Effects of light-by-light scattering in the Lamb shift and hyperfine structure of muonic hydrogen

A E Dorokhov,A P Martynenko,A E Radzhabov,F A Martynenko,D Melikhov,I Volobuev

doi:10.1051/epjconf/201922203010

Abstract

We calculate the meson exchange contribution to the interaction operator of muon and proton, which is determined by the meson coupling with two photon state. For the construction of transition form factor Meson → γγ we use the existing parametrizations based on experimental data including the monopole parametrization over photon four-momenta. For an estimate of the form factor value atzero photon four-momenta squared we use experimental data on the decay width ΓMeson→γγ. It is shown that scalar, pseudoscalar, axial vector and tensor mesons exchanges give significant contribution to the Lamb shift (LS) and hyperfine splitting (HFS) in muonic hydrogen which should be taken into account for a comparison with precise experimental data.

Highlights

The discrepancy between results for the proton charge radius obtained by different methods got the name "proton radius puzzle"
Measurements using electronic hydrogen lead to a different proton charge radius compared with those using muonic hydrogen
This problem arose after the CREMA experiments on Lamb shift measurement in muonic hydrogen [1, 2]

Summary

Introduction

The discrepancy between results for the proton charge radius obtained by different methods got the name "proton radius puzzle". Measurements using electronic hydrogen lead to a different proton charge radius compared with those using muonic hydrogen. This problem arose after the CREMA experiments on Lamb shift measurement in muonic hydrogen [1, 2]. Emerging new experimental data on the Lamb shift in electron hydrogen, as well as a new analysis of experiments already performed on the scattering of leptons by nucleons, show that the values of the proton charge radius obtained from electron and muon systems are approaching [3, 4]. The analysis of new interactions between the proton and the muon is important for future more accurate experiments. In this work we continue our investigations [5,6,7,8,9] (see [10,11,12,13,14]) of the role of one-meson exchange interactions in muonic hydrogen (μp)

Scalar meson exchange

Pseudoscalar meson exchange

Axial vector meson exchange

Tensor meson exchange

Findings

Conclusion