https://doi.org/10.1140/epjc/s10052-023-11866-4
Regular Article - Theoretical Physics
Chiral perturbation theory of the hyperfine splitting in (muonic) hydrogen
1
Institute of Nuclear Physics, Johannes Gutenberg Universität Mainz, 55099, Mainz, Germany
2
PRISMA+ Cluster of Excellence, Johannes Gutenberg Universität Mainz, 55099, Mainz, Germany
3
Laboratory for Particle Physics, Paul Scherrer Institute, 5232, Villigen PSI, Switzerland
Received:
22
May
2023
Accepted:
25
July
2023
Published online:
29
August
2023
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 
, which is 
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
PT). At leading orders it provides a prediction for the proton polarizability effects in hydrogen (H) and muonic hydrogen (
H). We find large cancellations among the various contributions leading to, within the uncertainties, a zero polarizability effect at leading order in the BPT expansion. This result is in significant disagreement with the current data-driven evaluations. The small polarizability effect implies a smaller Zemach radius 
, if one uses the well-known experimental 1S hfs in H or the 2S hfs in H. We, respectively, obtain 
fm, 
fm. The total proton-structure effect to the hfs at 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 
is 
© The Author(s) 2023
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