New measurement of the electron magnetic moment and the fine structure constant

A measurement using a one-electron quantum cyclotron gives the electron magnetic moment in Bohr magnetons, g/2=1.001 159 652 180 73 (28) [0.28 ppt], with an uncertainty 2.7 and 15 times smaller than for previous measurements in 2006 and 1987. The electron is used as a magnetometer to allow line shape statistics to accumulate, and its spontaneous emission rate determines the correction for its interaction with a cylindrical trap cavity. The new measurement and QED theory determine the fine structure constant, with alpha{-1}=137.035 999 084 (51) [0.37 ppb], and an uncertainty 20 times smaller than for any independent determination of alpha.     

New measurement of the electron magnetic moment using a one-electron quantum cyclotron

A new measurement resolves cyclotron and spin levels for a single-electron quantum cyclotron to obtain an electron magnetic moment, given by g/2=1.001 159 652 180 85 (76) [0.76 ppt]. The uncertainty is nearly 6 times lower than in the past, and g is shifted downward by 1.7 standard deviations. The new g, with a quantum electrodynamics (QED) calculation, determines the fine structure constant with a 0.7 ppb uncertainty--10 times smaller than for atom-recoil determinations. Remarkably, this 100 mK measurement probes for internal electron structure at 130 GeV.     

Radiative corrections to the polarizability of helium

The complete alpha(3) QED correction to the helium atom polarizability is computed assuming an infinite nuclear mass and found to be equal to 0.000030666(3) a.u., with the contribution from the electric-field dependence of the Bethe logarithm amounting to 0.000000193(2) a.u. After including the alpha(2) and alpha(3) corrections for the nuclear recoil and the leading part of the alpha(4) QED correction, we find that the molar polarizability of 4He is 0.51725419(9)(4) cm(3)/mol. The first of the two error bounds is dominated by the uncertainty of alpha(4) and higher-order QED corrections and the second reflects the uncertainty of the Avogadro constant.     

Does the electron have a structure?

... it ain't likely to have a radius of exactly zero, is the conclusion of H. G. Dehmelt⁽¹⁾ from his Nobel Prize (1989) winning observations on trapped electrons. There are small discrepancies between Dehmelt's observations and the theoretical predictions of quantum electrodynamics (QED), which assumes that the electron is a point particle. Here we present evidence in support of Dehmelt's contention that the electron has a structure. Essentially, we point out that the nonrelativistic limit of QED is at variance with a fundamental principle underlying all of physics, viz. the second law of thermodynamics.     

The anomalous magnetic moment of the electron

The value of the electron's magnetic moment is a fundamental quantity in physics. Its deviation from the value expected from Dirac theory has given enormous impetus to the field of quantum theory and especially to quantum electrodynamics (QED) as the relativistic quantum field theory of electrodynamics. In fact, the measured values both for free and for bound electrons are explained by corresponding QED calculations on the part per trillion and part per billion level of accuracy, respectively. This agreement is amongst the best known in physics today. In turn, it allows highly precise determinations of related fundamental constants like the fine structure constant α or the electron mass. The present article discusses the application of the continuous Stern–Gerlach effect to the precise measurement of magnetic moments, especially of the electron bound in highly charged ions and possible tests of calculations in the framework of QED of bound states. Also, a test of QED in a more general approach by the comparison of values for the fine structure constant derived from different measurements, will be discussed.     

QED theory of the nuclear magnetic shielding in hydrogenlike ions

The shielding of the nuclear magnetic moment by the bound electron in hydrogenlike ions is calculated ab initio with inclusion of relativistic, nuclear, and quantum electrodynamics (QED) effects. The QED correction is evaluated to all orders in the nuclear binding strength parameter and, independently, to the first order in the expansion in this parameter. The results obtained lay the basis for the high-precision determination of nuclear magnetic dipole moments from measurements of the g factor of hydrogenlike ions.     

Precision measurement of the three 2(3)P(J) helium fine structure intervals

The three 2(3)P fine structure intervals of 4H are measured at an improved accuracy that is sufficient to test two-electron QED theory and to determine the fine structure constant alpha to 14 parts in 10(9). The more accurate determination of alpha, to a precision higher than attained with the quantum Hall and Josephson effects, awaits the reconciliation of two inconsistent theoretical calculations now being compared term by term. A low pressure helium discharge presents experimental uncertainties quite different than for earlier measurements and allows direct measurements of light pressure shifts.     

Precise calculation of transition frequencies of hydrogen and deuterium based on a least-squares analysis

We combine a limited number of accurately measured transition frequencies in hydrogen and deuterium, recent quantum electrodynamics (QED) calculations, and, as an essential additional ingredient, a generalized least-squares analysis, to obtain precise and optimal predictions for hydrogen and deuterium transition frequencies. Some of the predicted transition frequencies have relative uncertainties more than an order of magnitude smaller than that of the g factor of the electron, which was previously the most accurate prediction of QED.     

High-accuracy measurement of the magnetic moment anomaly of the electron bound in hydrogenlike carbon

We present a new experimental value for the magnetic moment of the electron bound in hydrogenlike carbon (12C5+): g(exp) = 2.001 041 596 (5). This is the most precise determination of an atomic g(J) factor so far. The experiment was carried out on a single 12C5+ ion stored in a Penning trap. The high accuracy was made possible by spatially separating the induction of spin flips and the analysis of the spin direction. The current theoretical value amounts to g(th) = 2.001 041 591 (7). Together experiment and theory test the bound-state QED contributions to the g(J) factor of a bound electron to a precision of 1%.     

