Tests Of QED Research Articles

High-Precision Determination of g Factors and Masses of ^{20}Ne^{9+} and ^{22}Ne^{9+}.

We present the measurements of individual bound electron g factors of ^{20}Ne^{9+} and ^{22}Ne^{9+} on the relative level of 0.1 parts per billion. The comparison with theory represents the most stringent test of bound-state QED in strong electric fields. A dedicated mass measurement results in m(^{20}Ne)=19.992 440 168 77(9) u, which improves the current literature value by a factor of 18, disagrees by 4 standard deviations, and represents the most precisely measured mass value in atomic mass units. Together, these measurements yield an electron mass on the relative level of 0.1ppb with m_{e}=5.485 799 090 99(59)×10^{-4} u as well as a factor of seven improved m(^{22}Ne)=21.991 385 098 2(26) u.

DIMUS: super-compact Dimuonium Spectroscopy collider at Fermilab

While dimuonium (μ + μ -) — the “smallest QED atom” — has not yet been observed, it is of utmost fundamental interest. By virtue of the larger mass, dimuonium has greater sensitivity to beyond the standard model (BSM) effects than its cousins positronium or muonium, both discovered long ago, while not suffering from large QCD uncertainties. Dimuonium atoms can be created in e + e - collisions with large longitudinal momentum, allowing them to decay a small distance away from the beam crossing point and avoid prompt backgrounds. We envision a unique cost-effective and fast-timeline opportunity for copious production of (μ + μ -) atoms at the production threshold via a modest modification of existing Fermilab Accelerator Science and Technology (FAST) facility to arrange collisions of 408 MeV electrons and positrons at a 75° angle. This compact 23 m circumference collider (DIMUS) will allow for precision tests of QED and open the door for searches for new physics coupled to the muon. The FAST facility is perfectly suited for DIMUS as there are existing SRF accelerators and infrastructure, capable of producing high energy, high current electron and positron beams, sufficient for O(1032)cm2 s-1 luminosity and ∼0.5 million dimuons per year. The expansion will require installation of a second SRF cryomodule, positron production and accumulation system, fast injection/extraction kickers and two small circumference intersecting rings. An approximately meter-sized detector with several layers of modern pixelated silicon detector and crystal-based electromagnetic calorimeters will ensure observation of the decays of dimuonium to electron-positron pairs in presence of the Bhabba scattering background. An expansion of the system to include solenoidal magnet outside of the calorimeter system, a layer of steel shielding behind the magnet, and a set of dedicated muon detectors would extend the physics program of DIMUS to include precision studies of rare processes with muons, pions, and η mesons produced in e + e - collisions.

The Proton Structure in and out of Muonic Hydrogen

Laser spectroscopy of muonic atoms has been recently used to probe properties of light nuclei with unprecedented precision. We introduce nuclear effects in hydrogen-like atoms, nucleon structure quantities (form factors, structure functions, polarizabilities), and their effects in the Lamb shift and hyperfine splitting (HFS) of muonic hydrogen (μH). Updated theory predictions for the Lamb shift and HFS in μH are presented. We review the challenges of the ongoing effort to measure the ground-state HFS in μH and its impact on our understanding of the nucleon spin structure. To narrow down this search, we present a novel theory prediction obtained by scaling the measured HFS in hydrogen while leveraging radiative corrections. We also summarize recent developments in the spectroscopy of simple atomic and molecular systems and emphasize how they allow for precise determinations of fundamental constants, bound-state QED tests, and New Physics searches.

X‐ray Spectrometry Best Referee awards 2021

X‐ray Spectrometry Best Referee awards 2021

WKB electron wave functions in a tightly focused laser beam

Available laser technology is opening the possibility of testing QED experimentally in the so-called strong-field regime. This calls for developing theoretical tools to investigate strong-field QED processes in electromagnetic fields of complex spacetime structure. Here, we propose a scheme to compute electron wave functions in tightly focused laser beams by taking into account exactly the complex spacetime structure of the fields. The scheme is solely based on the validity of the Wentzel-Kramers-Brillouin (WKB) approximation and the resulting wave functions, unlike previously proposed ones [Phys. Rev. Lett. \textbf{113}, 040402 (2014)], do not rely on approximations on the classical electron trajectory. Moreover, a consistent procedure is indicated to take into account higher-order quantum effects within the WKB approach depending on higher-and-higher powers of the Planck constant. In the case of a plane-wave background field the found wave functions exactly reduce to the Volkov states, which are then written in a new and fully quasiclassical form. Finally, by using the leading-order WKB wave functions to compute the probabilities of nonlinear Compton scattering and nonlinear Breit-Wheeler pair production, it is explicitly shown that, if additionally the energies of the charges are sufficiently large that the latter are not significantly deflected by the field, the corresponding Baier's formulas are exactly reproduced for an otherwise arbitrary classical electron/positron trajectory.

