New Measurement of the 1S-3S Transition Frequency of Hydrogen: Contribution to the Proton Charge Radius Puzzle

Precision Calculation of the Electromagnetic Radii of the Proton and Neutron from Lattice QCD

We present lattice-QCD results for the electromagnetic form factors of the proton and neutron including both quark-connected and -disconnected contributions. The parametrization of the Q^{2} dependence of the form factors is combined with the extrapolation to the physical point. In this way, we determine the electric and magnetic radii and the magnetic moments of the proton and neutron. For the proton, we obtain at the physical pion mass and in the continuum and infinite-volume limit sqrt[⟨r_{E}^{2}⟩^{p}]=0.820(14)  fm, sqrt[⟨r_{M}^{2}⟩^{p}]=0.8111(89)  fm, and μ_{M}^{p}=2.739(66), where the errors include all systematics.

Precision-Spectroscopic Determination of the Binding Energy of a Two-Body Quantum System: The Hydrogen Atom and the Proton-Size Puzzle

Precision measurements in Rydberg states of H with principal quantum number n in the range between 20 and 30 are reported. In the presence of homogeneous electric fields with strengths below 2  V cm^{-1}, these Rydberg states are subject to a linear Stark effect with accurately calculable Stark shifts. From the spectral positions of field-independent and field-dependent Rydberg-Stark states, we derive the n=20 and 24 Bohr energies, and the ionization energy with respect to the 2 ^{2}S_{1/2}(f=0,1) [short 2S(0,1)] metastable states. Combining these results with the 2S(1)-1S(1) transition frequency [C. G. Parthey et al., Phys. Rev. Lett. 107, 203001 (2011)PRLTAO0031-900710.1103/PhysRevLett.107.203001; A. Matveev et al., Phys. Rev. Lett. 110, 230801 (2013)PRLTAO0031-900710.1103/PhysRevLett.110.230801] and the 1S hyperfine splitting [L. Essen et al., Nature (London) 229, 110 (1971)NATUAS0028-083610.1038/229110a0], we determine the ionization frequency of the 1S(0) ground state to be 3 288 087 922 407.2(3.7)_{stat}(1.8)_{syst}  kHz, which is the most precise value ever determined for the binding energy of a two-body quantum system. Using the 2S(0)-2P_{1/2}(1) interval [N. Bezginov et al., Science 365, 1007 (2019)SCIEAS0036-807510.1126/science.aau7807], we determine the Rydberg frequency to be cR_{∞}=3 289 841 960 204(15)_{stat}(7)_{syst}(13)_{2S-2P}  kHz in a procedure that is insensitive to the value of the proton charge radius. These new results are discussed in the context of the proton-size puzzle.

Collinear Laser Spectroscopy of 2 ^{3}S_{1}→2 ^{3}P_{J} Transitions in Helium-like ^{12}C^{4+}

Transition frequencies and fine-structure splittings of the 2 ^{3}S_{1}→2 ^{3}P_{J} transitions in helium-like ^{12}C^{4+} were measured by collinear laser spectroscopy on a 1-ppb level. Accuracy is increased by more than 3 orders of magnitude with respect to previous measurements, enabling tests of recent nonrelativistic (NR) QED calculations including terms up to mα^{7}. Deviations between the theoretical and experimental values are within theoretical uncertainties and are ascribed to mα^{8} and higher-order contributions in the series expansion of the NR QED calculations. Finally, prospects for an all-optical charge radius determination of light isotopes are evaluated.