The anomalous magnetic moment of the electron in hydrogenlike ions

The precise determination of the anomalous magnetic moment of the electron bound in hydrogen-like ions allows for a stringent test of quantum electrodynamics (QED)in the presence of strong electric fields. g-factor measurements on the electron bound in hydrogen-like ions ¹²C⁵⁺ and ¹⁶O⁷⁺, using single ions confined in a Penning trap, have yielded values in agreement with theory on the ppb level. If the QED calculations are considered correct, the results can in turn be used for a determination of fundamental constants like the electron mass m_e, the fine structure constant α or nuclear parameters. We report about presentdevelopments towards g-factor measurements also in medium-heavy and heavy highly-charged ions.     

A Penning trap for g-factor measurements in highly charged ions by laser-microwave double-resonance spectroscopy

Precise determination of bound-electron g-factors in heavy highly-charged ions (e.g. Bi^82?+?, U^91?+?) provides a stringent test of bound-state QED in extreme fields. With a laser-microwave double-resonance technique we will probe the microwave transitions between the Zeeman sub-levels of the hyperfine structure in highly charged ions. From this the bound electron g-factor g_J can be determined. We present the experimental progress of this novel method to measure the g-factor of the bound electron in highly charged ions.     

QED correction to asymmetry for polarized <Emphasis Type="Italic">ep</Emphasis> scattering from the method of electron structure functions

The electron structure function method is applied to calculate model-independent QED radiative corrections to the asymmetry of electron-proton scattering. Representations for both spin-independent and spin-dependent parts of the cross section are derived. Master formulas include the leading corrections in all orders and the main contribution of the second order and provide accuracy of the QED corrections at the level of one per mill. Numerical calculations illustrate our analytic results for both elastic and deep inelastic events.     

Tests of quantum electrodynamics using ion traps

Experiments in ion traps on the g factors for the free and the bound electron in low-Z, hydrogen-like ions have provided the most accurate tests of quantum-electrodynamics calculations. Moreover they have been used to determine new and precise values for fundamental constants. Extensions to more stringent tests using ions of higher values of the nuclear charge Z are on the way. Also other QED tests such as Lamb shifts or hyperfine structures in H-like ions using traps will be feasible in the near future. The tests in bound systems, however, will be limited by nuclear structure effects which are difficult to calculate. Assuming the QED calculations as correct, the experimental results may be used to determine nuclear contributions and thus support nuclear models. Contribution presented at the TCP06, Vancouver Island, 2006.     

First quantized electrodynamics

The parametrized Dirac wave equation represents position and time as operators, and can be formulated for many particles. It thus provides, unlike field-theoretic Quantum Electrodynamics (QED), an elementary and unrestricted representation of electrons entangled in space or time. The parametrized formalism leads directly and without further conjecture to the Bethe–Salpeter equation for bound states. The formalism also yields the Uehling shift of the hydrogenic spectrum, the anomalous magnetic moment of the electron to leading order in the fine structure constant, the Lamb shift and the axial anomaly of QED.     

Logarithms of alpha in QED bound states from the renormalization group

The velocity renormalization group is used to determine lnalpha contributions to QED bound state energies. The leading-order anomalous dimension for the potential gives the alpha(5)lnalpha Lamb shift. The next-to-leading-order anomalous dimension determines the alpha(6)lnalpha, alpha(7)ln (2)alpha, and alpha(8)ln (3)alpha corrections to the energy. These are used to obtain the alpha(8)ln (3)alpha Lamb shift and alpha(7)ln (2)alpha hyperfine splitting for hydrogen, muonium, and positronium, as well as the alpha(2)lnalpha and alpha(3)ln (2)alpha corrections to the ortho- and parapositronium lifetimes. This shows for the first time that these logarithms can be computed from the renormalization group.     

Photon equation of motion with application to the electron’s anomalous magnetic moment

The photon equation of motion previously applied to the Lamb shift is here applied to the anomalous magnetic moment of the electron. Exact agreement is obtained with the QED result of Schwinger. The photon theory treats the radiative correction to the photon in the presence of the electron rather than its inverse as in standard QED. The result is found to be first order in the photon-electron interaction rather than second order as in standard QED, introducing an ease of calculation hitherto unavailable.     

Order alpha(2) corrections to the decay rate of orthopositronium

Order alpha(2) corrections to the decay rate of orthopositronium are calculated in the framework of nonrelativistic QED. The resulting contribution is found to be in significant disagreement with one set of experimental measurements, though another experiment is in agreement with theory.     

Hopf-algebraic renormalization of QED in the linear covariant gauge

In the context of massless quantum electrodynamics (QED) with a linear covariant gauge fixing, the connection between the counterterm and the Hopf-algebraic approach to renormalization is examined. The coproduct formula of Green’s functions contains two invariant charges, which give rise to different renormalization group functions. All formulas are tested by explicit computations to third loop order. The possibility of a finite electron self-energy by fixing a generalized linear covariant gauge is discussed. An analysis of subdivergences leads to the conclusion that such a gauge only exists in quenched QED.     

Electron self-energy,vacuum polarization,and vertex correction

In the framework of the finite quantum electrodynamics developed in the previous paper, electron self-energy, vacuum polarization, and vertex correction are calculated. It has turned out that the electron-neutrino mass difference can be reproduced in a model where this mass difference is of pure electromagnetic origin. A positive sign of proton-neutron mass difference is obtained within our present theory. Furthermore, it is shown that our theory can give a clue to overcome the possible crisis of QED arising from the recent report of the discrepancy between theoretical and experimental values for the muon anomalous magnetic moment as an evidence for a possible breakdown of QED.     

Non-singlet splitting functions in QED

Iterative solution of QED evolution equations for non-singlet electron structure functions is considered. Analytical expressions in the fourth and fifth orders are presented in terms of splitting functions. Relation to the existing exponentiated solution is discussed.