High accuracy characterisation for the absolute energy of scandium Kα

This work reports the absolute characterisation of the Sc Kα profile. All component peaks are characterised for the first time. The satellite component centroids, line-widths, and relative intensities are determined. Energies are calibrated on an absolute basis. Sc and peak energies of 4090.699(10) eV and 4085.926(18) eV are reported, respectively, with estimated standard error uncertainties of 2.4 and 4.4 ppm. In this work, an electron gun operating at 20 kV, incident on high purity metals, produces the x-ray fluorescence, which Bragg diffracts via a Germanium (220) crystal to permit high-accuracy measurement of energy. The Kα emission spectrum of scandium (Z = 21) has not been measured in absolute energy in over 50 years. At the time the data was reported in ‘x units’ and the angstrom was not a well defined unit. That reported uncertainty was estimated to be approximately 50 ppm (parts per million) or 0.2 eV. The new profile characterisation combined with the absolute energy calibration provides an important definition for future studies in chemical speciation and condensed matter studies. Furthermore, the methodology described obtains a level of accuracy from relatively low energy x-rays to provide an important insight for future studies in fundamental parameters, pionic spectra and high-accuracy tests of QED.

The Lamb shift of the 1s state in hydrogen: Two-loop and three-loop contributions

We consider the 1s Lamb shift in hydrogen and helium ions, a quantity, required for an accurate determination of the Rydberg constant and the proton charge radius by means of hydrogen spectroscopy, as well as for precision tests of the bound-state QED. The dominant QED contribution to the uncertainty originates from α8m external-field contributions (i.e., the contributions at the non-recoil limit). We discuss the two- and three-loop cases and in particular, we revisit calculations of the coefficients B61,B60,C50 in standard notation.We have found a missing logarithmic contribution of order α2(Zα)6m. We have also obtained leading pure self-energy logarithmic contributions of order α2(Zα)8m and α2(Zα)9m and estimated the subleading terms of order α2(Zα)7m, α2(Zα)8m, and α2(Zα)9m. The determination of those higher-order contributions enabled us to improve the overall accuracy of the evaluation of the two-loop self-energy of the electron.We investigated the asymptotic behavior of the integrand related to the next-to-leading three-loop term (order α3(Zα)5m, coefficient C50 in standard notation) and applied it to approximate integration over the loop momentum. Our result for contributions to the 1s Lamb shift for the total three loop next-to-leading term is (−3.3±10.5)(α3/π3)(Zα)5m.Altogether, we have completed the evaluation of the logarithmic contributions to the 1s Lamb shift of order α8m and reduced the overall α8m uncertainty by approximately a factor of three for H, D, and He+ as compared with the most recent CODATA compilation.

Pair Creation with Strong Laser Fields, Compton Scale X Rays, and Heavy Nuclei

Electron-positron pair creation is considered when intense laser pulses collide head-on with <1 MeV x-ray photons in the presence of stationary Coulomb charges Z(-e). The analysis employs Coulomb-corrected Volkov states and is not limited to Born's approximation in Z. The cross section and the yield increase dramatically with increasing Z, potentially enabling (i)measurable yields with petawatt lasers and (ii)sensitive tests of strong-field QED.

Lifetimes and g-factors of the HFS states in H-like and Li-like bismuth

The LIBELLE experiment performed at the experimental storage ring at the GSI Helmholtz Center for Heavy Ion Research in Darmstadt, Germany, has successfully determined the ground state hyperfine (HFS) splittings in hydrogen-like () and lithium-like () bismuth. The study of HFS transitions in highly charged ions enables precision tests of QED in extreme electric and magnetic fields otherwise not attainable in laboratory experiments. Besides the transition wavelengths the time-resolved detection of fluorescence photons following the excitation of the ions by a pulsed laser system also allows the extraction of lifetimes of the upper HFS levels and g-factors of the bound 1s and 2s electrons for both charge states. While the lifetime of the upper HFS state in has already been measured in earlier experiments, an experimental value for lifetime of this state in is reported for the first time in this work.

Stringent tests of QED using highly charged ions

The present status of tests of QED with highly charged ions is reviewed. The theoretical predictions for the Lamb shift and the transition energies are compared with available experimental data. Recent achievements in studies of the hyperfine splitting and the $g$-factor isotope shift with highly charged ions are reported. Special attention is paid to tests of QED within and beyond the Furry picture at strong-coupling regime. Prospects for tests of QED at supercritical fields that can be created in low-energy heavy-ion collisions are discussed as well.

