Lattice QCD calculation of the two-photon exchange contribution to the muonic-hydrogen Lamb shift

TL;DR

This paper introduces a lattice QCD method to calculate the two-photon exchange contribution to the muonic-hydrogen Lamb shift, providing a new approach that aligns with previous results and addresses the proton radius puzzle.

Contribution

The paper develops a novel lattice QCD approach using the IVR method for calculating the TPE contribution to the Lamb shift, demonstrating its feasibility with preliminary results.

Findings

Preliminary TPE contribution agrees with previous calculations.

Method yields a result much smaller than the proton radius puzzle discrepancy.

Demonstrates potential for lattice QCD in precision QED calculations.

Abstract

We develop a method for lattice QCD calculation of the two-photon exchange (TPE) contribution to the muonic-hydrogen Lamb shift. To demonstrate the feasibility of this method, we also present an exploratory study with a gauge ensemble at $m_\pi = 142$ MeV. By adopting the infinite-volume reconstruction (IVR) method along with an optimized subtraction scheme, we obtain a preliminary result of the TPE contribution which agrees well with previous calculation using other methods and one magnitude smaller compare to the large $\sim300~\mu$eV discrepancy for the proton radius puzzle.