Muon $g-2$ anomaly and non-locality

TL;DR

This paper proposes that nonlocal theories can explain the muon g-2 anomaly by introducing a nonlocality scale, predicting different effects for electrons and tau particles, and setting bounds on the nonlocality scale.

Contribution

It introduces a nonlocal theoretical framework to account for the muon g-2 discrepancy and predicts flavor-dependent effects on anomalous magnetic moments.

Findings

Nonlocal corrections depend on fermion mass and nonlocality scale.

Electron g-2 remains close to standard model predictions.

Large tau g-2 anomaly predicted for certain nonlocality scales.

Abstract

We show that the discrepancy between the observed value of the muon anomalous moment and the standard model prediction can be explained in the framework of nonlocal theories. We compute the leading order and next to leading order nonlocal correction to the anomalous magnetic moment $\alpha_{NL}$ and we find that it depends on the nonlocality scale $M_f$ and the fermion mass $m_f$ as $\alpha_{NL} \propto m_f^2/M_f^2$. Such a dependence of the anomalous magnetic momentum allows to explain, in a flavor-blind nonlocality scale, why the observed anomalous magnetic moment of the electron is much closer to the standard model prediction, and permits to predict a large anomaly that should exist for the $\tau$ particle. We also determine the lower bounds on the nonlocality scale, for both flavor-blind and flavor-dependent scenarios.