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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

The proton charge radius

Nucleons (protons and neutrons) are the building blocks of atomic nuclei and are responsible for more than 99% of the visible matter in the Universe. Despite decades of efforts in studying its internal structure, there are still a number of puzzles surrounding the proton such as its spin and charge radius. Accurate knowledge about the proton charge radius is not only essential for understanding how QCD works in the nonperturbative region but also important for bound state QED calculations of atomic energy levels. It also has an impact on the Rydberg constant, one of the most precisely measured fundamental constants in nature. This review examines the latest situation concerning the proton charge radius in light of the new experimental results from both atomic hydrogen spectroscopy and electron-scattering measurements, with particular focus on the latter. Further, theoretical backgrounds and recent developments concerning the determination of the proton charge radius using different experimental techniques are also presented. Upcoming experiments are discussed, and the deuteron charge radius puzzle is mentioned at the end.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Model-independent extraction of the proton charge radius from PRad data

The proton radius puzzle has motivated several new experiments that aim to extract the proton charge radius and resolve the puzzle. Recently, PRad, a new electron–proton scattering experiment at Jefferson Lab, reported a proton charge radius of [Formula: see text]. The value was obtained by using a rational function model for the proton electric form factor. We perform a model-independent extraction using [Formula: see text]-expansion of the proton charge radius from PRad data. We find that the model-independent statistical error is more than 50% larger compared to the statistical error reported by PRad.

Astronomy & Astrophysics↗
DOE OSTI2021

The proton charge radius extracted from the initial-state radiation experiment at MAMI

Abstract We report on a comprehensive reinterpretation of the existing cross-section data for elastic electron-proton scattering obtained by the initial-state radiation technique, resulting in a significantly improved accuracy of the extracted proton charge radius. By refining the external energy corrections we have achieved an outstanding description of the radiative tail, essential for a detailed investigation of the proton finite-size effects on the measured cross sections. This development, together with a novel framework for determining the radius, based on a regression analysis of the cross sections employing a polynomial model for the form factor, led us to a new value for the charge radius, which is $$(0.878 \pm 0.011_\mathrm {stat.}\pm 0.031_\mathrm {sys.}\pm 0.002_\mathrm {mod.})\,\mathrm {fm}$$ ( 0.878 ± 0 . 011 stat . ± 0 . 031 sys . ± 0 . 002 mod . ) fm

Physics↗
DOE OSTI2023

Proton Electric Charge Radius from Lepton Scattering

A proton is a bound state of a strong interaction, governed by Quantum Chromodynamics (QCD). The electric charge radius of a proton, denoted by $r^{p}_{E}$, characterizes the spatial distribution of its electric charge carried by the quarks. It is an important input for bound-state Quantum Electrodynamic (QED) calculations of the hydrogen atomic energy levels. However, physicists have been puzzled by the large discrepancy between $r^{p}_{E}$ measurements from muonic hydrogen spectroscopy and those from ep elastic scattering and ordinary hydrogen spectroscopy for over a decade. Tremendous efforts, both theoretical and experimental, have been dedicated to providing various insights into this puzzle, but certain issues still remain unresolved, particularly in the field of lepton scatterings. This review will focus on lepton-scattering measurements of $r^{p}_{E}$, recent theoretical and experimental developments in this field, as well as future experiments using this technique.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Charge radii of the nucleon from its flavor dependent Dirac form factors

In this report we have determined the proton and the neutron charge radii from a global analysis of the proton and the neutron elastic form factors, after first performing a flavor decomposition of these form factors under charge symmetry in the light cone frame formulation. We then extracted the transverse mean-square radii of the flavor dependent quark distributions. In turn, these are related in a model-independent way to the proton and neutron charge radii but allow us to take into account motion effects of the recoiling nucleon for data at finite but high momentum transfer. In the proton case we find $\langle r_p \rangle$ = 0.852±0.002 (stat.) ± 0.009 (syst.) (fm), consistent with the proton charge radius obtained from muonic hydrogen spectroscopy. The current method improves on the precision of the $\langle r_p \rangle$; extraction based on the form factor measurements. Furthermore, we find no discrepancy in the $\langle r_p \rangle$ determination among the different electron scattering measurements, all of which, utilizing the current method of extraction, result in a value that is consistent with the smallest $\langle r_p \rangle$ extraction from the electron scattering measurements. Concerning the neutron case, past results relied solely on the neutron-electron scattering length measurements, which suffer from an underestimation of underlying systematic uncertainties inherent to the extraction technique. Utilizing the present method we have performed the first extraction of the neutron charge radius based on nucleon form factor data, and we find $\langle r^2_n \rangle$ = -0.122±0.004 (stat.) ± 0.010 (syst.) (fm 2 ).

