Muonic Hydrogen Experiment Research Articles

Numerical study of the “two components” model and background effects in muonic hydrogen experiments

In this study, we explore the X-ray time spectra of muonic oxygen in various H 2 + O 2 gaseous mixtures by means of numerical simulations based on a sophisticated kineticrate equations model. Our primary focus is on the “two components” hypothesis, which was put forward to account for the experimentally observed two successive exponential behaviors in the radiation time-distribution. To ensure an accurate representation of the physical processes in the experiments, we incorporate precise transition rate coefficients for the elastic and inelastic scattering between the muonic hydrogen atoms and other gas constituents, in our simulation code. Specifically, a crucial aspect in our approach is the utilization of the energy dependence of the muon transfer rate to oxygen, recently extracted from experimental data by the FAMU collaboration. The accurate knowledge of such muonic oxygen X-ray time spectra is vital for cutting-edge experiments like FAMU, where the hyperfine splitting in muonic hydrogen atoms is to be determined with high accuracy, as this time spectra serves as a significant part of the background for the desired signal.

Electromagnetic radii of the nucleon in soft-wall holographic QCD

We revisit the electromagnetic form factors of the proton and neutron in the original-minimal soft-wall holographic QCD, which has only two parameters, i.e., the mass scale κ and the twist parameter of the nucleon τ. We first fix τ=3 by the hard scattering rule, and extract κ=0.402 GeV from the world data (including the Mainz A1 data) of the Sachs magnetic form factor of the proton GMp. We then predict among others, the charge radius of the proton to be rp=0.831±0.008 fm, in perfect agreement with the recent charge radius of the proton measured by the PRad collaboration at Jefferson Lab, and in agreement with the muonic hydrogen experiments. Our prediction for the proton elastic form factor ratio μpGEp/GMp is also in very good agreement with the recent high precision Jefferson Lab recoil polarization experiment E08-007 for Q2=0.3−0.6 GeV2, and with the recent high precision Mainz A1 experiment for Q2<0.13 GeV2.

A Possible Explanation of the Proton Radius Puzzle Based on the Second Flavor of Muonic Hydrogen Atoms

The proton radius puzzle is one of the most fundamental challenges of modern physics. Before the year 2010, the proton charge radius rp was determined by the spectroscopic method, relying on the electron energy levels in hydrogen atoms, and by the elastic scattering of electrons on protons. In 2010, and then in 2013, two research teams determined rp from the experiment on muonic hydrogen atoms and they claimed rp to be by about 4% smaller than it was found from the experiments with electronic hydrogen atoms. Since then, several research groups performed corresponding experiments with electronic hydrogen atoms and obtained contradictory results: some of them claimed that they found the same value of rp as from the muonic hydrogen experiments, while others reconfirmed the larger value of rp. The conclusion of the latest papers (including reviews) is that the puzzle is not resolved yet. In the present paper, we bring to the attention of the research community, dealing with the proton radius puzzle, the contributing factor never taken into account in any previous calculations. This factor has to do with the hydrogen atoms of the second flavor, whose existence is confirmed in four different types of atomic experiments. We present a relatively simple model illustrating the role of this factor. We showed that disregarding the effect of even a relatively small admixture of the second flavor of muonic hydrogen atoms to the experimental gas of muonic hydrogen atoms could produce the erroneous result that the proton charge radius is by about 4% smaller than its actual value, so that the larger out of the two disputed values of the proton charge radius could be, in fact, correct.

Spectroscopy of HD+: Proton Charge Radius and the Rydberg Constant

The problem of the proton charge radius, its correlation with the Rydberg constant, difficulties in determination of the Rydberg constant using hydrogen atom spectroscopy, and redetermination of fundamental constants in the new CODATA18 revision are discussed. Theoretical and experimental aspects of precision spectroscopy of the molecular hydrogen ion HD+ are considered. It is shown that new experiments allow the Doppler broadening of spectral lines to be eliminated and a relative error of ~10–11 to be achieved in the transition frequency measurements. A comparison of these experiments and theoretical calculations leads to an unambiguous conclusion that the proton charge radius should be determined from the muonic hydrogen experiment and the Rydberg constant from the $$1S$$ – $$2S$$ transition in the ordinary hydrogen atom. Only in this case experiment and theory in HD+ are in reasonable consent.

The Rydberg constant and proton size from atomic hydrogen

At the core of the "proton radius puzzle" is a four-standard deviation discrepancy between the proton root-mean-square charge radii (rp) determined from the regular hydrogen (H) and the muonic hydrogen (µp) atoms. Using a cryogenic beam of H atoms, we measured the 2S-4P transition frequency in H, yielding the values of the Rydberg constant R∞ = 10973731.568076(96) per meterand rp = 0.8335(95) femtometer. Our rp value is 3.3 combined standard deviations smaller than the previous H world data, but in good agreement with the µp value. We motivate an asymmetric fit function, which eliminates line shifts from quantum interference of neighboring atomic resonances.

How big is the proton?

