TENTH-ORDER QED CONTRIBUTION TO THE ELECTRON g-2 AND HIGH PRECISION TEST OF QUANTUM ELECTRODYNAMICS

2014 ◽  
Vol 29 (02) ◽  
pp. 1430003 ◽  
Author(s):  
TOICHIRO KINOSHITA
Keyword(s):  
Perturbation Theory ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Feynman Diagrams ◽  
Current Status ◽  
Complete Evaluation ◽  
Code Generator ◽  
Parametric Integrals ◽  
Precision Test

This paper presents the current status of the theory of electron anomalous magnetic moment ae ≡(g-2)/2, including a complete evaluation of 12,672 Feynman diagrams in the tenth-order perturbation theory. To solve this problem, we developed a code-generator which converts Feynman diagrams automatically into fully renormalized Feynman-parametric integrals. They are evaluated numerically by an integration routine VEGAS. The preliminary result obtained thus far is 9.16 (58) (α/π)5, where (58) denotes the uncertainty in the last two digits. This leads to ae( theory ) = 1.159 652 181 78 (77) ×10-3, which is in agreement with the latest measurement ae ( exp :2008) = 1.159 652 180 73 (28) ×10-3. It shows that the Feynman–Dyson method of perturbative QED works up to the precision of 10-12.

scholarly journals Stochastic computation of g − 2 in QED

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Ryuichiro Kitano ◽  
Hiromasa Takaura ◽  
Shoji Hashimoto
Keyword(s):  
Perturbation Theory ◽  
Numerical Computation ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Stochastic Perturbation ◽  
Higher Order ◽  
Feynman Diagrams ◽  
Perturbative Series ◽  
Physical Quantities

Abstract We perform a numerical computation of the anomalous magnetic moment (g − 2) of the electron in QED by using the stochastic perturbation theory. Formulating QED on the lattice, we develop a method to calculate the coefficients of the perturbative series of g − 2 without the use of the Feynman diagrams. We demonstrate the feasibility of the method by performing a computation up to the α3 order and compare with the known results. This program provides us with a totally independent check of the results obtained by the Feynman diagrams and will be useful for the estimations of not-yet-calculated higher order values. This work provides an example of the application of the numerical stochastic perturbation theory to physical quantities, for which the external states have to be taken on-shell.

scholarly journals Quantum electrodynamics with self-conjugated equations with spinor wave functions for fermion fields

2021 ◽  
pp. 2150086
Author(s):  
V. P. Neznamov ◽  
V. E. Shemarulin
Keyword(s):  
Cross Sections ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Lamb Shift ◽  
Wave Functions ◽  
Self Energy ◽  
Fermion Fields ◽  
Spinor Wave

Quantum electrodynamics (QED) with self-conjugated equations with spinor wave functions for fermion fields is considered. In the low order of the perturbation theory, matrix elements of some of QED physical processes are calculated. The final results coincide with cross-sections calculated in the standard QED. The self-energy of an electron and amplitudes of processes associated with determination of the anomalous magnetic moment of an electron and Lamb shift are calculated. These results agree with the results in the standard QED. Distinctive feature of the developed theory is the fact that only states with positive energies are present in the intermediate virtual states in the calculations of the electron self-energy, anomalous magnetic moment of an electron and Lamb shift. Besides, in equations, masses of particles and antiparticles have the opposite signs.

scholarly journals Theory of the Anomalous Magnetic Moment of the Electron

Atoms ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 28 ◽  
Author(s):  
Tatsumi Aoyama ◽  
Toichiro Kinoshita ◽  
Makiko Nio
Keyword(s):  
Fine Structure ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Penning Trap ◽  
Weak Interactions ◽  
Perturbation Expansion ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Best Value

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.

scholarly journals Pion mass dependence of the HVP contribution to muon g – 2

2018 ◽  
Vol 175 ◽  
pp. 06010
Author(s):  
Maarten Golterman ◽  
Kim Maltman ◽  
Santiago Peris
Keyword(s):  
Perturbation Theory ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Pion Mass ◽  
Systematic Errors ◽  
Mass Dependence ◽  
Chiral Perturbation ◽  
Muon Anomalous Magnetic Moment ◽  
Chiral Extrapolation ◽  
Pion Mass Dependence

One of the systematic errors in some of the current lattice computations of the HVP contribution to the muon anomalous magnetic moment g – 2 is that associated with the extrapolation to the physical pion mass. We investigate this extrapolation assuming lattice pion masses in the range of 220 to 440 MeV with the help of two-loop chiral perturbation theory, and find that such an extrapolation is unlikely to lead to control of this systematic error at the 1% level. This remains true even if various proposed tricks to improve the chiral extrapolation are taken into account.