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

The PRad windowless gas flow target

In this work, we report on a windowless, high-density, gas flow target at Jefferson Lab that was used to measure $r_p$, the root-mean-square charge radius of the proton. To our knowledge, this is the first such system used in a fixed-target experiment at a (non-storage ring) electron accelerator. The target achieved its design goal of an areal density of 2$\times$10$^{18}$ atoms/cm$^2$, with the gas uniformly distributed over the 4 cm length of the cell and less than 1% residual gas outside the cell. This design eliminated scattering from the end caps of the target cell, a problem endemic to previous measurements of the proton charge radius in electron scattering experiments, and permitted a precise, model-independent extraction of $r_p$ by reaching unprecedentedly low values of $Q^2$, the square of the electron's transfer of four-momentum to the proton.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

The Complete α 8 m Contributions to the 1s Lamb Shift in Hydrogen

Precision studies of simple atoms, such as hydrogen, play an essential role in tests of bound-state QED and determining fundamental constants, such as the Rydberg constant and the proton charge radius. One of the QED predictions is for the Lamb shift of hydrogenic energy levels and, in particular, of the ground state. Here, the value of the 1s Lamb shift in hydrogen and deuterium is required for an accurate determination of the Rydberg constant and the proton charge radius utilizing data from high-resolution spectroscopy of hydrogen and deuterium atoms, as well as for precision tests of bound-state QED. The dominant QED contribution to the uncertainty is due to the α 8 m external-field contributions. We discuss here our recent results on the two- and three-loop contributions, which essentially reduce the theoretical uncertainty. Combined with recent calculations of Laporta on the slope of the Dirac form factor in the three-loop level, our results allow for completion of calculations of α 8 m contributions to the Lamb shift of the ground state in the hydrogen atom.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Lowest-order QED radiative corrections in unpolarized elastic electron–deuteron scattering beyond the ultra-relativistic limit for the proposed deuteron charge radius measurement at Jefferson laboratory

Analogous to the well-known proton charge radius puzzle, a similar puzzle exists for the deuteron charge radius, r d . There are discrepancies observed in the results of r d , measured from electron-deuteron (e - d) scattering experiments, as well as from atomic spectroscopy. In order to help resolve the charge radius puzzle of the deuteron, the PRad collaboration at Jefferson Lab has proposed an experiment for measuring r d , named DRad. This experiment is designed to measure the unpolarized elastic e - d scattering cross section in a low-Q 2 region. To extract the cross section with a high precision, having reliable knowledge of QED radiative corrections is important. Here, in this paper, we present complete numerical calculations of the lowest-order radiative corrections in e - d scattering for the DRad kinematics. The calculations have been performed within a covariant formalism and beyond the ultra-relativistic approximation ($m^2_e$ $\ll$ Q 2 ). Besides, we present a systematic uncertainty on r d arising from higher-order radiative corrections, estimated based on our cross-section results.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

A liquid hydrogen target for the MUSE experiment at PSI

A 280 ml liquid hydrogen target has been constructed and tested here for the MUSE experiment at PSI to investigate the proton charge radius via simultaneous measurement of elastic muon–proton and elastic electron–proton scattering. To control systematic uncertainties at a sub-percent level, strong constraints were put on the amount of material surrounding the target and on its temperature stability. The target system was successfully operated during a commissioning run at PSI at the end of 2018. The target temperature was stable at the 0.01 K level. This indicates a density stability at the 0.02% level, which is about a factor of ten better than required.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

The proton radius (puzzle?) and its relatives

We review determinations of the electric proton charge radius from a diverse set of low-energy observables. We explore under which conditions it can be related to Wilson coefficients of appropriate effective field theories. This discussion is generalized to other low-energy constants. This provides us with a unified framework to deal with a set of low-energy constants of the proton associated with its electromagnetic interactions. Unambiguous definitions of these objects are given, as well as their relation with expectation values of QCD operators. We show that the proton radius obtained from spectroscopy and lepton–proton scattering (when both the lepton and proton move with nonrelativistic velocities) is related to the same object of the underlying field theory with O ( α ) precision. The model dependence of these analyses is discussed. The prospects of constructing effective field theories valid for the kinematic configuration of present, or near-future, lepton–proton scattering experiments are explored.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Characterization of muon and electron beams in the Paul Scherrer Institute PiM1 channel for the MUSE experiment

The MUon Scattering Experiment, MUSE, at the Paul Scherrer Institute, Switzerland, investigates the proton charge radius puzzle, lepton universality, and two-photon exchange, via simultaneous measurements of elastic muon-proton and electron-proton scattering. The experiment uses the PiM1 secondary beam channel, which was designed for high precision pion scattering measurements. We review the properties of the beam line established for pions. We discuss the production processes that generate the electron and muon beams, and the simulations of these processes. Simulations of the π/μ/e beams through the channel using TURTLE and G4beamline are compared. The G4beamline simulation is then compared to several experimental measurements of the channel, including the momentum dispersion at the intermediate focal plane and target, the shape of the beam spot at the target, and timing measurements that allow the beam momenta to be determined. Finally, we conclude that the PiM1 channel can be used for high precision π, μ, and e scattering.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2024

