Abstract
We compute the general expression of the one-loop vertex correction in an arbitrary plane-wave background field for the case of two on-shell external electrons and an off-shell external photon. The properties of the vertex corrections under gauge transformations of the plane-wave background field and of the radiation field are studied. Concerning the divergences of the vertex correction, the infrared one is cured by assigning a finite mass to the photon, whereas the ultraviolet one is shown to be renormalized exactly as in vacuum. Finally, the corresponding expression of the vertex correction within the locally-constant crossed field is also derived and the high-field asymptotic is shown to scale according to the Ritus-Narozhny conjecture.
Highlights
The predictions of QED agree with experiments with impressive accuracy
The physical relevance of the Ritus-Narozhny conjecture is broadened by the so-called locally constant field approximation (LCFA), stating that in the limit of low-frequency plane waves the probabilities of QED processes reduce to the corresponding probabilities in a constant crossed field averaged over the phase-dependent plane-wave profile [12]
We have computed the general expression of the oneloop vertex correction in an arbitrary plane-wave background field for the case of two on-shell external electrons and an off-shell external photon
Summary
The predictions of QED agree with experiments with impressive accuracy (see, e.g., Refs. [1,2]). The one-loop vertex correction in a general plane wave (see Fig. 3) has never been evaluated, whereas, as we have mentioned, the corresponding quantity in a constant crossed field was computed in Refs. The physical relevance of the Ritus-Narozhny conjecture is broadened by the so-called locally constant field approximation (LCFA), stating that in the limit of low-frequency plane waves the probabilities of QED processes reduce to the corresponding probabilities in a constant crossed field averaged over the phase-dependent plane-wave profile [12]. [89] we have investigated the one-loop mass and polarization operator to show that, if one first performs in the general expression of these quantities the high-energy limit, one recovers the typical logarithmic behavior of QED as in vacuum The Appendix contains some technical considerations on a component of the vertex-correction function
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