Pulsed CW laser for long-term spectroscopic measurements at high power in deep-UV

We present a novel technique for in-vacuum cavity-enhanced UV spectroscopy that allows nearly continuous measurements over several days, minimizing mirror degradation caused by high-power UV radiation. Our method relies on pulsing of the cavity's internal power, which increases the UV intensity to maximum only for short periods when the studied atom is within the cavity mode volume while keeping the average power low to prevent mirror degradation. Additionally, this method significantly decreases laser-induced background on charged particle detectors. The described 244 nm laser system is designed for 1S-2S two-photon CW spectroscopy of muonium in the Mu-MASS project. It was tested to provide intracavity powers above 20 W, requiring maintenance only a few times a day. The pulsing technique demonstrates minimal impact on the radiation frequency, with no observed shifts exceeding 15 kHz. Our approach represents a promising new technique for high-precision spectroscopy of atoms in harsh UV environments and demonstrates the feasibility of CW spectroscopy of muonium.

Collinear Laser Spectroscopy of Helium-like 11B3+

Collinear laser spectroscopy in the 1s2s3S1→1s2p3P0,2 transitions of helium-like 11B3+ was performed using the HITRAP beamline at the GSI Helmholtz Centre. The ions were produced in an electron beam ion source, extracted, and accelerated to a beam energy of 4 keV/q. Results agree with previous measurements within uncertainty. Thus, it was demonstrated that the metastable state in He-like ions is sufficiently populated to carry out collinear laser spectroscopy. The measurement is a pilot experiment for a series of measurements that will be performed at a dedicated collinear laser spectroscopy setup at TU Darmstadt with light helium-like ions.

Muonium Lamb shift: theory update and experimental prospects

We review the theory of the Lamb shift for muonium, provide an updated numerical value and present the prospects of the Mu-MASS collaboration at PSI to improve upon their recent measurement. Due to its smaller nuclear mass, the contributions of the higher-order recoil corrections (160 kHz level) and nucleus self-energy (40 kHz level) are enhanced for muonium compared to hydrogen where those are below the level of the latest measurement performed by Hessels et al. and thus could not be tested yet. The ongoing upgrades to the Mu-MASS setup will open up the possibility to probe these contributions and improve the sensitivity of this measurement to searches for new physics in the muonic sector.

Measurement of a helium tune-out frequency: an independent test of quantum electrodynamics

Despite quantum electrodynamics (QED) being one of the most stringently tested theories underpinning modern physics, recent precision atomic spectroscopy measurements have uncovered several small discrepancies between experiment and theory. One particularly powerful experimental observable that tests QED independently of traditional energy level measurements is the "tune-out" frequency, where the dynamic polarizability vanishes and the atom does not interact with applied laser light. In this work, we measure the tune-out frequency for the 2³S₁ state of helium between transitions to the 2³P and 3³P manifolds and compare it with new theoretical QED calculations. The experimentally determined value of 725,736,700(260) megahertz differs from theory [725,736,252(9) megahertz] by 1.7 times the measurement uncertainty and resolves both the QED contributions and retardation corrections.

New Insights into the Nucleon's Electromagnetic Structure

We present a combined analysis of the electromagnetic form factors of the nucleon in the space- and timelike regions using dispersion theory. Our framework provides a consistent description of the experimental data over the full range of momentum transfer, in line with the strictures from analyticity and unitarity. The statistical uncertainties of the extracted form factors are estimated using the bootstrap method, while systematic errors are determined from variations of the spectral functions. We also perform a high-precision extraction of the nucleon radii and find good agreement with previous analyses of spacelike data alone. For the proton charge radius, we find r_{E}^{p}=0.840_{-0.002}^{+0.003} _{-0.002}^{+0.002}  fm, where the first error is statistical and the second one is systematic. The Zemach radius and third moment are in agreement with Lamb shift measurements and hyperfine splittings. The combined dataset of space- and timelike data disfavors a zero crossing of μ_{p}G_{E}^{p}/G_{M}^{p} in the spacelike region. Finally, we discuss the status and perspectives of modulus and phase of the form factors in the timelike region in the context of future experiments, as well as the onset of perturbative QCD.

