Energy interval 3S-1S in muonic hydrogen

TL;DR

This paper calculates the (3S-1S) energy interval in muonic hydrogen using quantum electrodynamics, incorporating various corrections to aid future experimental comparisons and improve proton radius measurements.

Contribution

It provides a detailed theoretical calculation of the muonic hydrogen (3S-1S) energy interval including higher-order corrections, enhancing precision for experimental validation.

Findings

Calculated energy interval with relativistic and vacuum polarization corrections.

Expressed nuclear structure effects via proton charge radius and form factors.

Results can refine proton charge radius measurements in future experiments.

Abstract

The energy interval $ (3S-1S) $ in muonic hydrogen is calculated on the basis of quasipotential approach in quantum electrodynamics. We take into account different corrections of orders $\alpha^3\div \alpha^6 $, which are determined by relativistic effects, the effects of vacuum polarization, nuclear structure and recoil, as well as combined corrections including the above. Nuclear structure effects are expressed in terms of the charge radius of the proton in the case of one-photon interaction and the proton electromagnetic form factors in the case of two-photon exchange interaction. The value of the energy interval (3S-1S) can be used for a comparison with future experimental data and determining the proton charge radius with greater accuracy.