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.
Highlights
Effective field theories (EFT) play a central role in modern physics. They cover almost all branches in physics such as nuclear systems derived from low-energy quantum chromodynamics [1], chiral perturbation theory [2,3,4,5], BCS theory formulated from conventional superconductivity [6], inflationary model in cosmology [7,8], gravitationally induced decoherence [9], and so on
Fermi developed the theory of beta decay to describe the elementary process n → p + e− + νe in the framework of quantum field theory [13]
Some years later, the development of the renormalization and the renormalization group techniques [14], along with the theorem derived by Appelquist and Carazzone [15]—which states that heavy mass particles can be decoupled from low energy dynamics under certain conditions—gave rise to the current EFT programme [16]
Summary
Effective field theories (EFT) play a central role in modern physics. They cover almost all branches in physics such as nuclear systems derived from low-energy quantum chromodynamics [1], chiral perturbation theory [2,3,4,5], BCS theory formulated from conventional superconductivity [6], inflationary model in cosmology [7,8], gravitationally induced decoherence [9], and so on. Effective theories allow us to simplify the description of a given physical process by taking into account the appropriate variables at a given energy scale, i.e., one can consider only the relevant degrees of freedom at a specific energy range It is basically a low energy dynamics valid below some energy scale and which does not depend on the behavior in the ultraviolet regime. One interesting set of EFT models are the so-called higherorder theories This class of theories are characterized basically by the modification of the free propagator through the introduction of higher-order kinetic terms in the Lagrangian, which leads to a modified propagator that exhibits a better asymptotic behavior.
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