Measurement of the 2S_{1/2}-8D_{5/2} Transition in Hydrogen

We present a measurement of the hydrogen 2S_{1/2}-8D_{5/2} transition performed with a cryogenic atomic beam. The measured resonance frequency is ν=770649561570.9(2.0)  kHz, which corresponds to a relative uncertainty of 2.6×10^{-12}. Combining our result with the most recent measurement of the 1S-2S transition, we find a proton radius of r_{p}=0.8584(51)  fm and a Rydberg constant of R_{∞}=10973731.568332(52)  m^{-1}. This result has a combined 3.1σ disagreement with the Committee on Data for Science and Technology (CODATA) 2018 recommended value.

CODATA Recommended Values of the Fundamental Physical Constants: 2018

We report the 2018 self-consistent values of constants and conversion factors of physics and chemistry recommended by the Committee on Data of the International Science Council. The recommended values can also be found at physics.nist.gov/constants. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through 31 December 2018. A discussion of the major improvements as well as inconsistencies within the data is given. The former include a decrease in the uncertainty of the dimensionless fine-structure constant and a nearly two orders of magnitude improvement of particle masses expressed in units of kg due to the transition to the revised International System of Units (SI) with an exact value for the Planck constant. Further, because the elementary charge, Boltzmann constant, and Avogadro constant also have exact values in the revised SI, many other constants are either exact or have significantly reduced uncertainties. Inconsistencies remain for the gravitational constant and the muon magnetic-moment anomaly. The proton charge radius puzzle has been partially resolved by improved measurements of hydrogen energy levels.

Fresh Extraction of the Proton Charge Radius from Electron Scattering

We present a novel method for extracting the proton radius from elastic electron-proton (ep) scattering data. The approach is based on interpolation via continued fractions augmented by statistical sampling and avoids any assumptions on the form of function used for the representation of data and subsequent extrapolation onto Q^{2}≃0. Applying the method to extant modern ep datasets, we find that all results are mutually consistent and, combining them, we arrive at r_{p}=0.847(8)  fm. This result compares favorably with values obtained from contemporary measurements of the Lamb shift in muonic hydrogen, transitions in electronic hydrogen, and muonic deuterium spectroscopy.

Ionization Energy of the Metastable 2 ^{1}S_{0} State of ^{4}He from Rydberg-Series Extrapolation

In a recent breakthrough in first-principles calculations of two-electron systems, Patkóś, Yerokhin, and Pachucki [Phys. Rev. A 103, 042809 (2021)PLRAAN2469-992610.1103/PhysRevA.103.042809] have performed the first complete calculation of the Lamb shift of the helium 2 ^{3}S_{1} and 2 ^{3}P_{J} triplet states up to the term in α^{7}m. Whereas their theoretical result of the frequency of the 2 ^{3}P←2 ^{3}S transition perfectly agrees with the experimental value, a more than 10σ discrepancy was identified for the 3 ^{3}D←2 ^{3}S and 3 ^{3}D←2 ^{3}P transitions, which hinders the determination of the He^{2+} charge radius from atomic spectroscopy. We present here a new measurement of the ionization energy of the 2 ^{1}S_{0} state of He [960 332 040.491(32) MHz] which we use in combination with the 2 ^{3}S_{1}←2 ^{1}S_{0} interval measured by Rengelink et al. [Nat. Phys. 14, 1132 (2018).NPAHAX1745-247310.1038/s41567-018-0242-5] and the 2 ^{3}P←2 ^{3}S_{1} interval measured by Zheng et al. [Phys. Rev. Lett. 119, 263002 (2017)PRLTAO0031-900710.1103/PhysRevLett.119.263002] and Cancio Pastor et al. [Phys. Rev. Lett. 92, 023001 (2004)PRLTAO0031-900710.1103/PhysRevLett.92.023001] to derive experimental ionization energies of the 2 ^{3}S_{1} state [1152 842 742.640(32) MHz] and the 2 ^{3}P centroid energy [876 106 247.025(39) MHz]. These values reveal disagreements with the α^{7}m Lamb shift prediction by 6.5σ and 10σ, respectively, and support the suggestion by Patkóš et al. of an unknown theoretical contribution to the Lamb shifts of the 2 ^{3}S and 2 ^{3}P states of He.

