Abstract
Because there are new projects on the determination of the hyperfine interval in the ground state of muonium, we revisit different approaches to constructing its theoretical prediction and comparison with experimental data. We discuss a controversy in the accuracy of two recent predictions [Mohr et al., Rev. Mod. Phys. 88, 035009 (2016), and Eides, Phys. Lett. B 795, 113 (2019)] and produce a constraint on possible systematic errors in the determination of the muonium hyperfine-structure interval interval theoretically or experimentally. In particular, a possible additional theoretical term, that may be either a missing ``regular'' theoretical contribution or a contribution due to new physics, is estimated as $\ensuremath{-}0.14(52)\phantom{\rule{0.28em}{0ex}}\mathrm{kHz}$. The constraint is based on all available data through a least-squares-adjustment procedure, including all their correlations. The result is close to the one of Eides [Phys. Lett. B 795, 113 (2019)].
Highlights
Theoretical predictions play important roles in physics, serving different purposes
We examine the legitimacy and accuracy of these two predictions. We demonstrate that both are legitimate but are most suitable for different purposes. We demonstrate that they have uncertainties different by approximately a factor of 2, they constrain a possible new physics term at roughly the same level [as −0.17(52) and −0.13(52) kHz, respectively]. [To make the results comparable, we apply the same theoretical expression, which marginally shifts the central value of prediction (2).] Both
It is clear that a comparison of the theoretical predictions above and the experimental data relies on the same set of theoretical and experimental information but uses different compositions of it
Summary
Theoretical predictions play important roles in physics, serving different purposes. Sometimes it is important to predict a possible value of a certain quantity prior its measurement which may simplify a related experiment, e.g., by reducing a possible region of scanning. Sometimes it serves as an overall consistency check of the data and theory. It is important to compare theory and experiment in order to look for a possible systematic error in both of them or to constrain a possible new physics term. The central value and the accuracy of a prediction depends on its purpose.
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