Revised value of the eighth-order contribution to the electron g-2

Stringent test of QED with hydrogen-like tin

Inner-shell electrons naturally sense the electric field close to the nucleus, which can reach extreme values beyond 1015 V cm-1 for the innermost electrons1. Especially in few-electron, highly charged ions, the interaction with the electromagnetic fields can be accurately calculated within quantum electrodynamics (QED), rendering these ions good candidates to test the validity of QED in strong fields. Consequently, their Lamb shifts were intensively studied in the past several decades2,3. Another approach is the measurement of gyromagnetic factors (g factors) in highly charged ions4-7. However, so far, either experimental accuracy or small field strength in low-Z ions5,6 limited the stringency of these QED tests. Here we report on our high-precision, high-field test of QED in hydrogen-like 118Sn49+. The highly charged ions were produced with the Heidelberg electron beam ion trap (EBIT)8 and injected into the ALPHATRAP Penning-trap setup9, in which the bound-electron g factor was measured with a precision of 0.5 parts per billion (ppb). For comparison, we present state-of-the-art theory calculations, which together test the underlying QED to about 0.012%, yielding a stringent test in the strong-field regime. With this measurement, we challenge the best tests by means of the Lamb shift and, with anticipated advances in the g-factor theory, surpass them by more than an order of magnitude.

QED contributions to electrong-2

In this paper I briefly describe the results of the numerical evaluation of the mass-independent 4-loop contribution to the electrong-2 in QED with 1100 digits of precision. In particular I also show the semi-analytical fit to the numerical value, which contains harmonic polylogarithms of eiπ/3, e2iπ/3and eiπ/2one-dimensional integrals of products of complete elliptic integrals and six finite parts of master integrals, evaluated up to 4800 digits. I give also some information about the methods and the program used.

Complete tenth-order QED contribution to the muon g-2

We report the result of our calculation of the complete tenth-order QED terms of the muon g-2. Our result is a(μ)((10))=753.29 (1.04) in units of (α/π)(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(μ), obtaining a(μ)((8))=130.8794 (63) in units of (α/π)(4). The new QED contribution is a(μ)(QED)=116,584,718,951 (80)×10(-14), which does not resolve the existing discrepancy between the standard-model prediction and measurement of a(μ).

Tenth-order QED contribution to the electron g-2 and an improved value of the fine structure constant

This letter presents the complete QED contribution to the electron g-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 (58)(α/π)(5). We also improve the eighth-order contribution obtaining -1.9097 (20)(α/π)(4), which includes the mass-dependent contributions. These results lead to a(e)(theory)=1,159,652,181.78(77)×10(-12). The improved value of the fine-structure constant α(-1)=137.035999173 (35) [0.25 ppb] is also derived from the theory and measurement of a(e).

New determination of the fine structure constant and test of the quantum electrodynamics

We report a new measurement of the ratio h/m(Rb) between the Planck constant and the mass of (87)Rb atom. A new value of the fine structure constant is deduced, α(-1)=137.035999037(91) with a relative uncertainty of 6.6×10(-10). Using this determination, we obtain a theoretical value of the electron anomaly a(e)=0.00115965218113(84), which is in agreement with the experimental measurement of Gabrielse [a(e)=0.00115965218073(28)]. The comparison of these values provides the most stringent test of the QED. Moreover, the precision is large enough to verify for the first time the muonic and hadronic contributions to this anomaly.

Precision physics of simple atoms and constraints on a light boson with ultraweak coupling

Constraint on spin-dependent and spin-independent Yukawa potential at atomic scale is developed. That covers constraints on a coupling constant of an additional photon γ* and a pseudovector boson. The mass range considered is from 1  eV/c2 to 1  MeV/c2. The strongest constraint on a coupling constant α' is at the level of a few parts in 10913) (for γ*) and below one part in 10(16) (for a pseudovector) corresponding to mass below 1  keV/c2. The constraints are derived from low-energy tests of quantum electrodynamics and are based on spectroscopic data on light hydrogenlike atoms and experiments with magnetic moments of leptons and light nuclei.

Perturbation theory without diagrams: the polaron case

Higher-order perturbative calculations in quantum (field) theory suffer from the factorial increase of the number of individual diagrams. Here I describe an approach which evaluates the total contribution numerically for finite temperature from the cumulant expansion of the corresponding observable followed by an extrapolation to zero temperature. This method (originally proposed by Bogolyubov and Plechko) is applied to the calculation of higher-order terms for the ground-state energy of the polaron. Using state-of-the-art multidimensional integration routines two new coefficients are obtained corresponding to a four- and five-loop calculation. Several analytical and numerical procedures have been implemented which were crucial for obtaining reliable results.

Combination of BLOCH oscillations with a Ramsey-Bordé interferometer: new determination of the fine structure constant

We report a new experimental scheme which combines atom interferometry with Bloch oscillations to provide a new measurement of the ratio h/mRb. By using Bloch oscillations, we impart to the atoms up to 1600 recoil momenta and thus we improve the accuracy on the recoil velocity measurement. The deduced value of h/mRb leads to a new determination of the fine structure constant alpha(-1) =137.03599945 (62) with a relative uncertainty of 4.6 x 10(-9). The comparison of this result with the value deduced from the measurement of the electron anomaly provides the most stringent test of QED.

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.