Reduced theoretical error for He+4 spectroscopy

We apply point-particle effective field theory (PPEFT) to electronic and muonic 4He+ ions, and use it to identify linear combinations of spectroscopic measurements for which the theoretical uncertainties are much smaller than for any particular energy levels. The error is reduced because these combinations are independent of all short-range physics effects up to a given order in the expansion in the small parameters R/a_B and(Z alpha) (where R and a_B are the ion's nuclear and Bohr radii). In particular, the theory error is not limited by the precision with which nuclear matrix elements can be computed, or compromised by the existence of any novel short-range interactions, should these exist. These combinations of 4He+ measurements therefore provide particularly precise tests of QED. The restriction to 4He+ arises because our analysis assumes a spherically symmetric nucleus, but the argument used is more general and extendable to both nuclei with spin, and to higher orders in R/a_B and (Z alpha).

Four-loop QED contributions to the electron g-2

The anomalous magnetic moment of the electron is one of the physical quantities measured with the highest precision. Such high precision demands a similar precision in the theoretical evaluations in order to obtain stringent tests of QED. In this talk I will summarize the situation of the theoretical calculations of the contributions to the electron g-2; then, I will describe in detail the results of the twenty-year long project of the evaluation of all the 891 mass-independent four-loop QED Feynman diagrams contributing to the electron g-2 [11], with the 1100-digits result and high-precision analytical fits. The consequences of this result on the QED tests and the determination of the fine structure constant will be also discussed.

High precision measurement of muonium hyperfine structure

MuSEUM (Muonium Spectroscopy Experiment Using Microwave) collaboration aims to measure the muonium hyperfine structure (MuHFS,vhfs) with a few ppb (parts per billion). MuHFS spectroscopy is a stringent test of the bound-state QED. From this measurement, the muon-proton magnetic moment ratio (μμ/μP) and the muon-electron mass ratio (mμ/me) can also be determined by applying a high magnetic field. In the previous MuHFS measurement carried out at Los Alamos Meson Physics Facility (LAMPF), the main uncertainty was caused by the lack of the statistics. MuSEUM collaboration uses the high intense pulsed muon beam at Japan Proton Accelerator Research Complex (J-PARC) to improve the statistical uncertainty. We are also developing our own experimental setups for the improvement of the systematic uncertainties. From June 2016, MuSEUM collaboration have carried out the MuHFS measurement in an extremely low magnetic field within 100 nT and now we are preparing for the measurement in a 1.7 T high magnetic field.

Three-Path Atom Interferometry with Large Momentum Separation.

We demonstrate the scale up of a symmetric three-path contrast interferometer to large momentum separation. The observed phase stability at separation of 112 photon recoil momenta exceeds the performance of earlier free-space interferometers. In addition to the symmetric interferometer geometry and Bose-Einstein condensate source, the robust scalability of our approach relies on the suppression of undesired diffraction phases through a careful choice of atom optics parameters. The interferometer phase evolution is quadratic with number of recoils, reaching a rate as high as 7×10^{7} rad/s. We discuss the applicability of our method towards a new measurement of the fine-structure constant and a test of QED.

Sub-Doppler Frequency Metrology in HD for Tests of Fundamental Physics.

Weak transitions in the (2,0) overtone band of the hydrogen deuteride molecule at λ=1.38 μm were measured in saturated absorption using the technique of noise-immune cavity-enhanced optical heterodyne molecular spectroscopy. Narrow Doppler-free lines were interrogated with a spectroscopy laser locked to a frequency comb laser referenced to an atomic clock to yield transition frequencies [R(1)=217105181895(20) kHz; R(2)=219042856621(28) kHz; R(3)=220704304951(28) kHz] at three orders of magnitude improved accuracy. These benchmark values provide a test of QED in the smallest neutral molecule, and they open up an avenue to resolve the proton radius puzzle, as well as constrain putative fifth forces and extra dimensions.

The nuclear magnetic moment of 208Bi and its relevance for a test of bound-state strong-field QED

The hyperfine structure splitting in the 6p3S3/24→6p27sP1/24 transition at 307 nm in atomic 208Bi was measured with collinear laser spectroscopy at ISOLDE, CERN. The hyperfine A and B factors of both states were determined with an order of magnitude improved accuracy. Based on these measurements, theoretical input for the hyperfine structure anomaly, and results from hyperfine measurements on hydrogen-like and lithium-like 209Bi80+,82+, the nuclear magnetic moment of 208Bi has been determined to μ(Bi208)=+4.570(10)μN. Using this value, the transition energy of the ground-state hyperfine splitting in hydrogen-like and lithium-like 208Bi80+,82+ and their specific difference of −67.491(5)(148) meV are predicted. This provides a means for an experimental confirmation of the cancellation of nuclear structure effects in the specific difference in order to exclude such contributions as the cause of the hyperfine puzzle, the recently reported 7-σ discrepancy between experiment and bound-state strong-field QED calculations of the specific difference in the hyperfine structure splitting of 209Bi80+,82+.

