Abstract
We discuss hadronic effects in the muonium hyperfine structure and derive an expression for the hadronic contribution to the hfs interval in form of the one-dimensional integral of the cross section of e+e- annihilation into hadrons. Higher-order hadronic contributions are also considered.
Highlights
Introduction and ResultsQuantum Electrodynamics (QED) provides an opportunity to determine characteristics of various particles and simple atomic systems
Any pure QED caclulation is incomplete even in the case of a purely leptonic system because of a contribution of the strong interaction originating from hadronic intermediate states
A contribution of the hadronic effects to the anomalous magnetic moment of the muon is about 60 ppm of its QED value. This value is larger than both the uncertainty of the QED calculations and experiment [2]
Summary
Quantum Electrodynamics (QED) provides an opportunity to determine characteristics of various particles and simple atomic systems. The expected progress in development of intensive muon sources for needs of particle physics offers an opportunity to increase the statistics of muonic events and to provide a much better source of muonium [9] In view of this increase of the experimental accuracy we need more precise theoretical calculations of various contributions and in particular of those for the hadronic vacuum polarization (Fig. 2). The accuracy of an incoming calculation [6] based on our expression (3) is of the 1%-level and we discuss here various corrections to (3) and in particular those due to the higher-order hadronic vacuum effects (Fig. 3). We found that there is only one higher-order correction to (3) above the uncertainty level of the calculation in [6] and it increases the vacuum polarization contribution by roughly 3%
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