Session EL: Hadrons: Form Factors

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 $0.831\pm 0.007_\textnormal{statistical}\pm 0.012_\textnormal{systematic}$. The value was obtained by using a rational function model for the proton electric form factor. We perform a model-independent extraction using $z$-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.   

e-p scattering measurement of proton radius with gas jet target @ MAMI

The proton radius puzzle is the incompatibility of the previously agreed proton charge radius measured by electron-proton scattering and hydrogen spectroscopy, against a smaller number from muonic hydrogen spectroscopy. This topic has been under extensive study since the last decade. New experiments and re-analysis of existing data are published continuously, but the puzzle remains unsolved. In late 2019, the PRad experiment measured the radius compatible with results from muonic hydrogen spectroscopy. It also reported a discrepancy of the proton electric form factor from previous scattering experiments in $Q^2$ range from $0.02(GeV/c)^2$ to $0.06(GeV/c)^2$. I will present the current status of an on-going experiment at Mainz Microtron, which has taken data early in 2020. This experiment uses two circularly movable spectrometers to remeasure the electron-proton scattering cross-section, covering the most controversial $Q^2$ range, as previously mentioned. It also helps evaluate the performance of a windowless jet gas target, which will be used for the MAGIX experiment in the future.   

The Physics Reach of MUSE

The MUon Scattering Experiment (MUSE), which takes place at the PiM1 beamline of the Paul Scherrer Institut (PSI), aims to simultaneously measure elastic $ep$ and $\mu p$ scattering in order to determine the proton charge radius. However with the beamline and kinematics available to the experiment, MUSE has a broader physics reach than extracting the proton radius. As the experiment uses both positively and negatively charged leptons, a precise two photon exchange measurement can be performed for both electrons and muons in the 0.002 < $Q^{2}$ < 0.08 (GeV/c)$^{2}$ and 0.26 < $\varepsilon$ < 0.94 regime. The experiment has both a LH$_2$ target and a carbon target, allowing for a variety of precise cross section measurements. With access to $\pi^{\pm}$ in the beam it is also possible to measure absolute and relative elastic pion cross sections to high precision with the MUSE detector. In this talk the physics reach of MUSE and projected uncertainties for the measurements will be discussed.   

An overview of the MUSE experiment at PSI

The MUon Scattering Experiment (MUSE) at the Paul Scherrer Institute (PSI) has been primarily motivated to investigate the proton charge radius in order to address the discrepancy between two candidate values from hydrogen spectroscopy, muonic-hydrogen spectroscopy and electron-proton scattering experiments. MUSE was proposed as the first experiment ever to perform simultaneous high-precision measurements of elastic electron-proton and muon-proton scattering. Measurements will be obtained for both positive and negative lepton charges. The beam is a mixture of electrons ($e$), muons ($\mu$) and pions ($\pi$) of chosen charge, run at momenta of 115, 160, 210 MeV/$c$. MUSE is equipped with a target system which consists of liquid hydrogen (LH2), Carbon and Polyethylene (CH$_2$) targets. MUSE measures scattered particles at scattering angles of $20^\circ- 100^\circ$ corresponding to transferred momenta of $0.002 - 0.08$ GeV$^2$/$c^2$. I will present an overview of the experimental setup including the present status and projected timeline.   

Study of Radiative-Correction Uncertainties in MUSE with ESEPP

The MUon Scattering Experiment (MUSE) at Paul Scherrer Institute (PSI) has been developed to measure elastic electron-proton and muon-proton scattering data with positively and negatively charged beams in a four-momentum-transfer range from 0.002 to 0.08 GeV$^2$. Each of the four sets of data will allow the extraction of the proton charge radius. In combination, the data test possible differences between the electron and muon interactions and additionally two-photon exchange effects. Accurate calculations of higher-order corrections to the Born cross section are an essential component in reducing uncertainties in measurements of the proton radius. In this talk, an event generator, ESEPP (Elastic Scattering of Electrons and Positrons on Protons), which takes account the first-order radiative corrections of elastic scattering of charged leptons ($e$$^{\pm}$ and $\mu$$^{\pm}$) on protons, is used to study the radiative corrections and their uncertainties in MUSE. The size of radiative corrections and uncertainties for electron and muon will be discussed.   

