Corrections of two-photon interactions in the fine and hyperfine structure of the P-energy levels of muonic hydrogen

TL;DR

This paper calculates corrections to the fine and hyperfine structure of muonic hydrogen's P-energy levels due to two-photon exchange and photon-photon interactions, improving theoretical precision in quantum electrodynamics.

Contribution

It introduces a new analytical approach to evaluate two-photon exchange corrections in muonic hydrogen using the quasipotential method.

Findings

Calculated corrections to P-state energy levels

Derived contributions from axial vector meson exchange

Enhanced understanding of nuclear structure effects

Abstract

In the framework of the quasipotential method in quantum electrodynamics we calculate corrections to the nuclear structure proportional to $r_N^2$ from two-photon exchange amplitudes in the fine and hyperfine structure of P-states in muonic hydrogen, as well as the photon-photon interaction amplitudes, leading to the exchange of the axial vector meson. In constructing the quasipotential of the muon-nucleus interaction, we use the method of projection operators on states of two particles with a definite spin and total angular momentum. Analytical calculation of the matrix elements is performed and contributions to the fine and hyperfine structure of the $2P_{1/2}$ and $2P_{3/2}$ levels are obtained.