Absorptive corrections to the electromagnetic form factor in high-energy elastic proton-proton scattering

Recently, it was noted that absorptive corrections to the electromagnetic form factor in high-energy proton-proton scattering are important for the theoretical interpretation of the p ↑ p and p ↑ A analyzing power A N ( t ) measurements with the Hydrogen Jet Target polarimeter (HJET) at RHIC. Here, a concise expression for the absorptive correction was derived within the eikonal approach. The resulting analysis reveals a systematic bias, nearly independent of the beam energy, in the experimental determination of the real-to-imaginary ratio ρ when absorption effects are overlooked in the data analysis. Quantification of this bias, as ρ meas = ρ + ( 0.036 ± 0.016 ) bias , was achieved using a Regge fit applied to available proton-proton measurements of ρ meas ( s ) and σ tot meas ( s ) . Considering the potential impact of such an effect on the experimentally determined A N ( t ) , one may enhance consistency between the HJET and STAR measurements of the hadronic spin-flip amplitude. While the sign of the bias in the value of ρ aligns with the anticipated effective increase in the proton charge radius in p p scattering due to absorption, it amplifies the observed discrepancy between σ tot meas and ρ meas values at s = 13 TeV as measured in the TOTEM experiment. Evaluation (using published TOTEM data) of the measured proton-proton d σ / d t dependence on the absorptive corrections indicated that possible soft photon corrections to the hadronic amplitude slope may be essential for such data analysis. Published by the American Physical Society 2024

43 PARTICLE ACCELERATORS↗
DOE OSTI2021

Elastic positron–proton scattering at low Q$^2$

Systematic differences in the the proton's charge radius, as determined by ordinary atoms and muonic atoms, have caused a resurgence of interest in elastic lepton scattering measurements. The proton's charge radius, defined as the slope of the charge form factor at Q$^2$=0, does not depend on the probe. Any difference in the apparent size of the proton, when determined from ordinary versus muonic hydrogen, could point to new physics or need for the higher order corrections. While recent measurements seem to now be in agreement, there is to date no high precision elastic scattering data with both electrons and positrons. A high precision proton radius measurement could be performed in Hall B at Jefferson Lab with a positron beam and the calorimeter based setup of the PRad experiment. This measurement could also be extended to deuterons where a similar discrepancy has been observed between the muonic and electronic determination of deuteron charge radius. A new, high precision measurement with positrons, when viewed alongside electron scattering measurements and the forthcoming MUSE muon scattering measurement, could help provide new insights into the origins of the proton radius puzzle, and also provide new experimental constraints on radiative correction calculations.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Direct comparison of using a Z -transformation instead of the traditional $Q^2$ for extraction of the proton radius from $e-p$ scattering data

A discrepancy in the determination of the proton’s charge radius, r p , between muonic hydrogen spectroscopy versus classic atomic spectroscopy and electron scattering data has become known as the proton radius puzzle. Extractions of r p from electron scattering data require determination of the slope of the proton’s charge form factor, $G$$^{p}_{E}$, in the limit of Q 2 → 0 through fitting and extrapolation. Some works have presented the Z-transformation fitting technique as the best choice for this type of extraction due to the true functional form of $G$$^{p}_{E}$ being mathematically guaranteed to exist within the parameter-space of the fit function. In this work, we test this claim by examining the mathematical bias and variances introduced by this technique as compared to the more traditional Q 2 fits using statistically sampled $G$$^{p}_{E}$ parameterizations with known input radii. Furthermore, our tests conclude that the quality of the Z-transformation technique depends on the range of data used. In the case of new experiments, the fit function and technique should be selected in advance by generating realistic pseudodata and assessing the power of different techniques.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

The size of the Proton: Recent Results from the PRad Experiment

Two new extremely high precision measurements of the proton rms charge radius performed in 2010-2013 with muonic hydrogen atom demonstrated up to six standard deviations smaller values than the accepted average from all previous experiments performed with different methods (scattering and atomic spectroscopy) on ordinary hydrogen. This discrepancy triggered the well-known ?proton radius puzzle? in hadronic physics. To address this puzzle, the PRad collaboration in spring of 2016 performed a novel magnetic-spectrometer-free ep-scattering experiment in Hall B at Jefferson Lab accumulating high statistics and a rich experimental data set. The specifics of the PRad experiment and the final physics results, including the extracted proton radius, as well as, the current status of the puzzle will be presented and discussed in this talk.

Gasparian, Ashot↗