Two-Loop Binding Corrections to the Electron Gyromagnetic Factor

Abstract

We compute corrections to the gyromagnetic factor of an electron bound in a hydrogen-like ion at order α 2 (Zα) 5 . This result removes a major uncertainty in predictions for silicon and carbon ions, used to determine the atomic mass of the electron.

Self-energy screening effects in the g factor of Li-like ions

“…Extensions of these tests towards heavier H-like ions are anticipated in the future [4]. The main obstacle for such extensions is presently on the theory side, caused by the insufficiently known two-loop QED effects [5][6][7].…”

“…We aim to cross-check the previously publishes results, to improve the numerical accuracy, and to perform a detailed analysis of consistency of the all-order numerical approach against the Zα-expansion calculations. To achieve this, we extend the existing Zα-expansion results by deriving the leading logarithmic contribution of order α 5 ln α and obtaining approximate results for the α 5 and α 6 contributions. Combining the two methods, we obtain improved estimations for the higher-order screening effects ∝1/Z 2+ and increase the accuracy of the theoretical description of the QED screening effects in light Li-like ions.…”

Improving the accuracy of the muon mass and magnetic moment anomaly via the bound-muon g factor

“…The corresponding two-loop contribution (given in Table I as "magnetic loop þ Uehling") is below the uncertainty at which we aim. We note that further two-loop corrections evaluated very recently for electronic ions, such as two-loop LBL scattering terms [16,67] may also contribute significantly. Their calculation can be extended to the case of muons in a straightforward manner employing the methods of Ref.…”

“…Binding corrections to the two-loop self-energy diagrams were determined up to order ðZαÞ 5 using formulas from Refs. [14,16,[41][42][43]. Finally, there is a two-loop diagram with a VP loop inserted in the virtual photon line of the one-loop vertex diagram (S(eVP)E in Table I); its ðZαÞ 0 contribution is included in the free g-factor, and binding corrections of order ðZαÞ 2 were computed according to Refs.…”

“…Fast progress in the theoretical understanding and experimental precision of the bound-electron g factor (see e.g., [8][9][10][11][12][13][14][15][16] and references therein) has enabled the most accurate determination of the mass of the electron in Penning trap g-factor experiments by means of the continuous SternGerlach effect [8,[17][18][19][20]. In this paper we put forward a similar method for the extraction of the mass of the muon by employing light muonic ions, by which we mean here bound systems solely consisting of a nucleus and a muon without further surrounding electrons.…”