Breit type equation for mesonic atoms

TL;DR

This paper extends the Breit equation to include finite size effects and relativistic corrections for mesonic atoms, providing a more comprehensive framework for analyzing energy shifts in pionic and kaonic hydrogen.

Contribution

It generalizes the Breit equation for spin-0 and spin-1/2 particles with hadron electromagnetic form factors, improving the calculation of energy corrections in mesonic atoms.

Findings

Relativistic corrections agree reasonably well with other methods.

Energy shift values are sensitive to hadronic form factor uncertainties.

The approach offers a refined tool for analyzing mesonic atom spectra.

Abstract

The finite size effects and relativistic corrections in pionic and kaonic hydrogen are evaluated by generalizing the Breit equation for a spin-0 - spin-1/2 amplitude with the inclusion of the hadron electromagnetic form factors. The agreement of the relativistic corrections to the energies of the mesonic atoms with other methods used to evaluate them is not exact, but reasonably good. The precision values of the energy shifts due to the strong interaction, extracted from data, are however subject to the hadronic form factor uncertainties.