Probing the quantum vacuum with petawatt lasers

Due to the bosonic nature of the photon, increasing the peak intensity through a combination of raising the pulse energy and decreasing the pulse duration will pile up more and more photons within the same finite region of space. In the absence of material, this continues until the vacuum is stressed to the point of breakdown and virtual particles become real. The critical intensity where this occurs for electrons and positrons – the so-called Schwinger limit – is predicted to be ∼ 1029 W/cm2. At substantially lower intensities, however, nonlinear aspects of the quantum vacuum associated with polarization of the vacuum can be explored. These studies become viable at the petawatt level where 1023 W/cm2 and above can be reached. This is an era into which we are just embarking that will provide critical tests of QED and theories beyond the Standard Model of particle physics.

Testing fundamental interactions on the helium atom

We critically examine the current status of theoretical calculations of the energies, the fine structure, and the isotope shift of the lowest-lying states of helium, searching for unresolved discrepancies with experiments. Calculations are performed within the quantum electrodynamics expansion in powers of the fine structure constant $\alpha$ and the electron-to-nucleus mass ratio $m/M$. For energies, theoretical results are complete through orders $\alpha^6m$ and $\alpha^6m^2/M$, with the resulting accuracy ranging from $0.5$ to $2$~MHz for the $n=2$ states. The fine-structure splitting of the $2^3P$ state is predicted with a much better accuracy, 1.7~kHz, as a consequence of a calculation of the next-order $\alpha^7m$ effect. An excellent agreement of the theoretical predictions with the recent measurements of the fine structure provides one of the best tests of the bound-state QED in few-electron systems and determines the fine-structure constant $\alpha$ with an accuracy of 31~ppb. The isotope shift between $^3$He and $^4$He is treated theoretically with a sub-kHz accuracy, which allows for a high-precision determination of the differences of the nuclear charge radii $\delta r^2$. Several such determinations, however, yield results that are in a 4$\sigma$ disagreement with each other, what remains unexplained. Apart from this, we find no significant discrepancies between theory and experiment for the helium atom. In the future, a calculation of the next-order $\alpha^7m$ effect for energy levels will enable determinations of the nuclear charge radii from atomic transition frequencies with an accuracy better than 1\%. Combined with the complementary determinations from muonic atoms, this will provide a sensitive test of universality in electromagnetic interactions of leptons and contribute to the solution of the proton charge radius puzzle.

Frequency-comb referenced collinear laser spectroscopy of Be+ for nuclear structure investigations and many-body QED tests

Absolute transition frequencies of the $2s\,^2{\rm{S}}_{1/2}$ $\rightarrow$ $2p\,^2{\rm{P}}_{1/2,3/2}$ transitions in Be$^+$ were measured with a frequency comb in stable and short-lived isotopes at ISOLDE (CERN) using collinear laser spectroscopy. Quasi-simultaneous measurements in copropagating and counterpropagating geometry were performed to become independent from acceleration voltage determinations for Doppler-shift corrections of the fast ion beam. Isotope shifts and fine structure splittings were obtained from the absolute transition frequencies with accuracies better than 1\,MHz and led to a precise determination of the nuclear charge radii of $^{7,10-12}$Be relative to the stable isotope $^9$Be. Moreover, an accurate determination of the $2p$ fine structure splitting allowed a test of high-precision bound-state QED calculations in the three-electron system. Here, we describe the laser spectroscopic method in detail, including several tests that were carried out to determine or estimate systematic uncertainties. Final values from two experimental runs at ISOLDE are presented and the results are discussed.

Collision-induced line-shape effects limiting the accuracy in Doppler-limited spectroscopy ofH2

Recent advances in theoretical calculations of ${\mathrm{H}}_{2}$ dissociation energies and ultra-accurate measurements of ${\mathrm{H}}_{2}$ transition frequencies give possibilities not only for testing QED and relativistic effects, but also for searching for physics beyond the standard model. In this paper we show that at the level of ${10}^{\ensuremath{-}4}\phantom{\rule{4pt}{0ex}}{\mathrm{cm}}^{\ensuremath{-}1}$ the uncertainty of the Doppler-limited ${\mathrm{H}}_{2}$ line position determination is dominated by collisional line-shape effects. We question the paradigm that the unperturbed transition energy can be determined from linear extrapolation of the line shift to zero pressure.