The Lamb shift of the 1s state in hydrogen: Two-loop and three-loop contributions
Abstract
We consider the 1s Lamb shift in hydrogen and helium ions, a quantity, required for an accurate determination of the Rydberg constant and the proton charge radius by means of hydrogen spectroscopy, as well as for precision tests of the bound-state QED. The dominant QED contribution to the uncertainty originates from α8 m external-field contributions (i.e., the contributions at the non-recoil limit). We discuss the two- and three-loop cases and in particular, we revisit calculations of the coefficients B61 ,B60 ,C50 in standard notation.
We have found a missing logarithmic contribution of order α2(Zα) 6 m. We have also obtained leading pure self-energy logarithmic contributions of order α2(Zα) 8 m and α2(Zα) 9 m and estimated the subleading terms of order α2(Zα) 7 m, α2(Zα) 8 m, and α2(Zα) 9 m. The determination of those higher-order contributions enabled us to improve the overall accuracy of the evaluation of the two-loop self-energy of the electron. We investigated the asymptotic behavior of the integrand related to the next-to-leading three-loop term (order α3(Zα) 5 m, coefficient C50 in standard notation) and applied it to approximate integration over the loop momentum. Our result for contributions to the 1s Lamb shift for the total three loop next-to-leading term is (- 3.3 ± 10.5) (α3 /π3)(Zα) 5 m. Altogether, we have completed the evaluation of the logarithmic contributions to the 1s Lamb shift of order α8 m and reduced the overall α8 m uncertainty by approximately a factor of three for H, D, and He+ as compared with the most recent CODATA compilation.- Publication:
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Physics Letters B
- Pub Date:
- August 2019
- DOI:
- 10.1016/j.physletb.2019.06.023
- arXiv:
- arXiv:1906.11105
- Bibcode:
- 2019PhLB..795..432K
- Keywords:
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- Physics - Atomic Physics;
- High Energy Physics - Phenomenology
- E-Print:
- 7 pages, 3 figures