Stable high power deep-uv enhancement cavity in ultra-high vacuum with fluoride coatings

We demonstrate the superior performance of dielectric fluoride coatings versus oxide coatings in long term vacuum operation of a high power deep-ultraviolet enhancement cavity. In ultra-high vacuum (10^-8 mbar), the fluoride optics can maintain up to 10 W of stable intracavity power on one hour time scales, a record-high at these vacuum levels, whereas for the oxide optics, we observe rapid degradation at lower intracavity powers with a rate that increases with power. After observing degradation in high vacuum, we can recover the fluoride and oxide optics with oxygen; however, this recovery process becomes ineffective after several applications. For the fluoride optics, we see that initial UV conditioning in an oxygen environment helps to improve the performances of the optics. In oxygen-rich environments from ∼10^-4 mbar, the fluoride optics can stably maintain up to 20 W of intracavity power on several-hour time scales whereas for the oxide optics there is immediate degradation with a rate that increases with decreasing oxygen pressure.

Deep-ultraviolet femtosecond laser source at 243 nm for hydrogen spectroscopy

This paper reports on the generation of a 100 MHz repetition rate, 1.7 mW average power and femtosecond deep-ultraviolet (DUV) 243 nm laser source. The infra-red output of a broadband Titanium-Sapphire (TiSa) laser containing 729 nm light is mixed with its second harmonic in a β-barium borate (BBO) crystal. By manipulating the group delay dispersion (GDD), we customize the spectral shape of TiSa resonator to improve conversion efficiency. This DUV laser is employed for direct frequency comb spectroscopy of hydrogen.

Testing Quantum Electrodynamics with Exotic Atoms

Precision study of few-electron, high-Z ions is a privileged field for probing high-field, bound-state quantum electrodynamics (BSQED). However, the accuracy of such tests is plagued by nuclear uncertainties, which are often larger than the BSQED effects under investigation. We propose an alternative method with exotic atoms and show that transitions may be found between circular Rydberg states where nuclear contributions are vanishing while BSQED effects remain large. When probed with newly available quantum sensing detectors, these systems offer gains in sensitivity of 1 to 2 orders of magnitude, while the mean electric field largely exceeds the Schwinger limit.

CODATA recommended values of the fundamental physical constants: 2018

We report the 2018 self-consistent values of constants and conversion factors of physics and chemistry recommended by the Committee on Data of the International Science Council (CODATA). The recommended values can also be found at physics.nist.gov/constants. The values are based on a least-squares adjustment that takes into account all theoretical and experimental data available through 31 December 2018. A discussion of the major improvements as well as inconsistencies within the data is given. The former include a decrease in the uncertainty of the dimensionless fine-structure constant and a nearly two orders of magnitude improvement of particle masses expressed in units of kg due to the transition to the revised International System of Units (SI) with an exact value for the Planck constant. Further, because the elementary charge, Boltzmann constant, and Avogadro constant also have exact values in the revised SI, many other constants are either exact or have significantly reduced uncertainties. Inconsistencies remain for the gravitational constant and the muon magnetic-moment anomaly. The proton charge radius puzzle has been partially resolved by improved measurements of hydrogen energy levels.

Measuring the α-particle charge radius with muonic helium-4 ions

The energy levels of hydrogen-like atomic systems can be calculated with great precision. Starting from their quantum mechanical solution, they have been refined over the years to include the electron spin, the relativistic and quantum field effects, and tiny energy shifts related to the complex structure of the nucleus. These energy shifts caused by the nuclear structure are vastly magnified in hydrogen-like systems formed by a negative muon and a nucleus, so spectroscopy of these muonic ions can be used to investigate the nuclear structure with high precision. Here we present the measurement of two 2S-2P transitions in the muonic helium-4 ion that yields a precise determination of the root-mean-square charge radius of the α particle of 1.67824(83) femtometres. This determination from atomic spectroscopy is in excellent agreement with the value from electron scattering¹, but a factor of 4.8 more precise, providing a benchmark for few-nucleon theories, lattice quantum chromodynamics and electron scattering. This agreement also constrains several beyond-standard-model theories proposed to explain the proton-radius puzzle^2-5, in line with recent determinations of the proton charge radius^6-9, and establishes spectroscopy of light muonic atoms and ions as a precise tool for studies of nuclear properties.

