Lamb Shift Measurements Research Articles

Muonic vs electronic dark forces: a complete EFT treatment for atomic spectroscopy

Precision atomic spectroscopy provides a solid model independent bound on the existence of new dark forces among the atomic constituents. We focus on the keV-GeV region investigating the sensitivity to such dark sectors of the recent measurements on muonic atoms at PSI. To this end we develop for the first time, the effective field theory that describes the leading effect of a new (pseudo-)vector or a (pseudo-)scalar particle of any mass at atomic energies. We identify in the Lamb Shift measurement in muonic deuterium (μD) and the 2s Hyperfine Splitting (HFS) in muonic hydrogen (μH) the most promising measurements to probe respectively spin-independent and spin-dependent new forces. Furthermore, we evaluate the expression of the vector force HFS finding that a future measurement of the 2s HFS in regular hydrogen could provide the strongest atomic bound for such a force for masses above 100 MeV.

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.

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 energy {mu }^{+} 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 higher {mu }^{+} 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.

A measurement of the atomic hydrogen Lamb shift and the proton charge radius.

The surprising discrepancy between results from different methods for measuring the proton charge radius is referred to as the proton radius puzzle. In particular, measurements using electrons seem to lead to a different radius compared with those using muons. Here, a direct measurement of the n = 2 Lamb shift of atomic hydrogen is presented. Our measurement determines the proton radius to be r p = 0.833 femtometers, with an uncertainty of ±0.010 femtometers. This electron-based measurement of r p agrees with that obtained from the analogous muon-based Lamb shift measurement but is not consistent with the larger radius that was obtained from the averaging of previous electron-based measurements.

ISR Experiment at A1-Collaboration

The discrepancy between the proton charge radius extracted from the muonic hydrogen Lamb shift measurement and the best present value obtained from the elastic scattering experiments, remains unexplained and represents a burning problem of today’s nuclear physics. In a pursuit of reconciling the puzzle an experiment is underway at MAMI, which exploits the radiative tail of the elastic peak to study the properties of electromagnetic processes and to extract the proton charge form factor $ \left( {\mathop G\nolimits_E^p } \right) $ at extremely small Q2. This paper reports on the latest results of the first such measurement performed at the three-spectrometer facility of the A1-Collaboration, which led to a precise validation of radiative corrections far away from elastic line and provided measurements of $ \mathop G\nolimits_E^p $ for 0.001 ≤ Q2 ≤ 0.017 (GeV/c)2.

The Mu-MASS (muonium laser spectroscopy) experiment

We present a new experiment, Mu-MASS, aiming for a 1000-fold improvement in the determination of the 1S-2S transition frequency of Muonium (M), the positive-muon/electron bound state. This substantial improvement beyond the current state-of-the-art relies on the novel cryogenic M converters and confinement techniques we developed, on the new excitation and detection schemes which we implemented for positronium spectroscopy and the tremendous advances in generation of UV radiation. This experiment is planned to be performed at the Paul Scherrer Institute (PSI). Interesting anomalies in the muon sector have accumulated: notably the famous anomalous muon magnetic moment (g-2) and the muonic hydrogen Lamb shift measurement which prompted the so-called proton charge radius puzzle. These tantalizing results triggered vibrant activity on both experimental and theoretical sides. Different explanations have been put forward including exciting solutions invoking New Physics beyond the Standard Model. Mu-MASS could contribute to clarifying the origin of these anomalies by providing robust and reliable values of fundamental constants such as the muon mass and a value of the Rydberg constant independent of finite size effects.

Wavelength-dispersive spectroscopy in the hard x-ray regime of a heavy highly-charged ion: the 1s Lamb shift in hydrogen-like gold

Accurate spectroscopy of highly-charged high-Z ions in a storage ring is demonstrated to be feasible by the use of specially adapted crystal optics. The method has been applied for the measurement of the 1s Lamb shift in hydrogen-like gold (Au+78) in a storage ring through spectroscopy of the Lyman x-rays. This measurement represents the first result obtained for a high-Z element using high-resolution wavelength-dispersive spectroscopy in the hard x-ray regime, paving the way for sensitivity to higher-order QED effects.

Lamb shift measurement of antihydrogen for determining the charge radius of antiproton and a stringent test of CPT symmetry

SynopsisMeasurements of Lamb shift in antihydrogen atom have been planned to extract the antiproton charge radius which has never been experimentally investigated. A hyperfine spin filter and a microwave cavity can be employed.

Production of dimeson atoms in high-energy collisions

The production of two-meson electromagnetic bound states and free meson pairs \( \pi^+\pi^-\) , \( K^+K^-\) , \( \pi^+K^{\mp}\) in relativistic collisions has been considered. It is shown that using of exact Coulomb wave functions for dimeson atom (DMA) allows one to calculate the yield of discrete states with the desired accuracy. The relative probabilities of production of DMA and meson pairs in the free state are estimated. The amplitude of DMA transition from 1S to 2P state, which is essential for the pionium Lamb shift measurements, has been obtained.

