Thermally versus dynamically assisted Schwinger pair production

Abstract

We study electron-positron pair production by the combination of a strong, constant electric field and a thermal background. We show that this process is similar to dynamically assisted Schwinger pair production, where the strong field is instead assisted by another coherent field, which is weaker but faster. We treat the interaction with the photons from the thermal background perturbatively, while the interaction with the electric field is nonperturbative (i.e. a Furry picture expansion in α). At O(α 2 ) we have ordinary perturbative Breit-Wheeler pair production assisted nonperturbatively by the electric field. Already at this order we recover the same exponential part of the probability as previous studies, which did not expand in α. This means that we do not have to consider higher orders, so our approach allows us to calculate the pre-exponential part of the probability, which has not been obtained before in this regime. Although the prefactor is in general subdominant compared to the exponential part, in this case it can be important because it scales as α 2 1 and is therefore much smaller than the prefactor at O(α 0 ) (pure Schwinger pair production). We show that, because of the exponential enhancement, O(α 2 ) still gives the dominant contribution for temperatures above a certain threshold, but, because of the small prefactor, the threshold is higher than what the exponential alone would suggest.

Observing thermal Schwinger pair production

“…The precise formula, including the prefactor of the exponential has recently been worked out in Ref. [52]. There it was also shown that the dominant contribution to the rate in this regime is given by Fig.…”

“…2 (b) shows the dominant Feynman diagram for thermal Schwinger pair production in the intermediate temperature regime. Applying the Optical Theorem, one can see that a unitarity cut of diagram (b) gives the Breit-Wheeler process [52], except that the effect of the electric field has been accounted for to all orders, giving a nonperturbative enhancement over the pure Breit-Wheeler process. In fact, Eq.…”

“…2 can be calculated in an arbitrary photon distribution, following the approach of Ref. [52], though in the high temperature regime these diagrams are not dominant. Considering the calculation in this distribution, it can be seen that these diagrams reproduce the perturbative Breit-Wheeler rate up to very small corrections, essentially because the photon gas is highly occupied at energies much greater than k B T CW (see Eqs.…”

Schwinger effect in compact space: A real time calculation

“…It is thus not excluded that a net contribution to the rate of pair production proportional to e −2πmR might appear at that order in perturbation theory. See [19] for the discussion of an analogous phenomenon in the thermal case, and [8,9] for a higher order real-time calculation for the zero-temperature, noncompact case.…”

“…References [13,14] discuss Schwinger pair production on compact spaces with two compact dimensions. The Schwinger effect at finite temperature has received more attention [10,11,[15][16][17][18][19] and is related to the spatially compact case as finite temperature effects can be captured by compactifying Euclidean time.…”