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- W4377010129 abstract "The ongoing experimental efforts to measure the hyperfine transition in muonic hydrogen prompt an accurate evaluation of the proton-structure effects. At the leading order in $alpha$, which is $O(alpha^5)$ in the hyperfine splitting (hfs), these effects are usually evaluated in a data-driven fashion, using the empirical information on the proton electromagnetic form factors and spin structure functions. Here we perform a first calculation based on the baryon chiral perturbation theory (B$chi$PT). At leading orders it provides a prediction for the proton polarizability effects in hydrogen (H) and muonic hydrogen ($mu$H). We find large cancellations among the various contributions leading to, within the uncertainties, a zero polarizability effect at leading order in the B$chi$PT expansion. This result is in significant disagreement with the current data-driven evaluations. The small polarizability effect implies a smaller Zemach radius $R_mathrm{Z}$, if one uses the well-known experimental $1S$ hfs in H or the $2S$ hfs in $mu$H. We, respectively, obtain $R_mathrm{Z}(mathrm{H}) = 1.010(9)$ fm, $R_mathrm{Z}(mumathrm{H}) = 1.040(33)$ fm. The total proton-structure effect to the hfs at $O(alpha^5)$ is then consistent with previous evaluations; the discrepancy in the polarizability is compensated by the smaller Zemach radius. Our recommended value for the $1S$ hfs in $mutext{H}$ is $182.640(18),mathrm{meV}.$" @default.
- W4377010129 created "2023-05-19" @default.
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- W4377010129 date "2023-05-16" @default.
- W4377010129 modified "2023-09-29" @default.
- W4377010129 title "Chiral perturbation theory of the hyperfine splitting in (muonic) hydrogen" @default.
- W4377010129 doi "https://doi.org/10.48550/arxiv.2305.09633" @default.
- W4377010129 hasPublicationYear "2023" @default.
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