# Two-photon exchange on neutron and the hyperfine splitting

## TL;DR

This paper calculates the two-photon exchange contribution to neutron hyperfine splitting, updating the neutron Zemach radius and estimating corrections, revealing significant effects in electronic and muonic hydrogen.

## Contribution

It provides the first detailed calculation of two-photon exchange effects on neutron hyperfine splitting, including updated neutron Zemach radius and correction estimates.

## Key findings

- Two-photon exchange contribution exceeds the leading Zemach term by an order of magnitude.
- The sign of the correction differs between electronic and muonic hydrogen.
- Updated neutron Zemach radius and recoil/polarizability corrections are provided.

## Abstract

We calculate the contribution from the two-photon exchange on the neutron to the hyperfine splitting of S energy levels. We update the value of the neutron Zemach radius, estimate total recoil and polarizability corrections. The resulting two-photon exchange in electronic atoms exceeds by an order of magnitude the leading Zemach term and has different sign both in electronic and muonic hydrogen.