Proton Charge Radius Research Articles

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

We present a new measurement of the 1S-3S two-photon transition frequency of hydrogen, realized with a continuous-wave excitation laser at 205nm on a room-temperature atomic beam, with a relative uncertainty of 9×10^{-13}. The proton charge radius deduced from this measurement, r_{p}=0.877(13) fm, is in very good agreement with the current CODATA-recommended value. This result contributes to the ongoing search to solve the proton charge radius puzzle, which arose from a discrepancy between the CODATA value and a more precise determination of r_{p} from muonic hydrogen spectroscopy.

Internal Structure of Charged Particles in a GRT Gravitational Model

With the help of an exact solution of the Einstein and Maxwell equations, the internal structure of a multiply connected space of wormhole type with two unclosed static throats leading out of it into two parallel vacuum spaces or into one space is investigated in GRT for a free electric field and dust-like matter. The given geometry is considered as a particle–antiparticle pair with fundamental constants arising in the form of first integrals in the solution of the Cauchy problem – electric charges ±e of opposite sign in the throats and rest mass m0 – the total gravitational mass of the inner world of the particle in the throat. With the help of the energy conservation law, the unremovable rotation of the internal structure is included and the projection of the angular momentum of which onto the rotation axis is identified with the z-projection of the spin of the charged particle. The radius of 2-Gaussian curvature of the throat R* is identified with the charge radius of the particle, and the z-projection of the magnetic moment and the g-factor are found. The feasibility of the given gravitational model is confirmed by the found condition of independence of the spin quantum number of the electron and the proton s = 1/2 of the charge radius R* and the relativistic rest mass m* of the rotating throat, which is reliably confirmed experimentally, and also by the coincidence with high accuracy of the proton radius calculated in the model R*p = 0.8412·10–13 cm with the value of the proton charge radius obtained experimentally by measuring the Lamb shift on muonic hydrogen. The electron in the given model also turns out to be a structured particle with radius R*e = 3.8617·10–11 cm.

Accurate Determination of the Values of Fundamental Physical Constants: The Basis of the New “Quantum” SI Units

The metric system appeared as the system of units designed for macroscopic (laboratory scale) measurements. The progress in accurate determination of the values of quantum constants (such as the Planck constant) in SI units shows that the capabilities in high-precision measurement of microscopic and macroscopic quantities in terms of the same units have increased substantially recently. At the same time, relative microscopic measurements (for example, the comparison of atomic transition frequencies or atomic masses) are often much more accurate than relative measurements of macroscopic quantities. This is the basis for the strategy to define units in microscopic phenomena and then use them on the laboratory scale, which plays a crucial role in practical methodological applications determined by everyday life and technologies. The international CODATA task group on fundamental constants regularly performs an overall analysis of the precision world data (the so-called Adjustment of the Fundamental Constants) and publishes their recommended values. The most recent evaluation was based on the data published by the end of 2014; here, we review the corresponding data and results. The accuracy in determination of the Boltzmann constant has increased, the consistency of the data on determination of the Planck constant has improved; it is these two dimensional constants that will be used in near future as the basis for the new definition of the kelvin and kilogram, respectively. The contradictions in determination of the Rydberg constant and the proton charge radius remain. The accuracy of determination of the fine structure constant and relative atomic weight of the electron has improved. Overall, we give a detailed review of the state of the art in precision determination of the values of fundamental constants. The mathematical procedure of the Adjustment, the new data and results are considered in detail. The limitations due to macroscopic properties of material standards (such as the International prototype of the kilogram) and the isotopic composition of substances involved in precision studies in general (as standard measures for the triple point of water) and, in particular, in the determination of the fundamental constants are discussed. The perspectives of the introduction of the new quantum units, which will be free from the mentioned problems, are considered. Many physicists feel no sympathy for the International system of units (SI), believing that it does not properly reflect the character of physical laws. In fact, there are three parallel systems, namely the systems of quantities, system of their units and the related standards. The definition of the units, in particular, the SI units, above all, reflects our ability to perform precision measurements of physical values under certain conditions, in particular, to create appropriate standards. This requirement is not related to the beauty of fundamental laws of nature. More accurate determination of the fundamental constants is one of the areas where we accumulate such experience.