Proton radius from electron scattering data

[Background] The proton charge radius extracted from recent muonic hydrogen Lamb shift measurements is significantly smaller than that extracted from atomic hydrogen and electron scattering measurements. [Purpose] In an attempt to understand the discrepancy, we review high-precision electron scattering results from Mainz, Jefferson Lab, Saskatoon and Stanford. [Method] We make use of stepwise regression techniques using the $F$-test as well as the Akaike information criterion to systematically determine the predictive variables to use for a given set and range of electron scattering data as well as to provide multivariate error estimates. [Results] Starting with the precision, low four-momentum transfer ($Q^2$) data from Mainz (1980) and Saskatoon (1974), we find that a stepwise regression of the Maclaurin series using the $F$-test as well as the Akaike information criterion justify using a linear extrapolation which yields a value for the proton radius that is consistent with the result obtained from muonic hydrogen measurements. Applying the same Maclaurin series and statistical criteria to the 2014 Rosenbluth results on $G_E$ from Mainz, we again find that the stepwise regression tends to favor a radius consistent with the muonic hydrogen radius but produces results that are extremely sensitive to the range of data included in the fit. Making use of the high-$Q^2$ data on $G_E$ to select functions which extrapolate to high $Q^2$, we find that a Pad\'e ($N=M=1$) statistical model works remarkably well, as does a dipole function with a 0.84 fm radius, $G_E(Q^2) = ( 1 + Q^2/0.66\,\mathrm{GeV}^2)^{-2}$. [Conclusions] From this statistical analysis, we conclude that the electron scattering result and the muonic hydrogen result are consistent. It is the atomic hydrogen results that are the outliers.

On the Absorber Thickness of Microcalorimetric Detectors in Experiments at Nuclear Storage Rings

Low-temperature calorimetric detectors are now successfully used in experiments on Lamb-Shift measurements at experimental storage rings. Strong Doppler broadening of the detected X-ray lines is a prominent feature of these experiments. Accordingly, an optimization procedure for the absorber thickness is proposed that considers the self-width of the X-ray detector line, the Doppler broadening, and the absorption efficiency, taking into account the possibility of the escape of secondary radiation. The optimum thickness for Sn-absorbers in this type of experiments is determined as 0.17 mm.

Understanding the proton radius puzzle: Nuclear structure effects in light muonic atoms

We present calculations of nuclear structure effects to the Lamb shift in light muonic atoms. We adopt a modern ab-initio approach by combining state-of-the-art nuclear potentials with the hyperspherical harmonics method. Our calculations are instrumental to the determination of nuclear charge radii in the Lamb shift measurements, which will shed light on the proton radius puzzle.

Proton Charge Radius (PRad) Experiment at Jefferson Lab

The puzzle of proton charge radius was recently raised by the measurement of muonic hydrogen Lamb shift at Paul Scherrer Institute (PSI), whose results were seven standard deviations smaller than the CODATA recommended value. To investigate this discrepancy, the PRad experiment was proposed and approved at Thomas Jefferson National Accelerator Facility (JLab). The experiment will extract the proton charge radius with a sub-percent accuracy by measuring the cross-sections of unpolarized electronproton elastic scattering in an unprecedented low Q 2 region (2×10−4 GeV2 /c2 ).

Lepton Universality Test in the Photoproduction of e^{-}e^{+} Versus μ^{-}μ^{+} Pairs on a Proton Target.

In view of the significantly different proton charge radius extracted from muonic hydrogen Lamb shift measurements as compared to electronic hydrogen spectroscopy or electron-scattering experiments, we study in this Letter the photoproduction of a lepton pair on a proton target in the limit of very small momentum transfer as a way to provide a test of the lepton universality when extracting the proton charge form factor. By detecting the recoiling proton in the γp→l^{-}l^{+}p reaction, we show that a measurement of a ratio of e^{-}e^{+}+μ^{-}μ^{+} over e^{-}e^{+} cross sections with an absolute precision of 7×10^{-4} would allow for a test to distinguish, at the 3σ level, between the two different proton charge radii currently extracted from muonic and electronic observables.

Spatial characterization of the internal gas target at the ESR for the FOCAL experiment

The FOCAL experiment involves a highly accurate twin crystal spectrometer, designed for the measurement of the ground state Lamb shift of stored highly charged ions, like hydrogen-like Au78+, via spectroscopy in the hard-x-ray regime with an accuracy down to the few-eV level where higher-order QED contributions become accessible. For this level of accuracy all geometrical parameters including the position of the x-ray source are of crucial importance. In this conference proceeding we present our efforts to characterize the internal gas target at the experiment storage ring at GSI Darmstadt where in 2012 the FOCAL experiment was conducted.