Possible two-photon absorption in the near-infrared region observed by cavity ring-down spectroscopy

Two-photon absorption spectra are difficult to observe using direct absorption spectroscopy especially in the near-infrared region. Cavity ring-down spectroscopy is a promising absorption spectroscopy technique which has been widely applied to linear and saturated single-photon absorption spectra. In the present study, we report the observation of a possible two-photon absorption in the near-infrared using cavity ring-down spectroscopy, namely a two-photon resonance of methane. Using an optical frequency comb, the single-photon wavenumber of the double-quantum transition has been determined to be 182 207 682.645 MHz with a standard deviation of 75 kHz.

Precision spectroscopy of atomic helium

Helium is a prototype three-body system and has long been a model system for developing quantum mechanics theory and computational methods. The fine-structure splitting in the 23P state of helium is considered to be the most suitable for determining the fine-structure constant α in atoms. After more than 50 years of efforts by many theorists and experimentalists, we are now working toward a determination of α with an accuracy of a few parts per billion, which can be compared to the results obtained by entirely different methods to verify the self-consistency of quantum electrodynamics. Moreover, the precision spectroscopy of helium allows determination of the nuclear charge radius, and it is expected to help resolve the 'proton radius puzzle'. In this review, we introduce the latest developments in the precision spectroscopy of the helium atom, especially the discrepancies among theoretical and experimental results, and give an outlook on future progress.

Crisis and catharsis in atomic physics

Precise measurement of an atomic hydrogen transition resolves the proton size puzzle

Two-photon frequency comb spectroscopy of atomic hydrogen

We have performed two-photon ultraviolet direct frequency comb spectroscopy on the 1S-3S transition in atomic hydrogen to illuminate the so-called proton radius puzzle and to demonstrate the potential of this method. The proton radius puzzle is a significant discrepancy between data obtained with muonic hydrogen and regular atomic hydrogen that could not be explained within the framework of quantum electrodynamics. By combining our result [f _1S-3S = 2,922,743,278,665.79(72) kilohertz] with a previous measurement of the 1S-2S transition frequency, we obtained new values for the Rydberg constant [R _∞ = 10,973,731.568226(38) per meter] and the proton charge radius [r _p = 0.8482(38) femtometers]. This result favors the muonic value over the world-average data as presented by the most recent published CODATA 2014 adjustment.

High-precision molecular measurement

Spectroscopy of hydrogen deuteride ions provides the proton-to-electron mass ratio

Intense beam of metastable Muonium

Precision spectroscopy of the Muonium Lamb shift and fine structure requires a robust source of 2S Muonium. To date, the beam-foil technique is the only demonstrated method for creating such a beam in vacuum. Previous experiments using this technique were statistics limited, and new measurements would benefit tremendously from the efficient 2S production at a low energy muon ( < 20  keV) facility. Such a source of abundant low energyμ + has only become available in recent years, e.g. at the Low-Energy Muon beamline at the Paul Scherrer Institute. Using this source, we report on the successful creation of an intense, directed beam of metastable Muonium. We find that even though the theoretical Muonium fraction is maximal in the low energy range of 2-5 keV, scattering by the foil and transport characteristics of the beamline favor slightly higherμ + energies of 7-10 keV. We estimate that an event detection rate of a few events per second for a future Lamb shift measurement is feasible, enabling an increase in precision by two orders of magnitude over previous determinations.