Deep-Ultraviolet Frequency Metrology of H_{2} for Tests of Molecular Quantum Theory.

Molecular hydrogen and its isotopic and ionic species are benchmark systems for testing quantum chemical theory. Advances in molecular energy structure calculations enable the experimental verification of quantum electrodynamics and potentially a determination of the proton charge radius from H_{2} spectroscopy. We measure the ground state energy in ortho-H_{2} relative to the first electronically excited state by Ramsey-comb laser spectroscopy on the EF^{1}Σ_{g}^{+}-X^{1}Σ_{g}^{+}(0,0) Q1 transition. The resulting transition frequency of 2 971 234 992 965(73)kHz is 2 orders of magnitude more accurate than previous measurements. This paves the way for a considerably improved determination of the dissociation energy (D_{0}) for fundamental tests with molecular hydrogen.

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.

Measurement of Proton Charge Radius by Low-Energy Electron Scattering

Measurement of Proton Charge Radius by Low-Energy Electron Scattering

Inherent Differences between Bound and Radiation Fields

The purpose of the paper is to use fundamental theoretical and experimental elements of electrodynamics for deriving properties of radiation fields and of bound fields. A wide variety of examples prove that radiation fields and bound fields do not represent the same physical object. This conclusion is new. Some examples belong to the classical domain and others belong to the quantum domain. Consequences of this outcome affect several physical issues. In particular, these fields should be treated separately. For this reason, changes must be introduced to the present form of the fields’ Lagrangian density of quantum electrodynamics, where the fields tensor Fuv is a sum of bound and radiation fields. Since the Lagrangian density is a key element of the theory, its revision may entail changes of other specific issues. The recent failure of quantum electrodynamics to explain the electron and the muon data of the proton charge radius supports this conclusion.

Proton Charge Radius from Electron Scattering

The rms-radius R of the proton charge distribution is a fundamental quantity needed for precision physics. This radius, traditionally determined from elastic electron-proton scattering via the slope of the Sachs form factor G e ( q 2 ) extrapolated to momentum transfer q 2 = 0 , shows a large scatter. We discuss the approaches used to analyze the e-p data, partly redo these analyses in order to identify the sources of the discrepancies and explore alternative parameterizations. The problem lies in the model dependence of the parameterized G ( q ) needed for the extrapolation. This shape of G ( q < q m i n ) is closely related to the shape of the charge density ρ ( r ) at large radii r, a quantity that is ignored in most analyses. When using our physics knowledge about this large-r density together with the information contained in the high-q data, the model dependence of the extrapolation is reduced, and different parameterizations of the pre-2010 data yield a consistent value for R = 0.887 ± 0.012 fm. This value disagrees with the more precise value 0.8409 ± 0.0004 fm determined from the Lamb shift in muonic hydrogen.

Analysis of Deeply Virtual Compton Scattering data at Jefferson Lab and proton tomography

The CLAS and Hall A collaborations at Jefferson Laboratory have recently released new results for the ep->ep{\gamma} reaction. We analyze these new data within the Generalized Parton Distribution formalism. Employing a fitter algorithm introduced and used in earlier works, we are able to extract from these data new constraints on the kinematical dependence of three Compton Form Factors. Based on experimental data, we subsequently extract the dependence of the proton charge radius on the quarks longitudinal momentum fraction.

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.

Proton radius from electron-proton scattering and chiral perturbation theory

We determine the root-mean-square proton charge radius, $R_{\rm p}$, from a fit to low-$Q^2$ electron-proton elastic scattering cross section data with the higher moments fixed (within uncertainties) to the values predicted by chiral perturbation theory. We obtain $R_{\rm p}=0.857(11)$ fm. This number falls between the value obtained from muonic hydrogen analyses and the CODATA value (based upon atomic hydrogen spectroscopy and electron-proton scattering determinations).

