One-loop binding corrections to the electron 
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 factor

Pachucki, Krzysztof; Puchalski, Mariusz

doi:10.1103/physreva.96.032503

Cited by 12 publications

(14 citation statements)

References 15 publications

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“…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.…”

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confidence: 69%

“…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.…”

mentioning

confidence: 69%

“…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][2][3][4][5][6][7][8][9][10]. Its theoretical and experimental values in 28 Si 13+ were found to be in excellent agreement [1].…”

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confidence: 99%

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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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confidence: 69%

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confidence: 69%

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confidence: 99%

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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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“…Considered together, selfinteraction and binding effects are described by a double expansion in α π and α Z . At one-loop level of self-interaction, g is known analytically including the very recently computed terms of order α π α 5 Z [21]. Higher order terms in α Z have been computed numerically [22].…”

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confidence: 99%

Two-Loop Binding Corrections to the Electron Gyromagnetic Factor

et al. 2018

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“…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.…”

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confidence: 99%

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

et al. 2018

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A theoretical description of the g factor of a muon bound in a nuclear potential is presented. Oneloop self-energy and multiloop vacuum polarization corrections are calculated, taking into account the interaction with the binding potential exactly. Nuclear effects on the bound-muon g factor are also evaluated. We put forward the measurement of the bound-muon g factor via the continuous Stern-Gerlach effect as an independent means to determine the muon's magnetic moment anomaly and mass. The scheme presented enables the increase of the accuracy of the mass by more than an order of magnitude.

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One-loop binding corrections to the electron g factor

Abstract: We calculate the one-loop electron self-energy correction of order α (Z α) 5 to the bound electron g factor. Our result is in agreement with the extrapolated numerical value and paves the way for the calculation of the analogous, but as yet unknown two-loop correction.

Cited by 12 publications

References 15 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

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

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