# QED corrections to the big-bang nucleosynthesis reaction rates

## TL;DR

This paper calculates radiative QED corrections to nuclear reaction rates in Big-Bang Nucleosynthesis, finding small but significant effects on elemental abundances, especially through pair production and vacuum polarisation.

## Contribution

It provides the first detailed computation of QED radiative corrections to BBN reaction rates, including pair production and vacuum polarisation effects.

## Key findings

- Pair production increases photon emission rates by about 0.2%.
- Corrections slightly alter elemental abundances, except for helium-4.
- Vacuum polarisation effects are small but relevant for reaction rate extrapolations.

## Abstract

We compute radiative corrections to nuclear reaction rates that determine the outcome of the Big-Bang Nucleosynthesis (BBN). Any nuclear reaction producing a photon with an energy above $2m_e$ must be supplemented by the corresponding reaction where the final state photon is replaced by an electron-positron pair. We find that pair production brings a typical $0.2 \%$ enhancement to photon emission rates, resulting in a similar size corrections to elemental abundances. The exception is $^4{\rm He}$ abundance, which is insensitive to the small changes in the nuclear reaction rates. We also investigate the effect of vacuum polarisation on the Coulomb barrier, which brings a small extra correction when reaction rates are extrapolated from the measured energies to the BBN Gamow peak energies.