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

Complex-mass shell renormalization of the higher-derivative electrodynamics