The Lamb shift of the 1s state in hydrogen: Twoloop and threeloop 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 boundstate QED. The dominant QED contribution to the uncertainty originates from α^{8} m externalfield contributions (i.e., the contributions at the nonrecoil limit). We discuss the two and threeloop cases and in particular, we revisit calculations of the coefficients B_{61} ,B_{60} ,C_{50} in standard notation.
We have found a missing logarithmic contribution of order α^{2}^{(Zα) 6} m. We have also obtained leading pure selfenergy logarithmic contributions of order α^{2}^{(Zα) 8} m and α^{2}^{(Zα) 9} m and estimated the subleading terms of order α^{2}^{(Zα) 7} m, α^{2}^{(Zα) 8} m, and α^{2}^{(Zα) 9} m. The determination of those higherorder contributions enabled us to improve the overall accuracy of the evaluation of the twoloop selfenergy of the electron.
We investigated the asymptotic behavior of the integrand related to the nexttoleading threeloop term (order α^{3}^{(Zα) 5} m, coefficient C_{50} 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 nexttoleading term is ( 3.3 ± 10.5) (α^{3} /π^{3})^{(Zα) 5} m.
Altogether, we have completed the evaluation of the logarithmic contributions to the 1s Lamb shift of order α^{8} m and reduced the overall α^{8} m uncertainty by approximately a factor of three for H, D, and He^{+} as compared with the most recent CODATA compilation.
 Publication:

Physics Letters B
 Pub Date:
 August 2019
 DOI:
 10.1016/j.physletb.2019.06.023
 arXiv:
 arXiv:1906.11105
 Bibcode:
 2019PhLB..795..432K
 Keywords:

 Physics  Atomic Physics;
 High Energy Physics  Phenomenology
 EPrint:
 7 pages, 3 figures