Deuteron charge radius and Rydberg constant from spectroscopy data in atomic deuterium

We give a pedagogical description of the method to extract the charge radii and Rydberg constant from laser spectroscopy in regular hydrogen (H) and deuterium (D) atoms, that is part of the CODATA least-squares adjustment (LSA) of the fundamental physical constants. We give a deuteron charge radius from D spectroscopy alone of 2.1415(45) fm. This value is independent of the measurements that lead to the proton charge radius, and five times more accurate than the value found in the CODATA Adjustment 10. The improvement is due to the use of a value for the transition in atomic deuterium which can be inferred from published data or found in a PhD thesis.

Novel applications of Lattice QCD: Parton Distributions, proton charge radius and neutron electric dipole moment

We briefly discuss the current status of lattice QCD simulations and review selective results on nucleon observables focusing on recent developments in the lattice QCD evaluation of the nucleon form factors and radii, parton distribution functions and their moments, and the neutron electric dipole moment. Nucleon charges and moments of parton distribution functions are presented using simulations generated at physical values of the quark masses, while exploratory studies are performed for the parton distribution functions and the neutron electric dipole moment at heavier than physical value of the pion mass.

Dispersion theoretical analysis of the nucleon form factors

We review the achievements of the project C.2 , that deals with a dispersion theoretical analysis of the nucleon form factors. We have analyzed the world data for the space-like and time-like form factors to extract nucleon radii and vector meson coupling constants. Our proton charge radius r P E ≃ 0.85 fm has gained prominence in the so-called proton radius puzzle, see Ref. [1]. We also have analyzed the strong energy dependence of the e + e − → pp amplitude at the nucleon-antinucleon threshold, two-photon exchange effects and isospin violation in the isovector nucleon form factors.

Restrained dark U(1)d at low energies

We investigate a spontaneously broken $U(1)_d$ gauge symmetry with a muon-specific dark Higgs. Our first goal is to verify how the presence of a new dark Higgs, $\phi$, and a dark gauge boson, $V$, can simultaneously face the anomalies from the muon magnetic moment and the proton charge radius. Secondly, by assuming that $V$ must decay to an electron-positron pair, we explore the corresponding parameter space determined with the low energy constraints coming from $ K \to \mu X$, electron $(g-2)_e$, $K \to \mu \nu_\mu e^+ e^-$, $K \to \mu \nu_\mu \mu^+ \mu^-$, $\tau \to \nu_\tau \mu \nu_\mu e^+ e^-$. We focus in the scenario where the $V$ mass is below $ \sim 2 m_\mu$ and the $\phi$ mass runs from few MeV till $250$ MeV, with V-photon mixing of the order $ \sim\mathcal{O}(10^{-3})$. Among weak process at low energies, we check the influence of the new light vector on kaon decays as well as on the scattering $e^+ e^- \rightarrow \mu^+ \mu^- e^+ e^-$ and discuss the impact of the dark Higgs on $e^+ e^- \rightarrow \mu^+ \mu^- \mu^+ \mu^- $. Finally, we consider contributions of the V-photon mixing in the decays $\pi^0 \to \gamma e^+ e^-$, $\eta \to \gamma e^+ e^-$, $\rho \to \pi e^+ e^-$, $K^* \to K e^+ e^-$ and $\phi (1020) \to \eta e^+ e^-$.

On the $\pi\pi$ π π continuum in the nucleon form factors and the proton radius puzzle

We present an improved determination of the $\pi\pi$ continuum contribution to the isovector spectral functions of the nucleon electromagnetic form factors. Our analysis includes the most up-to-date results for the $\pi\pi\to\bar N N$ partial waves extracted from Roy-Steiner equations, consistent input for the pion vector form factor, and a thorough discussion of isospin-violating effects and uncertainty estimates. As an application, we consider the $\pi\pi$ contribution to the isovector electric and magnetic radii by means of sum rules, which, in combination with the accurately known neutron electric radius, are found to slightly prefer a small proton charge radius.

