THE subject of quantum electrodynamics is extremely difficult, even for the case of a single electron. The usual method of solving the corresponding wave equation leads to divergent integrals. To avoid these, Prof. P. A. M. Dirac* uses the method of redundant variables. This does not abolish the difficulty, but presents it in a new form, which may be dealt with in two ways. The first of these needs only comparatively simple mathematics and is directly connected with an elegant general scheme, but unfortunately its wave functions apply only to a hypothetical world and so its physical interpretation is indirect. The second way has the advantage of a direct physical interpretation, but the mathematics is so complicated that it has not yet been solved even for what appears to be the simplest possible case. Both methods seem worth further study, failing the discovery of a third which would combine the advantages of both.

http://ieeexplore.ieee.org/iel5/3/22993/01069961.pdf

Quantum electrodynamics

https://www.zora.uzh.ch/id/eprint/191493/1/1-s2.0-S0370157320302556-main.pdf

The anomalous magnetic moment of the muon in the Standard Model

We update our standard model predictions for g − 2 of the muon and for the hadronic contributions to the running of the QED coupling, Δα(5)had(M2Z). Particular emphasis is put on recent changes in the hadronic contributions from new data in the 2π channel and from the energy region just below 2 GeV. In particular, for the e+e− → π+π− contribution we include the recent 'radiative return' data from KLOE and BaBar. We also include the recent BaBar data on other exclusive channels. We make a detailed study of the effect of replacing the measurements of the inclusive cross section, σ(e+e− → hadrons), by the sum of the exclusive channels in the energy interval GeV, which includes a QCD sum-rule analysis of this energy region. Our favoured prediction for the muon anomalous magnetic moment is (g − 2)/2 = (11 659 182.8 ± 4.9) × 10−10 which is 3.3 σ below the present world-average measurement. We compare our g − 2 value with other recent calculations. Our prediction for the QED coupling, obtained via Δα(5)had(MZ2) = (276.26 ± 1.38) × 10−4 , is α(M2Z)−1 = 128.944 ± 0.019.

(g-2)_mu and alpha(M_Z^2) re-evaluated using new precise data

Measurements of the fine-structure constant α require methods from across subfields and are thus powerful tests of the consistency of theory and experiment in physics. Using the recoil frequency of cesium-133 atoms in a matter-wave interferometer, we recorded the most accurate measurement of the fine-structure constant to date: α = 1/137.035999046(27) at 2.0 × 10 −10 accuracy. Using multiphoton interactions (Bragg diffraction and Bloch oscillations), we demonstrate the largest phase (12 million radians) of any Ramsey-Borde interferometer and control systematic effects at a level of 0.12 part per billion. Comparison with Penning trap measurements of the electron gyromagnetic anomaly g e − 2 via the Standard Model of particle physics is now limited by the uncertainty in g e − 2; a 2.5σ tension rejects dark photons as the reason for the unexplained part of the muon’s magnetic moment at a 99% confidence level. Implications for dark-sector candidates and electron substructure may be a sign of physics beyond the Standard Model that warrants further investigation.

https://science.sciencemag.org/content/sci/360/6385/191.full.pdf

Measurement of the fine-structure constant as a test of the Standard Model

We reevaluate the hadronic vacuum polarisation contributions to the muon magnetic anomaly and to the running of the electromagnetic coupling constant at the Z-boson mass. We include newest $e^+e^- \rightarrow \mathrm{hadrons}$ cross-section data (among others) from the BABAR and VEPP-2000 experiments. For the muon $(g-2)/2$ we find for the lowest-order hadronic contribution $(693.1 \pm 3.4)\times 10^{-10}$ , improving the precision of our previous evaluation by 21%. The full Standard Model prediction differs by $3.5\,\sigma $ from the experimental value. The five-quark hadronic contribution to $\alpha (m_Z^2)$ is evaluated to be $(276.0\pm 0.9)\times 10^{-4}$ .

/pdf/reevaluation-of-the-hadronic-vacuum-polarisation-3ho52mfpld.pdf

Reevaluation of the hadronic vacuum polarisation contributions to the Standard Model predictions of the muon $g-2$ and ${\alpha (m_Z^2)}$ using newest hadronic cross-section data

We report the result of our calculation of the complete tenth-order QED terms of the muon $g\ensuremath{-}2$. Our result is ${a}_{\ensuremath{\mu}}^{(10)}=753.29$ (1.04) in units of $(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$, which is about 4.5 s.d. larger than the leading-logarithmic estimate 663(20). We also improve the precision of the eighth-order QED term of ${a}_{\ensuremath{\mu}}$, obtaining ${a}_{\ensuremath{\mu}}^{(8)}=130.8794$ (63) in units of $(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{4}$. The new QED contribution is ${a}_{\ensuremath{\mu}}(\mathrm{QED})=116\text{ }584\text{ }718\text{ }951\text{ }(80)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}14}$, which does not resolve the existing discrepancy between the standard-model prediction and measurement of ${a}_{\ensuremath{\mu}}$.

