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.     

Electron Magnetic Moment in Highly Charged Ions: The ARTEMIS Experiment

The magnetic moment (g‐factor) of the electron is a fundamental quantity in physics that can be measured with high accuracy by spectroscopy in Penning traps. Its value has been predicted by theory, both for the case of the free (unbound) electron and for the electron bound in a highly charged ion. Precision measurements of the electron magnetic moment yield a stringent test of these predictions and can in turn be used for a determination of fundamental constants such as the fine structure constant or the atomic mass of the electron. For the bound‐electron magnetic‐moment measurement, two complementary approaches exist, one via the so‐called “continuous Stern–Gerlach effect”, applied to ions with zero‐spin nuclei, and one a spectroscopic approach, applied to ions with nonzero nuclear spin. Here, the latter approach is detailed, and an overview of the experiment and its status is given.     

Status of the lepton g − 2 and effects of hadronic corrections

The electron and muon anomalous magnetic moments (AMM) are measured in experiments and studied in the Standard Model (SM) with the highest precision accessible in particle physics. The comparison of the measured quantity with the SM prediction for the electron AMM provides the best determination of the fine structure constant. The muon AMM is more sensitive to the appearance of New Physics effects and, at present, there appears to be a three- to four-standard deviation between the SM and experiment. The lepton AMMs are pure relativistic quantum correction effects and therefore test the foundations of relativistic quantum field theory in general, and of quantum electrodynamics (QED) and SM in particular, with highest sensitivity. Special attention is paid to the studies of the hadronic contributions to the muon AMM which constitute the main source of theoretical uncertainties of the SM.     

Fundamental constants and tests of theory in Rydberg states of hydrogenlike ions

A comparison of precision frequency measurements to quantum electrodynamics (QED) predictions for Rydberg states of hydrogenlike ions can yield information on values of fundamental constants and test theory. With the results of a calculation of a key QED contribution reported here, the uncertainty in the theory of the energy levels is reduced to a level where such a comparison can yield an improved value of the Rydberg constant.     

New determination of the fine structure constant from the electron value and QED

Quantum electrodynamics (QED) predicts a relationship between the dimensionless magnetic moment of the electron (g) and the fine structure constant (alpha). A new measurement of g using a one-electron quantum cyclotron, together with a QED calculation involving 891 eighth-order Feynman diagrams, determine alpha(-1)=137.035 999 710 (96) [0.70 ppb]. The uncertainties are 10 times smaller than those of nearest rival methods that include atom-recoil measurements. Comparisons of measured and calculated g test QED most stringently, and set a limit on internal electron structure.     

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.     

Fundamental interactions

Trapped and stored charged particles, atoms and molecules offer a number of opportunities to measure exact values of important fundamental constants such as lepton magnetic anomalies, the fine structure constant and the electron mass. New Physics can be searched for by comparing precise measurements and highly accurate calculations of particle properties. Some recent experiments differ by a few standard deviations from standard theory predictions, such as the muon magnetic anomaly and ²¹Na β-decay; for a clarification further work is needed. This work is in part supported by the Dutch Stichting voor Fundamenteel Onderzoek der Materie under programme 48 (TRIμP).     

Atoms in flight and the remarkable connections between atomic and hadronic physics

Atomic physics and hadron physics are both based on Yang Mills gauge theory; in fact, quantum electrodynamics can be regarded as the zero-color limit of quantum chromodynamics. I review a number of areas where the techniques of atomic physics provide important insight into the theory of hadrons in QCD. For example, the Dirac-Coulomb equation, which predicts the spectroscopy and structure of hydrogenic atoms, has an analog in hadron physics in the form of light-front relativistic equations of motion which give a remarkable first approximation to the spectroscopy, dynamics, and structure of light hadrons. The renormalization scale for the running coupling, which is unambiguously set in QED, leads to a method for setting the renormalization scale in QCD. The production of atoms in flight provides a method for computing the formation of hadrons at the amplitude level. Conversely, many techniques which have been developed for hadron physics, such as scaling laws, evolution equations, and light-front quantization have equal utility for atomic physics, especially in the relativistic domain. I also present a new perspective for understanding the contributions to the cosmological constant from QED and QCD.     

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.     