Atomic Physics The discrepancy between the size of the proton extracted from the spectroscopy of muonic hydrogen and the value obtained by averaging previous results for “regular” hydrogen has puzzled physicists for the past 7 years. Now, Beyer et al. shed light on this puzzle (see the Perspective by Vassen). The authors obtained the size of the proton using very accurate spectroscopic measurements of regular hydrogen. Unexpectedly, this value was inconsistent with the average value of previous measurements of the same type. Also unexpectedly, it was consistent with the size extracted from the muonic hydrogen experiments. Resolving the puzzle must now include trying to understand how the old results relate to the new, as well as reexamining the sources of systematic errors in all experiments. Science , this issue p. [79][1]; see also p. [39][2] [1]: /lookup/doi/10.1126/science.aah6677 [2]: /lookup/doi/10.1126/science.aao3969

Theory of Lamb Shift in Muonic Hydrogen

There has been for a while a large discrepancy between the values of the proton charge radius measured by the Lamb shift in muonic hydrogen and by other methods. It has already been clear that theory of muonic hydrogen is reliable at the level of this discrepancy and an error there cannot be a reason for the contradiction. Still the status of theory at the level of the uncertainty of the muonic-hydrogen experiment (which is two orders of magnitude below the discrepancy level) requires an additional clarification. Here, we revisit theory of the 2p − 2s Lamb shift in muonic hydrogen. We summarize all the theoretical contributions in order α5m, including pure quantum electrodynamics (QED) ones as well as those which involve the proton-structure effects. Certain enhanced higher-order effects are also discussed. We basically confirm former QED calculations of other authors, present a review of recent calculations of the proton-structure effects, and treat self-consistently higher-order proton-finite-size corrections. We also overview theory of the 2p states. Eventually, we derive a value of the root-mean-square proton charge radius. It is found to be 0.840 29(55) fm, which is slightly different from that previously published in the literature (0.840 87(39) fm [Antognini et al., Science 339, 417 (2013)]).

Multipass laser cavity for efficient transverse illumination of an elongated volume.

A multipass laser cavity is presented which can be used to illuminate an elongated volume from a transverse direction. The illuminated volume can also have a very large transverse cross section. Convenient access to the illuminated volume is granted. The multipass cavity is very robust against misalignment, and no active stabilization is needed. The scheme is suitable for example in beam experiments, where the beam path must not be blocked by a laser mirror, or if the illuminated volume must be very large. This cavity was used for the muonic-hydrogen experiment in which 6 μm laser light illuminated a volume of 7 × 25 × 176 mm3, using mirrors that are only 12 mm in height. We present our measurement of the intensity distribution inside the multipass cavity and show that this is in good agreement with our simulation.

Pure bound field corrections to the atomic energy levels and the proton size puzzle

Reinforcement of the puzzle about the proton charge radius, rE, stimulated by the recent experiment with muonic hydrogen (Antognini et al. Science, 339, 417 (2013)) induced new discussions on the subject, and now some physicists are ready to adopt the exotic properties of the muon, lying beyond the Standard Model, to explain the difference between the results of muonic hydrogen experiments (rE = 0.840 87(39) fm) and the CODATA-2010 value rE = 0.8775(51) fm based on electron–proton scattering and hydrogen spectroscopy. In the present contribution we suggest a way to achieve progress in the entire problem via paying attention on some logical inconsistency of fundamental equations of atomic physics, constructed by analogy with corresponding classical equations without, however, taking into account the purely bound nature of electromagnetic fields generated by the electrically bound particles in stationary energy states. We suggest eliminating this inconsistency via introducing some appropriate correcting factors into these equations, which explicitly involve the requirement of total momentum conservation in the system “bound particles and their fields” in the absence of electromagnetic radiation. We further show that this approach allows us not only to eliminate long-standing discrepancies between theory and experiment in the precise physics of simple atoms, but also yields the same estimation (though with different uncertainties) for the proton size in the classic 2S–2P Lamb shift in hydrogen, 1S Lamb shift in hydrogen, and 2S–2P Lamb shift in muonic hydrogen, with the mean value rE = 0.841 fm. Finally, we suggest the crucial experiment for verification of the validity of pure bound field corrections: the measurement of decay rate of bound moun in various meso-atoms, especially at large Z, where the standard calculations and our predictions essentially deviate from each other, and some of the available experimental results (Yovanovitch. Phys. Rev. 117, 1580 (1960)) strongly support our approach.

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

PROTON RADIUS PUZZLE AND LARGE EXTRA DIMENSIONS

We propose a theoretical scenario to solve the proton radius puzzle which recently arises from the muonic hydrogen experiment. In this framework, (4+n)-dimensional theory is incorporated with modified gravity. The extra gravitational interaction between the proton and muon at very short range provides an energy shift which accounts for the discrepancy between spectroscopic results from muonic and electronic hydrogen experiments. Assuming the modified gravity is a small perturbation to the existing electromagnetic interaction, we find the puzzle can be solved with stringent constraint on the range of the new force. Our result not only provides a possible solution to the proton radius puzzle but also suggests a direction to test new physics at very small length scale.

