Higher-order logarithmic corrections and the two-loop self-energy of a 1s electron in hydrogen

Karshenboim, Savely G.; Ozawa, Akira und Ivanov, Vladimir G. (2019): Higher-order logarithmic corrections and the two-loop self-energy of a 1s electron in hydrogen. In: Physical Review A, Bd. 100, Nr. 3, 032515

Abstract

The leading computational QED uncertainty of the Lamb shift in the ls state in the hydrogen atom and helium ion is due to two-loop pure self-energy contributions. An exact evaluation in Z alpha has not yet been performed for Z = 1,2, while a calculation based on the Z alpha expansion has a limited accuracy. To improve it, we calculate a leading logarithmic contribution in order alpha(2)(Z alpha)(8)m and estimate the nonleading subterms in orders alpha(2)(Z alpha)(7)m and alpha(2)(Z alpha)(8)m. To further improve the accuracy, we take advantage of a combined evaluation of the numerical results of the exact calculations in Z alpha performed at Z = 10-30, and the results of the Z alpha expansion in order to reach the most accurate result, which can be done by fitting the data. The quality of the fit, including its reliability and accuracy, strongly depends on a theoretical input, which is the main target of this paper. Strictly speaking, we develop not a fit, but a theoretical approximation for the pure self-energy contribution, which may serve as a base for a robust fit. It is also important to estimate a deviation of the truncated function from the true one. For this purpose, we calculate the leading logarithmic term and estimate the subleading ones in order alpha(2)(Z alpha)(9)m. That allows us to find a reliable result which is more accurate than both fits over the numerical data and the results from the Z alpha expansion, which have been previously considered in literature. Performing the fit procedures, we focus our attention on the theoretical input which plays an essential role in the reliability and accuracy of the fit. Our results for the two-loop pure self-energy contribution to the 1s Lamb shift are expressed in a standard notation as B-60 = -72(7), G(60) (Z =1) = -80(6), and G(60 )(Z = 2) = -83(5). That significantly improves the theoretical accuracy of the 1s Lamb shift in hydrogen, deuterium, and in the helium ions.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Physik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 530 Physik
• ISSN: 2469-9926
• Sprache: Englisch