Über den magnetischen Formfaktor des Nukleons

1959 ◽  
Vol 14 (8) ◽  
pp. 699-707
Author(s):  
H. Eisenlohr ◽  
H. Salecker
Keyword(s):  
Perturbation Theory ◽  
Form Factor ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Form Factors ◽  
Sufficient Accuracy ◽  
Mean Square ◽  
Vector Form ◽  
High Q ◽  
Moment Distribution

This article deals with the form factor of the anomalous magnetic moment distribution of proton and neutron. It is first shown with three examples that the magnetic root mean square radius cannot be taken from the existing experiments with sufficient accuracy. Satisfactory agreement with the experimental results can be obtained with arbitrary values of rm2. We calculate the magnetic moment form factors depending on the energy momentum transfer q2 in perturbation theory and the 2 π meson contribution to the isotopic vector form factor with dispersion relations also in relation to q2, with and without π meson form factor. We get better agreement of the shape of the form factor with the phenomenological form factor of HOFSTADTER at the expense of the static magnetic moment. But the contribution of the high q2 values is still too large i.e. the structure is somewhat too concentrated **

Introductory remarks

1982 ◽  
Vol 304 (1482) ◽  
pp. 3-4
Keyword(s):  
World War Ii ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Power Series Expansion ◽  
Structure Constant ◽  
Fine Structure Constant ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Abelian Gauge

The title of this meeting, which refers to gauge theories, could equivalently have specified renormalizable quantum field theories. The first quantum field theory arose from the quantization by Dirac, Heisenberg and Pauli of Maxwell’s classical theory of electromagnetism. This immediately revealed the basic problem that although the smallness of the fine-structure constant appeared to give an excellent basis for a power-series expansion, corrections to lowest order calculations gave meaningless infinite results. Quantum electrodynamics (QED ) is, of course, an Abelian gauge theory, and the first major triumph o f fundamental physics after World War II was the removal of the infinities from the theory by the technique of renormalization developed by Schwinger, Feynman and Dyson, stimulated by the measurement of the Lamb shift and the anomalous magnetic moment of the electron. In the intervening years, especially through the beautiful experiments at Cern on the anomalous magnetic moment of the muon, the agreement between this theory and experiment has been pushed to the extreme technical limits of both measurement and calculation.

scholarly journals Testing dark matter with the anomalous magnetic moment in a dark matter quantum electrodynamics model

2017 ◽  
Vol 32 (33) ◽  
pp. 1750175
Author(s):  
Ashok K. Das ◽  
Jorge Gamboa ◽  
Fernando Méndez ◽  
Natalia Tapia
Keyword(s):  
Dark Matter ◽  
Magnetic Moment ◽  
Anomalous Magnetic Moment ◽  
Quantum Electrodynamics ◽  
Heavy Fermions ◽  
Mass Ratio ◽  
Dark Photon ◽  
The Masses ◽  
Visible Photon

We consider a model of dark quantum electrodynamics (QEDs) which is coupled to a visible photon through a kinetic mixing term. We compute the [Formula: see text] for the dark fermion, where [Formula: see text] is its gyromagnetic factor. We show that the [Formula: see text] of the dark fermion is related to the [Formula: see text] of (visible) QEDs through a constant which depends on the kinetic mixing factor. We determine [Formula: see text] as a function of the mass ratio [Formula: see text], where [Formula: see text] and [Formula: see text] denote the masses of the dark photon and the dark fermion, respectively, and we show how [Formula: see text] becomes very different for light and heavy fermions around [Formula: see text] eV.

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