Proton-electron mass ratio from laser spectroscopy of HD+ at the part-per-trillion level

Recent mass measurements of light atomic nuclei in Penning traps have indicated possible inconsistencies in closely related physical constants such as the proton-electron and deuteron-proton mass ratios. These quantities also influence the predicted vibrational spectrum of the deuterated molecular hydrogen ion (HD+) in its electronic ground state. We used Doppler-free two-photon laser spectroscopy to measure the frequency of the v = 0→9 overtone transition (v, vibrational quantum number) of this spectrum with an uncertainty of 2.9 parts per trillion. By leveraging high-precision ab initio calculations, we converted our measurement to tight constraints on the proton-electron and deuteron-proton mass ratios, consistent with the most recent Penning trap determinations of these quantities. This results in a precision of 21 parts per trillion for the value of the proton-electron mass ratio.

The proton radius puzzle – 9 years later

High-precision measurements of the proton radius via scattering, electric hydrogen spectroscopy and muonic hydrogen spectroscopy do not agree on the level of more than 5 σ. This proton radius puzzle persists now for almost a decade. This paper gives a short summary over the progress in the solution of the puzzle as well as an overview over the planned experiments to finally solve this puzzle at the interface of atomic and nuclear physics.

Study of Two-Photon Exchange via the Beam Transverse Single Spin Asymmetry in Electron-Proton Elastic Scattering at Forward Angles over a Wide Energy Range

We report on a new measurement of the beam transverse single spin asymmetry in electron-proton elastic scattering, A_{⊥}^{ep}, at five beam energies from 315.1 to 1508.4 MeV and at a scattering angle of 30°<θ<40°. The covered Q^{2} values are 0.032, 0.057, 0.082, 0.218, 0.613 (GeV/c)^{2}. The measurement clearly indicates significant inelastic contributions to the two-photon-exchange (TPE) amplitude in the low-Q^{2} kinematic region. No theoretical calculation is able to reproduce our result. Comparison with a calculation based on unitarity, which only takes into account elastic and πN inelastic intermediate states, suggests that there are other inelastic intermediate states such as ππN, KΛ, and ηN. Covering a wide energy range, our new high-precision data provide a benchmark to study those intermediate states.

Investigation of the fine structure of antihydrogen

At the historic Shelter Island Conference on the Foundations of Quantum Mechanics in 1947, Willis Lamb reported an unexpected feature in the fine structure of atomic hydrogen: a separation of the 2S1/2 and 2P1/2 states1. The observation of this separation, now known as the Lamb shift, marked an important event in the evolution of modern physics, inspiring others to develop the theory of quantum electrodynamics2-5. Quantum electrodynamics also describes antimatter, but it has only recently become possible to synthesize and trap atomic antimatter to probe its structure. Mirroring the historical development of quantum atomic physics in the twentieth century, modern measurements on anti-atoms represent a unique approach for testing quantum electrodynamics and the foundational symmetries of the standard model. Here we report measurements of the fine structure in the n = 2 states of antihydrogen, the antimatter counterpart of the hydrogen atom. Using optical excitation of the 1S-2P Lyman-α transitions in antihydrogen6, we determine their frequencies in a magnetic field of 1 tesla to a precision of 16 parts per billion. Assuming the standard Zeeman and hyperfine interactions, we infer the zero-field fine-structure splitting (2P1/2-2P3/2) in antihydrogen. The resulting value is consistent with the predictions of quantum electrodynamics to a precision of 2 per cent. Using our previously measured value of the 1S-2S transition frequency6,7, we find that the classic Lamb shift in antihydrogen (2S1/2-2P1/2 splitting at zero field) is consistent with theory at a level of 11 per cent. Our observations represent an important step towards precision measurements of the fine structure and the Lamb shift in the antihydrogen spectrum as tests of the charge-parity-time symmetry8 and towards the determination of other fundamental quantities, such as the antiproton charge radius9,10, in this antimatter system.