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.     

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.     

Precise measurement of positronium hyperfine splitting using the Zeeman effect

Positronium is an ideal system for the research of the quantum electrodynamics (QED) in bound state. The hyperfine splitting (HFS) of positronium, Δ_HFS, gives a good test of the bound state calculations and probes new physics beyond the Standard Model. A new method of QED calculations has revealed the discrepancy by 15 ppm (3.9σ) of Δ_HFS between the QED prediction and the experimental average. There would be possibility of new physics or common systematic uncertainties in the previous all experiments. We describe a new experiment to reduce possible systematic uncertainties and will provide an independent check of the discrepancy. We are now taking data and the current result of Δ_HFS?=?203.395 1 ±0.002 4 (stat., 12 ppm) ±0.001 9 (sys., 9.5 ppm) GHz has been obtained so far. A measurement with a precision of O(ppm) is expected within a year.     

Search for a possible variation of the fine structure constant

The determination of the fine structure constant α and the search for its possible variation are considered. We focus on the role of the fine structure constant in modern physics and discuss precision tests of quantum electrodynamics.Different methods of a search for possible variations of fundamental constants are compared and those related to optical measurements are considered in detail.     

Polarization of an electron-positron vacuum by a strong magnetic field with an allowance made for the anomalous magnetic moments of particles

Given the anomalous magnetic moments of electrons and positrons in the one-loop approximation, we calculate the exact Lagrangian of an intense constant magnetic field that replaces the Heisenberg-Euler Lagrangian in traditional quantum electrodynamics (QED). We have established that the derived generalization of the Lagrangian is real for arbitrary magnetic fields. In a weak field, the calculated Lagrangian matches the standard Heisenberg-Euler formula. In extremely strong fields, the field dependence of the Lagrangian completely disappears and the Lagrangian tends to a constant determined by the anomalous magnetic moments of the particles.     

g factor of hydrogenlike ²⁸Si¹³⁺

We determined the experimental value of the g factor of the electron bound in hydrogenlike 2?Si13? by using a single ion confined in a cylindrical Penning trap. From the ratio of the ion's cyclotron frequency and the induced spin flip frequency, we obtain g = 1.995 348 958 7(5)(3)(8). It is in excellent agreement with the state-of-the-art theoretical value of 1.995 348 958 0(17), which includes QED contributions up to the two-loop level of the order of (Zα)2 and (Zα)? and represents a stringent test of bound-state quantum electrodynamics calculations.     

Classical and Quantum Radiation Reaction for Linear Acceleration

We investigate the effect of radiation reaction on the motion of a wave packet of a charged scalar particle linearly accelerated in quantum electrodynamics (QED). We give the details of the calculations for the case where the particle is accelerated by a static potential that were outlined in Higuchi and Martin Phys. Rev. D 70 (2004) 081701(R) and present similar results in the case of a time-dependent but space-independent potential. In particular, we calculate the expectation value of the position of the charged particle after the acceleration, to first-order in the fine structure constant in the ℏ→ 0 limit, and find that the change in the expectation value of the position (the position shift) due to radiation reaction agrees exactly with the result obtained using the Lorentz-Dirac force in classical electrodynamics for both potentials.     

Electron self-field interaction and internal resonance

Recent proposals that an electron might contain an “imprisoned” photon in its field system suggest a wave resonance which allows the QED determination of the electron g-factor to established the precise value of the fine structure constant, given its approximate value as 1/137. The value of α⁻¹ is found to be 137.03599, in precise accord with its measured value.     

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.     

Effects of QED and Beyond from the Atomic Binding Energy

Atomic binding energies are calculated at utmost precision. A report on the current status of Lamb-shift predictions for hydrogenlike ions, including all quantum electrodynamical corrections to first and second order in the fine structure constant α is presented. All relevant nuclear effects are taken into account. High-precision calculations for the Lamb shift in hydrogen are presented. The hyperfine structure splitting and the g factor of a bound electron in the strong electromagnetic field of a heavy nucleus is considered. Special emphasis is also put on parity violation effects in atomic systems. For all systems possible investigations beyond precision tests of quantum electrodynamics are considered. This revised version was published online in July 2006 with corrections to the Cover Date.     

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.