Meson exchange in lepton-nucleon scattering and proton radius puzzle

TL;DR

This paper investigates the two-photon exchange contribution involving sigma meson exchange in lepton-proton scattering, analyzing its impact on the proton radius puzzle and estimating its effect on muonic hydrogen energy levels.

Contribution

It provides an analytical formula for the sigma meson exchange amplitude at Q2=0 and estimates its effect on muonic hydrogen energy levels, offering insights into the proton radius puzzle.

Findings

The amplitude grows sharply but remains finite at Q2=0.

The sigma meson exchange causes a shift in muonic hydrogen energy levels about 30 times smaller than needed to solve the proton radius puzzle.

The estimated energy shift exceeds the measurement precision of muonic hydrogen experiments.

Abstract

We study two-photon contribution to the elastic lepton-proton scattering, associated with sigma meson exchange, with special attention paid to the low-Q2 region. We show that the corresponding amplitude grows sharply but remains finite at Q2->0. The analytical formula for the amplitude at Q2=0 is obtained. We also estimate the shift of the muonic hydrogen energy levels, induced by sigma meson exchange. For the 2S level the shift is approximately 30 times smaller than needed to resolve the proton radius puzzle, but still exceeds the precision of the muonic hydrogen measurements.