Cryogenic atomic hydrogen beam apparatus with velocity characterization

Precision spectroscopy of hydrogen often relies on effusive thermal atomic beams, and the uncertainty in the velocity distribution of these beams can introduce systematic errors and complicate lineshape models. Here, we present an apparatus capable of high signal-to-noise studies of these velocity distributions at cryogenic temperatures for both ground state (1S) and metastable (2S) hydrogen using a simple time-of-flight technique. We also investigate how the cryogenic nozzle geometry affects these results.

Doppler-Free Two-Photon Cavity Ring-Down Spectroscopy of a Nitrous Oxide (N2O) Vibrational Overtone Transition

We report Doppler-free two-photon absorption of N₂O at λ = 4.53 μm, measured by cavity ring-down spectroscopy. High power was achieved by optical self-locking of a quantum cascade laser to a linear resonator of finesse F = 22730 , and accurate laser detuning over a 400 MHz range was measured relative to an optical frequency comb. At a sample pressure of p = 0.13 kPa, we report a large two-photon cross-section per molecule of σ 13 ( 2 ) = 8.0 × 10 - 41 cm⁴ s for the Q(18) rovibrational transition at a resonant frequency of ν ₀ = 66179400.8 MHz.

A small proton charge radius from an electron-proton scattering experiment

Elastic electron-proton scattering (e-p) and the spectroscopy of hydrogen atoms are the two methods traditionally used to determine the proton charge radius, r_p. In 2010, a new method using muonic hydrogen atoms¹ found a substantial discrepancy compared with previous results², which became known as the 'proton radius puzzle'. Despite experimental and theoretical efforts, the puzzle remains unresolved. In fact, there is a discrepancy between the two most recent spectroscopic measurements conducted on ordinary hydrogen^3,4. Here we report on the proton charge radius experiment at Jefferson Laboratory (PRad), a high-precision e-p experiment that was established after the discrepancy was identified. We used a magnetic-spectrometer-free method along with a windowless hydrogen gas target, which overcame several limitations of previous e-p experiments and enabled measurements at very small forward-scattering angles. Our result, r_p = 0.831 ± 0.007_stat ± 0.012_syst femtometres, is smaller than the most recent high-precision e-p measurement⁵ and 2.7 standard deviations smaller than the average of all e-p experimental results⁶. The smaller r_p we have now measured supports the value found by two previous muonic hydrogen experiments^1,7. In addition, our finding agrees with the revised value (announced in 2019) for the Rydberg constant⁸-one of the most accurately evaluated fundamental constants in physics.

High-Precision Ramsey-Comb Spectroscopy Based on High-Harmonic Generation

High-harmonic generation (HHG) is widely used for up-conversion of amplified (near) infrared ultrafast laser pulses to short wavelengths. We demonstrate that Ramsey-comb spectroscopy, based on two such pulses derived from a frequency-comb laser, enables us to observe phase effects in this process with a few mrad precision. As a result, we could perform the most accurate spectroscopic measurement based on light from HHG, illustrated with a determination of the 5p^{6}→5p^{5}8s^{2}[3/2]_{1} transition at 110 nm in ^{132}Xe. We improve its relative accuracy 10^{4} times to a value of 2.3×10^{-10}. This is 3.6 times better than shown before involving HHG, and promising to enable 1S-2S spectroscopy of He^{+} for fundamental tests.

Theory of the Anomalous Magnetic Moment of the Electron

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.

