Two-Loop Euler-Heisenberg QED Pair-Production Rate

TL;DR

This paper analyzes the divergence and pair-production rate in two-loop Euler-Heisenberg QED, showing that the leading divergence and imaginary part behavior are proportional to the one-loop case, confirming earlier results.

Contribution

It demonstrates that the divergence structure and pair-production rate at two loops mirror the one-loop case, providing a consistency check and extending previous analyses.

Findings

Leading divergence at two loops matches one-loop case up to a factor

Imaginary part of two-loop Lagrangian proportional to one-loop result

Confirms earlier Ritus analysis and mass renormalization consistency

Abstract

We study the divergence of large-order perturbation theory in the worldline expression for the two-loop Euler-Heisenberg QED effective Lagrangian in a constant magnetic field. The leading rate of divergence is identical, up to an overall factor, to that of the one-loop case. From this we deduce, using Borel summation techniques, that the leading behaviour of the imaginary part of the two-loop effective Lagrangian for a constant E field, giving the pair-production rate, is proportional to the one-loop result. This also serves as a test of the mass renormalization, and confirms the earlier analysis by Ritus.