Chiral perturbation theory of the hyperfine splitting in (muonic) hydrogen
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arXiv
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| Natura: | Preprint |
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2023
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| _version_ | 1866929229600391168 |
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| author | Hagelstein, Franziska Lensky, Vadim Pascalutsa, Vladimir |
| author_facet | Hagelstein, Franziska Lensky, Vadim Pascalutsa, Vladimir |
| contents | 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 $α$, which is $O(α^5)$ 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$χ$PT). At leading orders it provides a prediction for the proton polarizability effects in hydrogen (H) and muonic hydrogen ($μ$H). We find large cancellations among the various contributions leading to, within the uncertainties, a zero polarizability effect at leading order in the B$χ$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 $μ$H. We, respectively, obtain $R_\mathrm{Z}(\mathrm{H}) = 1.010(9)$ fm, $R_\mathrm{Z}(μ\mathrm{H}) = 1.040(33)$ fm. The total proton-structure effect to the hfs at $O(α^5)$ 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 $μ\text{H}$ is $182.640(18)\,\mathrm{meV}.$ |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_09633 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Chiral perturbation theory of the hyperfine splitting in (muonic) hydrogen Hagelstein, Franziska Lensky, Vadim Pascalutsa, Vladimir Nuclear Theory High Energy Physics - Phenomenology Atomic Physics 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 $α$, which is $O(α^5)$ 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$χ$PT). At leading orders it provides a prediction for the proton polarizability effects in hydrogen (H) and muonic hydrogen ($μ$H). We find large cancellations among the various contributions leading to, within the uncertainties, a zero polarizability effect at leading order in the B$χ$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 $μ$H. We, respectively, obtain $R_\mathrm{Z}(\mathrm{H}) = 1.010(9)$ fm, $R_\mathrm{Z}(μ\mathrm{H}) = 1.040(33)$ fm. The total proton-structure effect to the hfs at $O(α^5)$ 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 $μ\text{H}$ is $182.640(18)\,\mathrm{meV}.$ |
| title | Chiral perturbation theory of the hyperfine splitting in (muonic) hydrogen |
| topic | Nuclear Theory High Energy Physics - Phenomenology Atomic Physics |
| url | https://arxiv.org/abs/2305.09633 |