Observation of the 1S-2P Lyman-α transition in antihydrogen

In 1906, Theodore Lyman discovered his eponymous series of transitions in the extreme-ultraviolet region of the atomic hydrogen spectrum1,2. The patterns in the hydrogen spectrum helped to establish the emerging theory of quantum mechanics, which we now know governs the world at the atomic scale. Since then, studies involving the Lyman-α line-the 1S-2P transition at a wavelength of 121.6 nanometres-have played an important part in physics and astronomy, as one of the most fundamental atomic transitions in the Universe. For example, this transition has long been used by astronomers studying the intergalactic medium and testing cosmological models via the so-called 'Lyman-α forest'3 of absorption lines at different redshifts. Here we report the observation of the Lyman-α transition in the antihydrogen atom, the antimatter counterpart of hydrogen. Using narrow-line-width, nanosecond-pulsed laser radiation, the 1S-2P transition was excited in magnetically trapped antihydrogen. The transition frequency at a field of 1.033 tesla was determined to be 2,466,051.7 ± 0.12 gigahertz (1σ uncertainty) and agrees with the prediction for hydrogen to a precision of 5 × 10-8. Comparisons of the properties of antihydrogen with those of its well-studied matter equivalent allow precision tests of fundamental symmetries between matter and antimatter. Alongside the ground-state hyperfine4,5 and 1S-2S transitions6,7 recently observed in antihydrogen, the Lyman-α transition will permit laser cooling of antihydrogen8,9, thus providing a cold and dense sample of anti-atoms for precision spectroscopy and gravity measurements10. In addition to the observation of this fundamental transition, this work represents both a decisive technological step towards laser cooling of antihydrogen, and the extension of antimatter spectroscopy to quantum states possessing orbital angular momentum.

Nucleon axial radius and muonic hydrogen-a new analysis and review

Weak capture in muonic hydrogen (μH) as a probe of the chiral properties and nucleon structure predictions of quantum chromodynamics (QCD) is reviewed. A recent determination of the axial-vector charge radius squared, [Formula: see text], from a model independent z expansion analysis of neutrino-nucleon scattering data is employed in conjunction with the MuCap measurement of the singlet muonic hydrogen capture rate, [Formula: see text], to update the induced pseudoscalar nucleon coupling [Formula: see text] derived from experiment, and [Formula: see text] predicted by chiral perturbation theory. Accounting for correlated errors this implies [Formula: see text], confirming theory at the 8% level. If instead, the predicted expression for [Formula: see text] is employed as input, then the capture rate alone determines [Formula: see text], or together with the independent z expansion neutrino scattering result, a weighted average [Formula: see text]. Sources of theoretical uncertainty are critically examined and potential experimental improvements are described that can reduce the capture rate error by about a factor of 3. Muonic hydrogen can thus provide a precise and independent [Formula: see text] value which may be compared with other determinations, such as ongoing lattice gauge theory calculations. The importance of an improved [Formula: see text] determination for phenomenology is illustrated by considering the impact on critical neutrino-nucleus cross sections at neutrino oscillation experiments.

Nonadiabatic Relativistic Correction to the Dissociation Energy of H_{2}, D_{2}, and HD

The relativistic correction to the dissociation energy of H_{2}, D_{2}, and HD molecules has been accurately calculated without expansion in the small electron-nucleus mass ratio. The obtained results indicate the significance of nonadiabatic effects and resolve the discrepancy of theoretical predictions with recent experimental values for H_{2} and D_{2}. While the theoretical accuracy is now significantly improved and is higher than the experimental one, we observe about 3σ discrepancy for the dissociation energy of HD, which requires further investigation.

The proton size puzzle: experiment vs theory

Current status of the proton size puzzle from experimental and theoretical points of view is briefly discussed. The interest to these studies is primarily related to experiments conducted by the CREMA collaboration (Charge Radius Experi- ments with Muonic Atoms) with muonic hydrogen and deuterium by methods of laser spectroscopy. As a result a more accurate value of the proton charge radius was found to be rp = 0:84184(67) fm, which is different from the value recommended by CODATA for 7σ. In the second part we discuss recent calculations of the contribution of light pseudoscalar (PS) and axial-vector (AV) mesons to the interaction operator of a muon and a proton in muonic hydrogen atom, with the coupling of mesons to the muon being via two-photon intermediate state. Numerical estimates of the contributions to the hyperfine structure of the spectrum of the S and P levels are presented. It is shown that such contribution to the hyperfine splitting in muonic hydrogen is rather important for a comparison with precise experimental data.