies in the class of non-local field theories that have been proposed as an ultraviolet completion of 4-D Quantum Field Theory (QFT) with generalizing the kinetic energy operators to an infinite series of higher derivatives inspired by string field theory and ghost-free non-local approaches to quantum gravity. We explicitly calculate the vector and chiral anomalies in a string-inspired non-local extension of QED. We show that the vector anomaly vanishes as required by gauge-invariance and the Ward identity. On the other hand, although the chiral anomaly vanishes to the leading order with massless fermions, it nonetheless does not vanish with the massive fermions and we calculate it to the leading order in scale of non-locality. We also calculate the non-local vector and axial currents explicitly, and present an illustrative example by applying our results to the decay of π_0 \rightarrow γγ.