Complete Tenth-Order QED Contribution to the Muon g − 2

This Letter presents the complete QED contribution to the electron $g\ensuremath{-}2$ up to the tenth order. With the help of the automatic code generator, we evaluate all 12 672 diagrams of the tenth-order diagrams and obtain $9.16\text{ }(58)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$. We also improve the eighth-order contribution obtaining $\ensuremath{-}1.9097\text{ }(20)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{4}$, which includes the mass-dependent contributions. These results lead to ${a}_{e}(\mathrm{\text{theory}})=1\text{ }159\text{ }652\text{ }181.78(77)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$. The improved value of the fine-structure constant ${\ensuremath{\alpha}}^{\ensuremath{-}1}=137.035\text{ }999\text{ }173\text{ }(35)$ [0.25 ppb] is also derived from the theory and measurement of ${a}_{e}$.

Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant

The anomalous magnetic moment of the electron a e measured in a Penning trap occupies a unique position among high precision measurements of physical constants in the sense that it can be compared directly with the theoretical calculation based on the renormalized quantum electrodynamics (QED) to high orders of perturbation expansion in the fine structure constant α , with an effective parameter α / π . Both numerical and analytic evaluations of a e up to ( α / π ) 4 are firmly established. The coefficient of ( α / π ) 5 has been obtained recently by an extensive numerical integration. The contributions of hadronic and weak interactions have also been estimated. The sum of all these terms leads to a e ( theory ) = 1 159 652 181.606 ( 11 ) ( 12 ) ( 229 ) × 10 − 12 , where the first two uncertainties are from the tenth-order QED term and the hadronic term, respectively. The third and largest uncertainty comes from the current best value of the fine-structure constant derived from the cesium recoil measurement: α − 1 ( Cs ) = 137.035 999 046 ( 27 ) . The discrepancy between a e ( theory ) and a e ( ( experiment ) ) is 2.4 σ . Assuming that the standard model is valid so that a e (theory) = a e (experiment) holds, we obtain α − 1 ( a e ) = 137.035 999 1496 ( 13 ) ( 14 ) ( 330 ) , which is nearly as accurate as α − 1 ( Cs ) . The uncertainties are from the tenth-order QED term, hadronic term, and the best measurement of a e , in this order.

/pdf/theory-of-the-anomalous-magnetic-moment-of-the-electron-1e1lea17gp.pdf

Theory of the Anomalous Magnetic Moment of the Electron

This paper presents a detailed account of the evaluation of the electron anomalous magnetic moment ${a}_{e}$ which arises from a gauge-invariant set, called Set V, consisting of 6354 tenth-order Feynman diagrams without closed lepton loops. The latest value of the sum of Set V diagrams evaluated by the Monte Carlo integration routine VEGAS is 8.726 $(336)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$, which replaces the very preliminary value reported in 2012. Combining it with 6318 previously published tenth-order diagrams, we obtain 7.795 $(336)(\ensuremath{\alpha}/\ensuremath{\pi}{)}^{5}$ as the complete mass-independent tenth-order term. Together with the improved value of the eighth-order term this leads to ${a}_{e}(\text{theory})=1\text{ }159\text{ }652\text{ }181.643\text{ }(25)(23)(16)(763)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}12}$, where the first three uncertainties are from the eighth-order, tenth-order, and hadronic and elecroweak terms. The fourth and largest uncertainty is from ${\ensuremath{\alpha}}^{\ensuremath{-}1}=137.035\text{ }999\text{ }049\text{ }(90)$, the fine-structure constant derived from the rubidium recoil measurement. Thus, ${a}_{e}(\text{experiment})\ensuremath{-}{a}_{e}(\text{theory})=\ensuremath{-}0.91\text{ }(0.82)\ifmmode\times\else\texttimes\fi{}1{0}^{\ensuremath{-}12}$. Assuming the validity of the standard model, we obtain the fine-structure constant ${\ensuremath{\alpha}}^{\ensuremath{-}1}({a}_{e})=\phantom{\rule{0ex}{0ex}}137.035\text{ }999\text{ }1570\text{ }(29)(27)(18)(331)$, where uncertainties are from the eighth-order, tenth-order, and hadronic and electroweak terms, and the measurement of ${a}_{e}$. This is the most precise value of $\ensuremath{\alpha}$ available at present and provides a stringent constraint on possible theories beyond the standard model.

Tenth-Order Electron Anomalous Magnetic Moment --- Contribution of Diagrams without Closed Lepton Loops

We present the first observation of a flavor-singlet scalar meson as light as the pion in ${N}_{f}=8$ QCD on the lattice, using the highly improved staggered quark action. Such a light scalar meson can be regarded as a composite Higgs with mass 125 GeV. In accord with our previous lattice results showing that the theory exhibits walking behavior, the light scalar may be a technidilaton, a pseudo-Nambu-Goldstone boson of the approximate scale symmetry in walking technicolor.

Tatsumi Aoyama

Papers

Complete Tenth-Order QED Contribution to the Muon g − 2

Tenth-Order QED Contribution to the Electron g-2 and an Improved Value of the Fine Structure Constant

Theory of the Anomalous Magnetic Moment of the Electron

Tenth-Order Electron Anomalous Magnetic Moment --- Contribution of Diagrams without Closed Lepton Loops

Light composite scalar in eight-flavor QCD on the lattice