Schwinger Pair Production at Finite Temperature

TL;DR

This paper calculates the finite-temperature correction to Schwinger pair production for charged scalars using the worldline formalism, revealing threshold behaviors and potential higher-order effects that regularize singularities.

Contribution

It introduces a method to compute thermal corrections to pair production rates at one loop using worldline instantons, including all finite-temperature effects and thresholds.

Findings

Thermal correction becomes significant above a threshold temperature $T=eE/2m$.

Decay rates exhibit singularities at each threshold, indicating the need for higher-order effects.

The formalism extends to inhomogeneous fields at finite temperature.

Abstract

Thermal corrections to Schwinger pair production are potentially important in particle physics, nuclear physics and cosmology. However, the lowest-order contribution, arising at one loop, has proved difficult to calculate unambiguously. We show that this thermal correction may be calculated for charged scalars using the worldline formalism, where each term in the decay rate is associated with a worldline instanton. We calculate all finite-temperature worldline instantons, their actions and fluctuations prefactors, thus determining the complete one-loop decay rate at finite temperature. The thermal contribution to the decay rate becomes nonzero at a threshold temperature $T=eE/2m$, above which it dominates the zero temperature result. This is the lowest of an infinite set of thresholds at $T=neE/2m$. The decay rate is singular at each threshold as a consequence of the failure of the quadratic approximation to the worldline path integral. We argue that that higher-order effects will make the decay rates finite everywhere, and model those effects by the inclusion of hard thermal loop damping rates. We also demonstrate that the formalism developed here generalizes to the case of finite-temperature pair production in inhomogeneous fields.