Session DH: Form Factors and Charge Distributions

Flavor decomposition of the nucleon form factor $F_1$ at very large momentum transfer

At large momentum transfer dominance of the Sachs magnetic form factor, GM, in the Dirac form factor, $F_1$, allows determination of the $F_1$ flavor structure of the nucleon from the measurement of the cross section ratio of the D(e,e'n) and D(e,e'p) reactions. We will present an analysis of the range of momentum transfer up to 18 GeV$^2$ which could be experimentally accessed at JLab Hall A with the future experiments. A potential zero crossing of the down quark contribution to the proton $F_1$ would be discussed in the framework of the GPDs.   

Extracting the Proton Structure Function Moments from World Data

We present an extraction of the lowest three moments of the proton structure functions $F_L$ and $F_2$ from available world data between $Q^2$ = 0.75 and 45.0 (GeV/c)$^2$. This analysis leverages in particular new data from DESY at low Bjorken $x$ and from Jefferson Lab at high $x$, allowing the moments to be determined relatively free from uncertainties due to extrapolations into unmeasured regions. The moments are compared with several parton distribution function parameterizations.   

Possible diquark signatures in the elastic nucleon form factors

There has been considerable interest in the elastic nucleon form factors ever since the discovery that the proton form-factor ratio, $G_E^p/G_M^p$, decreases nearly linearly above roughly $Q^2=\rm1\,GeV^2$. More recent measurements of the neutron form-factor ratio, $G_E^n/G_M^n$, up to $\rm 3.4\,GeV^2$ have made it possible to constrain calculations using both proton and neutron data in the $Q^2$ regime where the interesting behavior of the proton was first observed. Calculations based on QCD's Dyson-Schwinger equations, as well as certain relativistic constituent quark models, suggest that the observed behavior is related to the importance of diquark degrees of freedom. To understand this connection, it is particularly useful to consider the flavor-separated form factors, which can be extracted by combining proton and neutron data, and assuming charge symmetry. Distinctly different behavior is seen for the $u-$ and $d-$quarks. The behaviors of the different quark flavors and the connection to diquarks can also be understood using naive scaling arguments, although this approach has yet to be made more rigorous. This talk will discuss how measurements of the nucleon form factors at high $Q^2$ provides a rich opportunity to better understand the structure of the nucleon.   

New measurement of the proton form factor ratio with polarized beam and target

The form factors are fundamental properties of the nucleon representing the effect of its structure on the response to electromagnetic probes. The ratio of the electric and magnetic form factors of the proton has been measured with doubly polarized elastic electron-proton scattering at $Q^2$ = 2.06 and 5.66 (GeV/c)$^2$ using the double spin asymmetry for a target spin aligned nearly perpendicular to the beam direction. This alternative measurement of $G^p_E/G^p_M$ has verified and confirmed the dramatic discrepancy at high $Q^2$ between the Rosenbluth separation and polarization transfer methods with a different technique and systematic uncertainties uncorrelated to those of the recoil-polarization measurements. The measurement of the form factor ratio at $Q^2$ = 2.06 (GeV/c)$^2$ is in agreement with an earlier measurement with the polarized target technique at similar kinematics. The four-momentum transfer squared of $Q^2$ = 5.66 (GeV/c)$^2$ represents the highest $Q^2$ value reached with the double spin asymmetry to date. The results of this experiment will be presented.   

The CLAS Two Photon Exchange Experiment

There is a large discrepancy between the proton electron form factor (GEp(Q2)) measured using the Rosenbluth separation and polarization transfer methods. The most likely explanation of this discrepancy is the inclusion of two-photon exchange (TPE) amplitude contributions to the elastic electron-proton cross section. The TPE contribution can be extracted in a model-independent way from the measured ratio of the cross sections of positron-proton and electron-proton elastic scattering. This ratio was measured in Hall B at Jefferson Lab using a simultaneous mixed tertiary beam of electrons and positrons incident on a liquid hydrogen target in the center of the CLAS detector in 2010-2011. This talk will present the analysis techniques used to identify the elastic scattering events, and some preliminary results at Q2 = 1.4 (GeV/c)2.   

$Q^2$ dependence of Two Photon Exchange Effects at $\epsilon=0.884$

A large discrepancy has been observed between proton electromagnetic form factor ratios $G^p_E/G^p_M$ measured by Rosenbluth separation and polarization transfer experiments. One possible source of this discrepancy is effects due to two-photon exchange (TPE) not being properly accounted for in radiative corrections. We have used a mixed beam of electrons and positrons elastically scattered from a liquid hydrogen target in the CLAS detector at Jefferson Lab to determine the cross section ratio $R=\sigma(e^+p)/\sigma(e^-p)$. This ratio provides a model-independent method of determining the TPE effects in elastic electron scattering. This talk will present the motivation for this measurement and the experimental method used to extract $R$. We will present for the first time results showing the $Q^2$ dependence of $R$ at an average $\epsilon=0.884$ for $0.3\leq Q^2\leq 1.25$ GeV$^2$. The implications of the results will be discussed.   

Separated Response Functions in Exclusive, Forward $\pi^{\pm}$ Electroproduction on $^2$H

The study of exclusive $\pi^{\pm}$ electroproduction on the nucleon, including separation of the various structure functions, is of interest for a number of reasons. The ratio $R_L=\sigma_L^{\pi^-}/\sigma_L^{\pi^+}$ is sensitive to isoscalar contamination to the dominant isovector pion exchange amplitude, which is the basis for the determination of the charged pion form factor, $F_{\pi}(Q^2)$, from electroproduction data. Furthermore, $R_L$ is an experimentally accessible ratio of longitudinal photon observables, and its value may have implications for constraining polarized GPDs. A change in $R_T =\sigma_T^{\pi^-}/\sigma_T^{\pi^+}$ from unity at small $-t$, to 1/4 at large $-t$, would suggest a transition from coupling to a (virtual) pion to coupling to individual quarks. If there is a partial cancellation of nonperturbative QCD contributions, the ratio may show an earlier approach to pQCD than the individual cross sections. We report the results of our study from Jefferson Lab Hall C, where the first complete separation of the four unpolarized electromagnetic structure functions were obtained in forward, exclusive $\pi^{\pm}$ electroproduction at central qsq values of 0.6, 1.0, 1.6 gevsq at $W$=1.95 GeV, and $Q^2=2.45$ gevsq at $W$=2.22 GeV.   

Pion Structure from Large to Small Distance Scales

Meson electroproduction data play an important role in our understanding of hadron structure. The importance of the pion in this has been recognized and has already resulted in many activities to measure the pion's properties and understanding its structure. At large distance scales studies of the transverse pion charge radius could provide information on how QCD describes the interaction and existence of elementary particles. Increasing the virtual photon mass ($Q^2$) in electron scattering experiments allows one to reach smaller distance scales. In this regime one becomes more and more sensitive to the partonic picture where hard and soft physics have been shown to factorize. In this talk we will discuss the reconstruction of the transverse pion charge radius distribution from measurements of the charged pion form factor. This analysis was carried out based on recent work on the proton, which used a numerical inverse Fourier transform method, taking into account the limited experimental knowledge of the form factor at higher $Q^2$ and the experimental uncertainties of existing data. We will also discuss opportunities for pion form factor measurements at large $Q^2$ at $12~GeV$ JLab.