Is the proton radius a player in the redefinition of the International System of Units?

It is now recognized that the International System of Units (SI units) will be redefined in terms of fundamental constants, even if the date when this will occur is still under debate. Actually, the best estimate of fundamental constant values is given by a least-squares adjustment, carried out under the auspices of the Committee on Data for Science and Technology (CODATA) Task Group on Fundamental Constants. This adjustment provides a significant measure of the correctness and overall consistency of the basic theories and experimental methods of physics using the values of the constants obtained from widely differing experiments. The physical theories that underlie this adjustment are assumed to be valid, such as quantum electrodynamics (QED). Testing QED, one of the most precise theories is the aim of many accurate experiments. The calculations and the corresponding experiments can be carried out either on a boundless system, such as the electron magnetic moment anomaly, or on a bound system, such as atomic hydrogen. The value of fundamental constants can be deduced from the comparison of theory and experiment. For example, using QED calculations, the value of the fine structure constant given by the CODATA is mainly inferred from the measurement of the electron magnetic moment anomaly carried out by Gabrielse's group. (Hanneke et al. 2008 Phys. Rev. Lett. 100, 120801) The value of the Rydberg constant is known from two-photon spectroscopy of hydrogen combined with accurate theoretical quantities. The Rydberg constant, determined by the comparison of theory and experiment using atomic hydrogen, is known with a relative uncertainty of 6.6×10(-12). It is one of the most accurate fundamental constants to date. A careful analysis shows that knowledge of the electrical size of the proton is nowadays a limitation in this comparison. The aim of muonic hydrogen spectroscopy was to obtain an accurate value of the proton charge radius. However, the value deduced from this experiment contradicts other less accurate determinations. This problem is known as the proton radius puzzle. This new determination of the proton radius may affect the value of the Rydberg constant . This constant is related to many fundamental constants; in particular, links the two possible ways proposed for the redefinition of the kilogram, the Avogadro constant N(A) and the Planck constant h. However, the current relative uncertainty on the experimental determinations of N(A) or h is three orders of magnitude larger than the 'possible' shift of the Rydberg constant, which may be shown by the new value of the size of the proton radius determined from muonic hydrogen. The proton radius puzzle will not interfere in the redefinition of the kilogram. After a short introduction to the properties of the proton, we will describe the muonic hydrogen experiment. There is intense theoretical activity as a result of our observation. A brief summary of possible theoretical explanations at the date of writing of the paper will be given. The contribution of the proton radius puzzle to the redefinition of SI-based units will then be examined.

Nuclear Structure Corrections in Muonic Deuterium

The muonic hydrogen experiment measuring the 2P-2S transition energy [R. Pohl etal., Nature (London) 466, 213 (2010)] is significantly discrepant with theoretical predictions based on quantum electrodynamics. A possible approach to resolve this conundrum is to compare experimental values with theoretical predictions in another system, muonic deuterium μD. The only correction which might be questioned in μD is that due to the deuteron polarizability. We investigate this effect in detail and observe cancellation with the elastic contribution. The total value obtained for the deuteron structure correction in the 2P-2S transition is 1.680(16)meV.

SIZING THE PROTON

A NEW EXPERIMENT indicates that the proton may be significantly smaller than previously believed, a result that could change the value of key physical constants, reports a group led by physicist Randolf Pohl of the Max Planck Institute for Quantum Optics, in Germany ( Nature 2010, 466, 213). The group studied muonic hydrogen, in which the hydrogen atom’s usual electron is replaced with a muon, a particle that has the same charge but is 200 times heavier than an electron. The researchers used laser pulses to probe the energy difference between two states of the atom and then used that difference to calculate the proton’s charge radius, a measure of the spread of its positive charge. From the muonic hydrogen experiment, Pohl and coworkers found that the charge radius of the proton is 0.84184 femtometers. That radius differs significantly from the previously accepted value of 0.8768 fm, which the International Council for Science’s Committee on Data ...

Planar LAAPDs: temperature dependence, performance, and application in low-energy X-ray spectroscopy

An experiment measuring the 2S Lamb shift in muonic hydrogen ( μ - p ) was performed at the Paul Scherrer Institute, Switzerland. It required small and compact detectors for 1.9 keV X-rays (2P–1S transition) with an energy resolution around 25% at 2 keV, a time resolution better than 100 ns, a large solid angle coverage, and insensitivity to a 5 T magnetic field. We chose Large Area Avalanche Photodiodes (LAAPDs) from Radiation Monitoring Devices as X-ray detectors, and they were used during the last data taking period in 2003. For X-ray spectroscopy applications, these LAAPDs have to be cooled in order to suppress the dark current noise; hence, a series of tests were performed to choose the optimal operation temperature. Specifically, the temperature dependence of gain, energy resolution, dark current, excess noise factor, and detector response linearity was studied. Finally, details of the LAAPDs application in the muonic hydrogen experiment as well as their response to α particles are presented.