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Description
Particle interactions are strongly modified in the presence of intense background electromagnetic fields. Due to an exchange of energy and momentum with the field, some processes prohibited in its absence might become allowed. Besides, in a field some virtual particles might go on shell. Furthermore, intense background fields can create a vacuum instability (Schwinger pair production). It was also observed that a class of field-dressed radiative corrections grows as increasing powers of the background field strength. This implies that in a strong enough field the conventional perturbative expansion in QED might break down (Ritus-Narozhny conjecture). Studies of such a regime would require a (partial) all-order resummation.
Naturally, we are interested in probabilities of various QED processes. It would be more convenient, though, to extract them from the appropriate radiative corrections via the Cutkosky cutting rules. The latter are related to unitarity but have been rigorously established for a field-free QFT. Therefore, they might still require an explicit generalization to the presence of a strong background field.
To this end, here we compare the explicit expression for the non-exchange term in the probability of the trident process $e^\pm \rightarrow e^\pm e^- e^+$ with the two-loop bubble contribution to the mass operator. For the sake of definiteness and simplicity, we confine to a special case of a constant crossed field. For one, its symmetry makes the explicit calculations easier. Besides, such a field doesn't spontaneously produce pairs from the vacuum, thus allowing us to focus on the effects related to the Ritus-Narozhny conjecture. Explicit calculations are made by adopting the FeynCalc package.
Our findings are a step towards the study of the cutting rules in a background field and, more generally, the implications of the Ritus-Narozhny conjecture.
