On the low-energy limit of the QED N-photon amplitudes

TL;DR

This paper derives explicit formulas for low-energy limits of one-loop N-photon amplitudes in scalar and spinor QED, including two-loop corrections up to ten photons, revealing helicity-dependent vanishing properties.

Contribution

It provides a comprehensive formula for low-energy N-photon amplitudes and extends results to two-loop order for up to ten photons in QED.

Findings

Odd helicity photon amplitudes vanish at low energy to all loop orders.

Explicit formulas for one-loop N-photon amplitudes are derived.

Two-loop corrections are computed for up to ten photons.

Abstract

We derive an explicit formula for the low energy limits of the one-loop, on-shell, massive N-photon amplitudes, for arbitrary N and all helicity assignments, in scalar and spinor QED. The two-loop corrections to the same amplitudes are obtained for up to the ten point case. All photon amplitudes with an odd number of `+' helicities are shown to vanish in this limit to all loop orders.