Muon $g-2$ anomaly and non-locality

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.