Electron EM-mass melting in strong fields

We study the response of the electron mass to an externally applied electrical field. As a consequence of nonlinear electromagnetic (EM) effective action, the mass of a particle diminishes in the presence of an externally applied electric field. We consider modification of the muon anomalous magnetic moment $g-2$ due to electron loop insert in higher order. Since the virtual electron pair is in close proximity to the muon, it experiences strong field phenomena. We show that the current theory-experiment muon $g-2$ discrepancy could originate in the (virtual) electron mass \textit{non-perturbative} modification by the strong muon EM field. The magnitude of the electron mass modification can be also assessed via enhancement of $e^+e^-$-pair production in strong fields.