Irreducible Three-Loop Vacuum-Polarization Correction in Muonic Bound Systems

TL;DR

This paper calculates three-loop vacuum-polarization corrections in muonic ions with Z=1 to 6, revealing significant energy shifts that are crucial for precision measurements and eliminating numerical uncertainties of previous methods.

Contribution

It introduces a new calculation method for three-loop corrections in muonic systems, reducing numerical uncertainties and providing more accurate energy shift estimates.

Findings

Corrections are comparable to leading two-loop effects.

Energy shifts are phenomenologically significant.

Method reduces numerical uncertainties.

Abstract

Three-loop electronic vacuum-polarization corrections due to irreducible diagrams are evaluated for two-body muonic ions with nuclear charge numbers 1 <= Z <= 6. The corrections are of order alpha^3 (Zalpha)^2 m_r, where alpha is the fine-structure constant and m_r is the reduced mass. Numerically, the energy corrections are found to be of the same order-of-magnitude as the largest of the order alpha^2 (Zalpha)^6 m_r corrections, and are thus phenomenologically interesting. Our method of calculation eliminates numerical uncertainty encountered in other approaches.