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This theoretical physics study presents a comprehensive calculation of the hyperfine splitting in muonic hydrogen (μH), accounting for quantum electrodynamic effects, recoil corrections, and proton structure contributions. The authors calculate all effects contributing more than 1 part per million to arrive at a predicted ground state hyperfine splitting energy of 182,626 μeV with an uncertainty of 5 μeV. The proton structure correction was derived using data from ordinary hydrogen hyperfine splitting measurements.
Why it matters
This precise theoretical prediction is essential for interpreting experimental measurements of muonic hydrogen, which can test quantum electrodynamics and help resolve discrepancies in our understanding of proton structure. The calculation provides a benchmark against which future high-precision spectroscopic experiments can be compared to search for physics beyond the Standard Model.
arXiv:2604.06930v2 Announce Type: replace
Abstract: This work attempts to present a complete theory of the $mu$H hyperfine splitting, including all contributions above 1 ppm. Quantum electrodynamic and recoil corrections are calculated directly, while the proton structure correction is obtained with the help of the H hyperfine splitting. The resulting theoretical prediction for the ground state of $mu$H is $E_mathrm{hfs} = 182,626(5)$ $mu$eV.