Muonic hydrogen and the proton size

Abstract

We reexamine the structure of the $n=2$ levels of muonic hydrogen using a two-body potential that includes all relativistic, recoil and one loop corrections. The potential was originally derived from QED to describe the muonium atom and accounts for all contributions to order ${\alpha }^5$. Since one loop corrections are included, the anomalous magnetic moment contributions of the muon can be identified and replaced by the proton anomalous magnetic moment to describe muonic hydrogen with a point-like proton. This serves as a convenient starting point to include the dominant electron vacuum polarization corrections to the spectrum and extract the proton's mean squared radius $r_p=\sqrt{⟨r^2⟩}$. Our results are consistent with other theoretical calculations that find that the muonic hydrogen value for $r_p$ is smaller than the result obtained from electron scattering.

18 pages, 2 Tables, content added

References in corpus (2)

• Big-Bang Nucleosynthesis
• New measurement of the $1S-3S$ transition frequency of hydrogen: contribution to the proton charge radius puzzle

Cited by in corpus (4)

• Relativistic and Recoil Corrections to Vacuum polarization in muonic systems: Three--photon exchange, gauge invariance and numerical values
• Bound Deuteron-Antideuteron System (Deuteronium): Leading Radiative and Internal-Structure Corrections to Bound-State Energies
• Nuclear deformation effects on charge radius measurements of the proton and deuteron
• Vacuum polarization corrections to the $n=2$ and $n=3$ levels in muonic ${}^4$He