Extraction of the Proton Charge Radius from Experiments

Static properties of hadrons such as their radii and other moments of the electric and magnetic distributions can only be extracted using theoretical methods and not directly measured from experiments. As a result, discrepancies between the extracted values from different precision measurements can exist. The proton charge radius, $r_p$, which is either extracted from electron proton elastic scattering data or from hydrogen atom spectroscopy seems to be no exception. The value $r_p = 0.84087(39)$ fm extracted from muonic hydrogen spectroscopy is about 4% smaller than that obtained from electron proton scattering or standard hydrogen spectroscopy. The resolution of this so called proton radius puzzle has been attempted in many different ways over the past six years. The present article reviews these attempts with a focus on the methods of extracting the radius.

Is the proton radius puzzle evidence of extra dimensions?

The proton charge radius inferred from muonic hydrogen spectroscopy is not compatible with the previous value given by CODATA-2010, which, on its turn, essentially relies on measurements of the electron-proton interaction. The proton's new size was extracted from the 2S-2P Lamb shift in the muonic hydrogen, which showed an energy excess of 0.3 meV in comparison to the theoretical prediction, evaluated with the CODATA radius. Higher-dimensional gravity is a candidate to explain this discrepancy, since the muon-proton gravitational interaction is stronger than the electron-proton interaction and, in the context of braneworld models, the gravitational potential can be hugely amplified in short distances when compared to the Newtonian potential. Motivated by these ideas, we study a muonic hydrogen confined in a thick brane. We show that the muon-proton gravitational interaction modified by extra dimensions can provide the additional separation of 0.3 meV between 2S and 2P states. In this scenario, the gravitational energy depends on the higher-dimensional Planck mass and indirectly on the brane thickness. Studying the behavior of the gravitational energy with respect to the brane thickness in a realistic range, we find constraints for the fundamental Planck mass that solve the proton radius puzzle and are consistent with previous experimental bounds.

Active fiber-based retroreflector providing phase-retracing anti-parallel laser beams for precision spectroscopy.

We present an active fiber-based retroreflector providing high quality phase-retracing anti-parallel Gaussian laser beams for precision spectroscopy of Doppler sensitive transitions. Our design is well-suited for a number of applications where implementing optical cavities is technically challenging and corner cubes fail to match the demanded requirements, most importantly retracing wavefronts and preservation of the laser polarization. To illustrate the performance of the system, we use it for spectroscopy of the 2S-4P transition in atomic hydrogen and demonstrate an average suppression of the first order Doppler shift to 4 parts in 106 of the full collinear shift. This high degree of cancellation combined with our cryogenic source of hydrogen atoms in the metastable 2S state is sufficient to enable determinations of the Rydberg constant and the proton charge radius with competitive uncertainties. Advantages over the usual Doppler cancellation based on corner cube type retroreflectors are discussed as well as an alternative method using a high finesse cavity.

Elements of QED-NRQED effective field theory: NLO scattering at leading power

The proton radius puzzle, i.e. the large discrepancy in the extraction of the proton charge radius between regular and muonic hydrogen, challenges our understanding of the structure of the proton. It can also be an indication of a new force that couples to muons, but not to electrons. An effective field theory analysis using Non Relativistic Quantum Electrodynamics (NRQED) indicates that the muonic hydrogen result can be interpreted as a large, compared to some model estimates, muon-proton spin-independent contact interaction. The muonic hydrogen result can be tested by a muon-proton scattering experiment, MUSE, that is planned at the Paul Scherrer Institute in Switzerland. The typical momenta of the muons in this experiment are of the order of the muon mass. In this energy regime the muons are relativistic but the protons are still non-relativistic. The interaction between the muons and protons can be described by a hybrid QED-NRQED effective field theory. We present some elements of this effective field theory. In particular we consider ${\cal O}(Z\alpha)$ scattering up to power $m^2/M^2$, where $m$ ($M$) is the muon (proton) mass and $Z=1$ for a proton, and ${\cal O}(Z^2\alpha^2)$ scattering at leading power. We show how the former reproduces Rosenbluth scattering up to power $m^2/M^2$ and the latter the relativistic scattering off a static potential. Proton structure corrections at ${\cal O}(Z^2\alpha^2)$ will be considered in a subsequent paper.