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All sourcesNASA NTRSDOE OSTI
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 OSTI2026

The MUSE Target Chamber Post Veto

The Muon Scattering Experiment (MUSE) was developed to address the proton radius puzzle through simultaneous electron–proton and muon-proton scattering using the Paul Scherrer Institute’s πM1 secondary beamline. MUSE uses a large-solid-angle, non-magnetic spectrometer to detect beam particles scattering from a liquid hydrogen cell contained within a vacuum chamber. Due to the large scattering windows, the structural integrity of the chamber is supported by posts located at small scattering angles. While out of the acceptance, particles in the tails of the beam distribution can strike these posts, causing a significant trigger background. We describe the design and performance of the Target Chamber Post Veto (TCPV) detector installed inside the vacuum chamber to remove these background events at the trigger level.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Construction and Commissioning of Gas Electron Multiplier (GEM) Detectors in Advanced Assembly Design for Low-Energy Applications at High Rates and Analysis of GEM Data From the Muse Experiment at PSI

The search beyond the Standard Model explores dark matter and a potential fifth force. DarkLight@ARIEL investigates the dark photon as a mediator between ordinary and dark matter. The experiment aims to measure the process e?Ta ? e?TaX ? e?Ta(e?e+), by detecting a charged lepton pair in the final state. The spectrometers will be instrumented with Gas Electron Multiplier (GEM) detectors with minimal material budget for tracking. A novel GEM construction technique is employed for fabricating 25 cm x 40 cm GEM detectors, where all layers are mechanically stretched and assembled within a double frame. The dissertation outlines physics motivation, methods, experimental setup, and the role of GEM detectors in DarkLight. A comprehensive discussion on GEM detectors, focusing on the "NS2" technique, including design, parts, assembly, testing, and performance evaluation will be discussed. The proton has garnered attention due to discrepancies in measuring its charge radius using muonic hydrogen and electron-based methods. The 2010 muonic hydrogen measurement of the proton charge radius Rp = 0.84184(67) fm, showed a significant 7? discrepancy compared to the previously known value of Rp = 0.8775(51) fm, giving rise to the proton radius puzzle. Through simultaneous measurements of e ? p and ? ? p elastic scattering, MUSE facilitates a precise and direct comparison of the proton radius. The physics background of the proton radius puzzle, measurement techniques, the approach adopted by the MUSE experiment, its significance and the experimental setup will be discussed. Furthermore, the role of GEM detectors, along with an in-depth analysis of their data and efficiency will be discussed and evaluated.

Mohammed Prem Nazeer, Sahara↗
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 OSTI2025

The MUSE beamline calorimeter

The MUon Scattering Experiment (MUSE) was motivated by the proton radius puzzle arising from the discrepancy between muonic hydrogen spectroscopy and electron–proton measurements. The MUSE physics goals also include testing lepton universality, precisely measuring two-photon exchange contribution, and testing radiative corrections. MUSE addresses these physics goals through simultaneous measurement of high precision cross sections for electron–proton and muon–proton scattering using a mixed-species beam. The experiment will run at both positive and negative beam polarities. Measuring precise cross sections requires understanding both the incident beam energy and the radiative corrections. For this purpose, a lead-glass calorimeter was installed at the end of the beam line in the MUSE detector system. Here, in this article, we discuss the detector specifications, calibration and performance. We demonstrate that the detector performance is well reproduced by simulation, and meets experimental requirements.

Calorimeter↗
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↗
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

