Complex-mass shell renormalization of the higher-derivative electrodynamics

TL;DR

This paper extends QED with higher-derivative terms, leading to finite one-loop corrections, a complex massive mode, and requires a complex-mass shell renormalization scheme, with applications to electron magnetic moments and potentials.

Contribution

It introduces a complex-mass shell renormalization framework for higher-derivative QED, addressing the instability of massive modes and providing new insights into radiative corrections.

Findings

Finite one-loop electron self-energy and vertex corrections without regularization.

Emergence of a complex massive mode with a finite decay width.

Estimation of bounds on the massive parameter from electron magnetic moment measurements.

Abstract

We consider a higher-derivative extension of QED modified by the addition of a gauge-invariant dimension-6 kinetic operator in the U(1) gauge sector. The Feynman diagrams at one-loop level are then computed. The modification in the spin-1 sector leads the electron self-energy and vertex corrections diagrams finite in the ultraviolet regime. Indeed, no regularization prescription is used to calculate these diagrams because the modified propagator always occurs coupled to conserved currents. Moreover, besides the usual massless pole in the spin-1 sector, there is the emergence of a massive one, which becomes complex when computing the radiative corrections at one-loop order. This imaginary part defines the finite decay width of the massive mode. To check consistency, we also derive the decay length using the electron--positron elastic scattering and show that both results are equivalent. Because the presence of this unstable mode, the standard renormalization procedures cannot be used and is necessary adopt an appropriate framework to perform the perturbative renormalization. For this purpose, we apply the complex-mass shell scheme (CMS) to renormalize the aforementioned model. As an application of the formalism developed, we estimate a quantum bound on the massive parameter using the measurement of the electron anomalous magnetic moment and compute the Uehling potential. At the end, the renormalization group is analyzed.