Forward virtual Compton scattering and the Lamb shift in chiral perturbation theory

TL;DR

This paper calculates the proton's structure functions and polarizability corrections to the Lamb shift using chiral perturbation theory, linking sum rules and providing numerical estimates for hydrogen and muonic hydrogen.

Contribution

It extends chiral perturbation theory to compute structure functions and Lamb shift corrections, connecting sum rules with deep inelastic scattering results.

Findings

Calculated proton structure functions at one loop in chiral perturbation theory.

Derived the leading chiral contribution to the Lamb shift in hydrogen and muonic hydrogen.

Provided numerical estimates for the polarizability correction to the Lamb shift.

Abstract

We compute the spin-independent structure functions of the forward virtual-photon Compton tensor of the proton at one loop using heavy baryon chiral perturbation theory and dispersion relations. We study the relation between both approaches. We use these results to generalize some sum rules to virtual photon transfer momentum and relate them with sum rules in deep inelastic scattering. We then compute the leading chiral term of the polarizability correction to the Lamb shift of the hydrogen and muonic hydrogen. We obtain -87.05/n^3 Hz and -0.148/n^3 meV for the correction to the hydrogen and muonic hydrogen Lamb shift respectively.