Two-loop QED corrections with closed fermion loops for the bound-electron<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>g</mml:mi></mml:math>factor

Yerokhin, V. A.; Harman, Z.

doi:10.1103/physreva.88.042502

Cited by 43 publications

(41 citation statements)

References 37 publications

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“…At high nuclear charges, where Zα ≈ 1, an expansion in Zα is not applicable. So far, the two-loop diagrams with two electric vacuum polarization (VP) loops and those with one electric VP and one self-energy (SE) loop were evaluated nonperturbatively in Zα [20].For a broad range of Z, the two-loop SE corrections, which are by far the hardest to calculate, constitute the largest source of uncertainty. This holds true even at Z = 6, after a recent high-precision evaluation of the one-loop SE corrections [4,18].…”

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Theory of the two-loop self-energy correction to the g factor in nonperturbative Coulomb fields

Sikora

Cakir

Oreshkina

et al. 2020

Phys. Rev. Research

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Two-loop self-energy corrections to the bound-electron g factor are investigated theoretically to all orders in the nuclear binding strength parameter Zα. The separation of divergences is performed by dimensional regularization, and the contributing diagrams are regrouped into specific categories to yield finite results. We evaluate numerically the loop-after-loop terms, and the remaining diagrams by treating the Coulomb interaction in the electron propagators up to first order. The results show that such two-loop terms are mandatory to take into account for projected near-future stringent tests of quantum electrodynamics and for the determination of fundamental constants through the g factor. PACS numbers: 06.20.Jr, 21.10.Ky, 31.30.jn, 31.15.ac, 32.10.Dk The g factor of one-electron ions can be measured and calculated with an exceptional accuracy [1-10]. Its theoretical and experimental values in 28 Si 13+ were found to be in excellent agreement [1]. Since then, the experimental uncertainty decreased by an order of magnitude [2]. Such measurements also allowed an improved determination of the electron mass [11] (see also [12,13]). It is anticipated that boundelectron g factor measurements will also enable in the foreseeable future an independent determination of the fine-structure constant α [14,15].To push forward the boundaries of theory, quantum electrodynamic (QED) corrections at the one-and two-loop level need to be calculated with increasing accuracy. One-loop corrections have been evaluated both as a power series in Zα (with Z being the atomic number) and non-perturbatively in this parameter (see e.g. [16][17][18]). Two-loop corrections were evaluated up to fourth order in Zα [16,19]. Contributions of order α 2 (Zα) 5 were completed very recently [10]. At high nuclear charges, where Zα ≈ 1, an expansion in Zα is not applicable. So far, the two-loop diagrams with two electric vacuum polarization (VP) loops and those with one electric VP and one self-energy (SE) loop were evaluated nonperturbatively in Zα [20].For a broad range of Z, the two-loop SE corrections, which are by far the hardest to calculate, constitute the largest source of uncertainty. This holds true even at Z = 6, after a recent high-precision evaluation of the one-loop SE corrections [4,18]. We thus see that higher-order terms in Zα are also necessary at lower nuclear charges, if an ultimate precision is required. Therefore, in the current Letter we present the theoretical framework for the non-perturbative evaluation of the two-loop SE terms.There are three two-loop SE diagrams contributing to the binding energy of a hydrogenlike ion, namely, the loopafter-loop (LAL), the nested loops (N) and the overlapping loops (O) diagrams. Their calculation has been presented in detail in Refs. [21][22][23][24][25][26]. The corresponding diagrams for the g factor can be generated by magnetic vertex insertions into the Lamb shift diagrams, yielding three nonequivalent diagrams in each of the above classes, shown in Fig. 1.Basic analysis.-We derived ...

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Theory of the two-loop self-energy correction to the g factor in nonperturbative Coulomb fields

Sikora

Cakir

Oreshkina

et al. 2020

Phys. Rev. Research

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“…The fit performed in [15,16] resulted in b 50 (fit) = −4.0(5.1). Here we directly determine contributions to b 50 beyond the already known vacuum-polarization effects b VP 50 [25,28]. We write b 50 = b VP 50 + ∆b 50 and set out to compute…”

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“…Diagrams with the external magnetic field coupling to the virtual electron loop are expected to be small [25]. In this class, we consider only the so-called magnetic loop contributions [37], examples of which are shown in Fig.…”

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Two-Loop Binding Corrections to the Electron Gyromagnetic Factor

et al. 2018

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“…These results could be further improved by combining theoretical and experimental values for two different H-like ions (Sturm et al, 2014). This idea of combining precise g-factor measurements and QED calculations (Czarnecki and Szafron, 2016;Sturm et al, 2013a;Yerokhin and Harman, 2013), has recently yielded a 13-fold improvement on the electron mass determination (Köhler et al, 2015;Sturm et al, 2014;Zatorski et al, 2017).…”

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Highly charged ions: Optical clocks and applications in fundamental physics

et al. 2018

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Recent developments in frequency metrology and optical clocks have been based on electronic transitions in atoms and singly charged ions as references. The control over all relevant degrees of freedom in these atoms has enabled relative frequency uncertainties at a level of a few parts in 10 −18 . This accomplishment not only allows for extremely accurate time and frequency measurements, but also to probe our understanding of fundamental physics, such as a possible variation of fundamental constants, a violation of the local Lorentz invariance, and the existence of forces beyond the Standard Model of Physics. In addition, novel clocks are driving the development of sophisticated technical applications. Crucial for applications of clocks in fundamental physics are a high sensitivity to effects beyond the Standard Model and Einstein's Theory of Relativity and a small frequency uncertainty of the clock. Highly charged ions offer both. They have been proposed as highly accurate clocks, since they possess optical transitions which can be extremely narrow and less sensitive to external perturbations compared to current atomic clock species. The large selection of highly charged ions in different charge states offers narrow transitions that are among the most sensitive ones for a change in the finestructure constant and the electron-to-proton mass ratio, as well as other new physics effects. Recent experimental advances in trapping and sympathetic cooling of highly charged ions will in the future enable advanced quantum logic techniques for controlling motional and internal degrees of freedom and thus enable high accuracy optical spectroscopy. Theoretical progress in calculating the properties of selected highly charged ions has allowed the evaluation of systematic shifts and the prediction of the sensitivity to the "new physics" effects. New theoretical challenges and opportunities emerge from relativistic, quantum electrodynamics, and nuclear size contributions that become comparable with interelectronic correlations. This article reviews the current status of theory and experiment in the field, addresses specific electronic configurations and systems which show the most promising properties for research, their potential limitations, and the techniques for their study.

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Two-loop QED corrections with closed fermion loops for the bound-electrongfactor

Cited by 43 publications

References 37 publications

Theory of the two-loop self-energy correction to the g factor in nonperturbative Coulomb fields

Theory of the two-loop self-energy correction to the g factor in nonperturbative Coulomb fields

Two-Loop Binding Corrections to the Electron Gyromagnetic Factor

Highly charged ions: Optical clocks and applications in fundamental physics

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