Measurement of the Neutron Magnetic Form Factor at High $Q^2$ Using the Ratio Method on the Deuteron$^{1}$

The elastic electromagnetic form factors are important observables for understanding the structure of the nucleon. Measuring all four elastic form factors,$G^p_E$,$G^p_M$,$G^n_E$,and $G^n_M$,at high $Q^2$ is a central part of the physics programs at Jefferson Lab. In this talk we will focus on the measurement of neutron magnetic form factor, $G^n_M$, at high $Q^2$ using the CLAS12 detector. To extract $G_{M}^{n}$ we use the ratio of quasi-elastic $e-n$ to $e-p$ scattering on a deuteron target. This method reduces the impact of systematic uncertainties like luminosity, etc. We apply acceptance matching in constructing the ratio. We use the measured electron information and, assuming QE kinematics, predict the path of both a neutron and a proton through CLAS12. If both paths strike CLAS12 we keep the event. A precise measurement of the ratio requires determining neutron detection efficiency (NDE) of the calorimeter in CLAS12. To do that we use the $p(e,e'\pi^+)n$ reaction on hydrogen target to produce tagged neutrons. We use the measured $e'$ and $\pi^+$ to predict where the neutron will strike CLAS12 and then search for neutron in that region. In this talk, We will discuss our methods and show preliminary results for the CLAS12 NDE. $^{1}$Supported by the US Department of Energy   

Probing $^{3}$He and $^{3}$H in the Quasi-Elastic Regime

Quasi-elastic electron scattering was used to probe nucleons on the nucleus of the mirror $^{3}$He and $^{3}$H nuclei, in a Q$^{2}$ range of 0.5-3GeV$^{2}$/c$^{2}$ in Hall A at Jefferson Lab. The unique sealed gas targets contained 53.37 mg/cm$^{2}$ and 85.1 mg/cm$^{2}$ of $^{3}$He and $^{3}$H, respectively. The beam energies were 2.2 GeV and 4.3 GeV, with a maximum current of 22 $\mu$A. This talk presents the details of the physics analysis and the preliminary results of the $^{3}$He(e,e') and $^{3}$H(e,e') data and how it can be used to learn about the magnetic form factor of the neutron.   

Studying Neutral Current Elastic Scattering and the Strange Axial Form Factor in MicroBooNE

Neutrino neutral-current elastic scattering is sensitive to the axial form factor of the proton and affords a unique method to access the strangeness contribution to the axial form factor $G_A^s(Q^2)$ and to the proton spin $\Delta s$. The MicroBooNE experiment is an 85-ton active mass liquid argon time projection chamber located at the Fermilab Booster Neutrino Beamline. MicroBooNE is able to detect protons with kinetic energy as low as 50 MeV. We present an inclusive differential cross section measurement of a signal with one proton and no other particles (NC1p) in the final state. We report the progress toward the measurement of exclusive neutral-current elastic scattering cross section and $\Delta s$ extraction using a subset of MicroBooNE’s data.   

Elastic nucleon form factors at high momentum transfer and GPDs

Generalized parton distributions (GPDs) provide a description of nucleon structure that goes well beyond the longitudinal information contained in pdfs. Exclusive processes such as deeply virtual Compton scattering (DVCS) and deeply virtual meson production (DVMP) are critical to determining GPDs, and efforts to study these processes are ongoing. At present, however, the data from DVCS and DVMP are limited, and one of the strongest constraints on GPDs comes from the fact that the GPDs $H^q$ and $E^q$, when integrated over Bjorken x, are simply related to the elastic Dirac and Pauli nucleon form factors (FFs) respectively. At Jefferson Laboratory (JLab), accurate measurements of the elastic nucleon FFs have become possible up to quite high values of momentum transfer, and these data have transformed our understanding of nucleon structure. The JLab Super Bigbite Spectrometer (SBS) program will continue this trend, greatly improving both the accuracy and momentum range with which the elastic FFs are known. We will review the current knowledge of the elastic nucleon FFs, the expectations of the SBS program, and the implications for our evolving knowledge of GPDs.