The Lamb shift of the 1$s$ state in hydrogen: Two-loop and three-loop contributions - INSPIRE

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The Lamb shift of the 1 $s$ state in hydrogen: Two-loop and three-loop contributions

Jun 26, 2019

6 pages

Published in:

Phys.Lett.B 795 (2019) 432-437

Published: Aug 10, 2019

e-Print:

1906.11105 [physics.atom-ph]

DOI:

10.1016/j.physletb.2019.06.023 (publication)

Report number:

TUM-HEP-1179/18

View in:

ADS Abstract Service

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Abstract: (Elsevier)

We consider the 1 s 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 α8m 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)6m . We have also obtained leading pure self-energy logarithmic contributions of order α2(Zα)8m and α2(Zα)9m and estimated the subleading terms of order α2(Zα)7m , α2(Zα)8m , and α2(Zα)9m . 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)5m , coefficient C50 in standard notation) and applied it to approximate integration over the loop momentum. Our result for contributions to the 1 s Lamb shift for the total three loop next-to-leading term is (−3.3±10.5)(α3/π3)(Zα)5m . Altogether, we have completed the evaluation of the logarithmic contributions to the 1 s Lamb shift of order α8m and reduced the overall α8m uncertainty by approximately a factor of three for H, D, and He + as compared with the most recent CODATA compilation.

Note:

7 pages, 3 figures

quantum electrodynamics: perturbation theory
perturbation theory: higher-order
p: charge radius
helium: ion
hydrogen: ion
Lamb shift
precision measurement
atom: excited state

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