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 OSTI2021

Realization of a high luminosity muon beam at the Jefferson Lab

The proton is the major component of the visible matter of our universe, so being able to determine its fundamental properties, such as its charge radius, is of vital importance. In recent years, several experiments have been performed for the accurate measurement of the proton radius with different experimental techniques. The main and most common are based on two different techniques: ep scattering and Lamb shift spectroscopy of regular hydrogen atoms. The latter can also be performed on muonic hydrogen atoms with a significant improvement in accuracy. Recent measurements that use this method have highlighted a discrepancy between the results obtained with the diffusion of electrons and those obtained with the spectroscopic technique leading to the so-called ?proton radius puzzle?. The explanation of why this difference between the measured values exists is still a matter of discussion. The last attempt to address the puzzle was the PRad Experiment. It was performed with a unique experimental setup that gave the scientists an excellent control on the systematic errors that are usually present in electron-proton scattering experiments. This has significantly increased the precision of the measurement, bringing it in the same area as the spectroscopic ones done on muonic hydrogen atoms, which are considered the most precise. However, to solve the puzzle once and for all, even more precise electron scattering measurements are needed. Alternatively, new methods can be used, such as eg. muon-proton scattering at low transferred momenta in order to lower the systematic errors that comes with the measurement. This thesis tries to address this problem by studying the set up of an intense muon beam at the Jefferson Laboratory (JLab) that can be used to carry out a high-precision m ? p scattering experiment. Using Montecarlo simulations I studied the muon production resulting from the interaction of the primary electron beam with the beam-dump at JLab Hall-A. The simulations were performed using the FLUKA package via the FLAIR graphical interface. In this study, I modified an existing geometry (built for the ?Beam Dump eXperiment?) and performed several studies in order to optimize the muon beam parameters. In order to estimate the beam intensity, I studied the muon generation and transportation through the concrete bunker surrounding the Hall-A beam-dump. Detailed studies on muon attenuation and dispersion at different depth allowed me to track the beam profile in space and momentum as a function of the distance from the beam-dump. Last, but not least, I studied a possible tagging system for the muon beam. The tagging system will allow us to know with good precision (O(1=1000)) the energy of each muon of the beam. Based on the results obtained, I created an event generator that incorporates the detailed description of the muon beam (energy, position, emittance) useful to define and optimize the experimental setup for a future measurement of the proton radius at the JLab.

Fulci, Antonino↗
DOE OSTI2025

The nuclear charge radius of 13 C

The size is a key property of a nucleus. Accurate nuclear radii are extracted from elastic electron scattering, laser spectroscopy, and muonic atom spectroscopy. The results are not always compatible, as the proton-radius puzzle has shown most dramatically. Beyond helium, precision data from muonic and electronic sources are scarce in the light-mass region. The stable isotopes of carbon are an exception. We present a laser spectroscopic measurement of the root-mean-square (rms) charge radius of 13 C and compare this with ab initio nuclear structure calculations. Measuring all hyperfine components of the 2 3 S → 2 3 P fine-structure triplet in 13 C 4+ ions referenced to a frequency comb allows us to determine its center-of-gravity with accuracy better than 2 MHz although second-order hyperfine-structure effects shift individual lines by several GHz. We improved the uncertainty of R c ( 13 C) determined with electrons by a factor of 6 and found a 3σ discrepancy with the muonic atom result of similar accuracy.

Müller, Patrick [Technical Univ. of Darmstadt (Ger↗
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 OSTI2020

A High Precision Measurement of the Proton Charge Radius at JLab

The elastic electron-proton (e-p) scattering and the spectroscopy of hydrogen atoms are the two traditional methods to determine the proton charge radius (r p ). In 2010, a new method using muonic hydrogen (µH) 1 spectroscopy reported a r p result that was nearly ten times more precise but significantly smaller than the values from the compilation of all previous r p measurements. This discrepancy is often referred to as the "proton charge radius puzzle". In order to investigate the puzzle, the PRad experiment (E12-11-106) was first proposed in 2011 and performed in 2016 in Hall B at the Thomas Jefferson National Accelerator Facility, with both 1.1 and 2.2 GeV electron beams. The experiment measured the e-p elastic scattering cross sections in an unprecedented low values of momentum transfer squared region (Q 2 = 2.1× 10 -4 -0.06 (GeV/c) 2 ), with a sub-percent precision. The PRad experiment utilized a calorimetric method that was magnetic-spectrometer-free. Its detector setup included a large acceptance and high resolution calorimeter (HyCal), and two large-area, high spatial-resolution Gas Electron Multiplier (GEM) detectors. To have a better control over the systematic uncertainties, the absolute e-p elastic scattering cross section was normalized to that of the well-known Møller scattering process, which was measured simultaneously during the experiment. For each beam energy, all data with different Q 2 were collected simultaneously with the same detector setup, therefore sharing the same integrated luminosity. The windowless H 2 gas-flow target utilized in the experiment largely removed a typical background source, the target cell windows. The proton charge radius was determined as r p = 0.831±0.007 stat. ±0.012 p fm, which is smaller than the average r p from previous e-p elastic scattering experiments, but in agreement with the µH spectroscopic results within the experimental uncertainties.

Source record↗
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 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 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↗