Muonium spectrum beyond the nonrelativistic limit

TL;DR

This paper extends the Gell-Mann-Low theorem to compute the muonium bound state spectrum numerically, accurately capturing fine and hyperfine structures near the nonrelativistic limit and comparing results with light-front quantization.

Contribution

It introduces a generalized approach for calculating relativistic bound states and demonstrates its effectiveness for the muonium system across different regimes.

Findings

Accurately reproduces fine and hyperfine structures near the nonrelativistic limit

Provides numerical spectrum for relativistic alpha = 0.3

Shows consistency with light-front quantization results

Abstract

A generalization of the Gell-Mann-Low theorem is applied to the antimuon-electron system. The bound state spectrum is extracted numerically. As a result, fine and hyperfine structure are reproduced correctly near the nonrelativistic limit (and for arbitrary masses). We compare the spectrum for the relativistic value alpha = 0.3 with corresponding calculations in light-front quantization.