Model-independent determination of the Lamb shift in muonic hydrogen and the proton radius

We obtain a model independent expression for the muonic hydrogen Lamb shift. This expression includes the leading logarithmic ${\cal O}(m_{\mu}\alpha^6)$ terms, as well as the leading ${\cal O}(m_{\mu}\alpha^5 \frac{m_{\mu}^2}{m_{\rho}^2})$ hadronic effects. The latter are controlled by the chiral theory, which allows for their model independent determination. In this paper we give the missing piece for their complete expression including the pion and Delta particles. Out of this analysis and the experimental measurement of the muonic hydrogen Lamb shift we determine the electromagnetic proton radius: $r_p=0.8412(15)$ fm. This number is at 6.8$\sigma$ variance with respect to the CODATA value. The accuracy of our result is limited by uncomputed terms of ${\cal O}(m_{\mu}\alpha^5\frac{m_{\mu}^3}{m_{\rho}^3},m_{\mu}\alpha^6)$. This parametric control of the uncertainties allows us to obtain a model independent determination of the error, which is dominated by hadronic effects.

Theoretical constraints and systematic effects in the determination of the proton form factors

We calculate the two-photon exchange corrections to electron-proton scattering with nucleon and $\mathrm{\ensuremath{\Delta}}$ intermediate states. The results show a dependence on the elastic nucleon and nucleon-$\mathrm{\ensuremath{\Delta}}$-transition form factors used as input which leads to significant changes compared to previous calculations. We discuss the relevance of these corrections and apply them to the most recent and precise data set and world data from electron-proton scattering. Using this, we show how the form factor extraction from these data is influenced by the subsequent inclusion of physical constraints. The determination of the proton charge radius from scattering data is shown to be dominated by the enforcement of a realistic spectral function. Additionally, the third Zemach moment from the resulting form factors is calculated. The obtained radius and Zemach moment are shown to be consistent with Lamb shift measurements in muonic hydrogen.

The muonic hydrogen Lamb shift and the proton radius

We obtain a model independent expression for the muonic hydrogen Lamb shift up to O(mμα6,mμα5mμ2mρ2). The hadronic effects are controlled by the chiral theory, which allows for their model independent determination. We give their complete expression including the pion and Delta particles. Out of this analysis and the experimental measurement of the muonic hydrogen Lamb shift we determine the electromagnetic proton radius: rp=0.8412(15) fm. This number is at 6.8σ variance with respect to the CODATA value. The parametric control of the uncertainties allows us to obtain a model independent determination of the error, which is dominated by hadronic effects.

The PRad experiment and the proton radius puzzle

New results from the recent muonic hydrogen experiments seriously questioned our knowledge of the charge radius, rp. The new value, with its unprecedented less than sub-percent precision, is currently up to eight standard deviation smaller than the average value from all previous experiments, triggering the well-known proton charge radius in nuclear and atomic physics. The PRad collaboration is currently preparing a novel, magnetic-spectrometer-free ep scattering experiment in Hall B at JLab for a new independent rp measurement to address this growing puzzle in physics. scattering method, in which the slope of the extracted electric form factor, G p ,a t lowQ 2 defines the rms radius of the proton, rp. The average value of rp for this method, given by a model independent analysis of electron scattering data is rp = 0.870(26) fm (1). Several known experimental factors limit the precision in these experiments, and the typical uncertainties of individual experiments currently are at the level of 2%. Recently, a new state-of-the-art experiment was performed at MAMI Mainz giving rp = 0.879(8) fm (2), and it is consistent with previous ep scattering results. (ii) The spectroscopy of electronic (ordinary) hydrogen atom through the Lamb shift measurements defines the radius, rp .T he value ofrp from this method is currently consistent with the ep scattering results: rp = 0.8775(51) fm (3). (iii) Recently developed method using the Lamb shift measurements from the muonic hydrogen. The muonic hydrogen result (rp = 0.8409(4) fm) (4, 5), with its unprecedented less than 0.1% precision, is currently up to eight standard deviation smaller than the average value from all previous experiments, triggering the well-known proton radius in nuclear and atomic physics. So far, all theoretical efforts and more precise simulations failed to explain this discrepancy on the value of a fundamental quantity - rp. The current situation critically requires performing new

Puzzling out the proton radius puzzle

The discrepancy between the proton charge radius extracted from the muonic hydrogen Lamb shift measurement and the best present value obtained from the elastic scattering experiments, remains unexplained and represents a burning problem of today's nuclear physics: after more than 50 years of research the radius of a basic constituent of matter is still not understood. This paper presents a summary of the best existing proton radius measurements, followed by an overview of the possible explanations for the observed inconsistency between the hydrogen and the muonic-hydrogen data. In the last part the upcoming experiments, dedicated to remeasuring the proton radius, are described.