Physics

Measurements of the nucleon spin structure functions are necessary to provide fundamental tests of QCD and the quark structure of hadrons. Deep inelastic electron or muon scattering with polarized beams and polarized targets directly probes the distribution of the spin on the nucleon quark constituents. The data can be used to extract the proton and neutron spin structure functions, and , for a direct test of quark models of nucleon structure. In addition the data can be used to test a number of sum rules based on various integrals of and over x, the Bjorken scaling variable. The most important of these is the Bjorken sum rule [1] which relates the integral of for the proton and neutron to a number measured in neutron beta decay. The Bjorken sum rule is based on current algebra and a few fundamental principles at the root of QCD and the standard model. Ellis and Jaffe have written two other sum rules [2] for the separate integrals over of the proton and neutron that are related to weak decays. The Ellis-Jaffe sum rules are derived with some model dependent assumptions, and therefore are less fundamental than the Bjorken sum role. However they provide powerful constraints for testing nucleon structure.

In the past several years a new generation of experiments by the SMC group [3,4] at CERN and by E142 [5] and E143 [6] at SLAC have provided new data that considerably extend the previous limited results from EMC [7] and SLAC [8,9] more than a decade ago. These new data offer the chance to see the spin distributions with precision and enough kinematic coverage to be effective tests of the sum rules. The proton measurements from EMC and earlier SLAC experiments disagree with the Ellis-Jaffe sum rule, and this can be interpreted as evidence that the spin in the proton is not carried by the quarks. Both the recent SMC and E143 results confirm that the Ellis-Jaffe sum rule is not satisfied. However agreement is found with the Bjorken sum rule within the experimental error for both experiments.

At one end of the kinematic range, in the very deep inelastic scattering region, the work of the SMC and E143 experiments needs to be extended to give a good picture of the momentum transfer dependence of the spin structure function . While the Bjorken scaling variable , (where M is the nucleon mass, and E, E' are the beam and final energies) covers the range of 0 to 1, E143 could measure only down to x=0.03, at a . The SMC x range extends to x=0.005, at . However, at x=0.03, the SMC value is 7 (GeV/c) leaving a wide gap between experiments, and with only 2 points to describe the dependence of the structure function at fixed x (the older EMC experiment has a few data points in the same region of x with similar values of as SMC).

The need to fill this gap and extend the low x range at the highest attainable value of has motivated the approval of SLAC E155, which will use an improved version of the polarized target constructed by the University of Virginia for the successful E143 run. Using electrons of up to 52 GeV beam energy, E155 will extend x down to about 0.012 while remaining at , with two spectrometers. It will add two more valuable sets of data points to our knowledge of the spin structure functions in the entire range of x, and in a broader and more detailed range of .

The experiment has been approved for 3 months of beam time in End Station A. It will determine the spin structure functions and of the proton and neutron over a range in Bjorken scaling variable and momentum transfer .

This will extend the range of precision spin structure measurements at low x, cutting the unmeasured region near x= 0 in half. These data will double the range of precision measurements and allow a search for non- scaling higher-twist contributions to the spin structure functions. With careful attention to systematic errors, with measurements of contributions from in transverse asymmetries, and with measurements of possible higher- twist contributions, these data will allow precision tests of the sum rules.

The kinematic range covered by these SLAC experiments is limited by physical constraints of the SLAC facilities, which favor the deep inelastic scattering (DIS) region. The important region of the nucleon resonances has been studied in the past only in a restricted way. An early SLAC experiment [10], carried out a low resolution survey of this region, with indications that the resonance displayed a negative virtual photon cross section asymmetry . This quantity measures the ratio of the difference of photon absorption cross sections (for nucleon helicity non-flip and helicity flip states,) to the transverse photon cross section

is a function of the momentum transfer and of the final state invariant mass W. Thus, with its transverse spin orientation partner , they are more appropriate quantities to describe the nucleon spin structure in the low regime than the related asymptotic functions that are studied in deep inelastic scattering.

Experiment E143 has refined to some extent the past SLAC measurements, with data taken at 9.7 GeV beam energy. However, it is expected that although the statistical errors of these data will improve on the existing results, there will be little improvement in the resolution of the features of the spectrum and of the asymmetries. Moreover, the experimental setup for E143 allowed for only two values of the momentum transfer to be studied, so the very important low dependence of the spin asymmetries remains unknown. Also, the study of the transverse target spin configuration was limited, due to time constraints, to data at 29 GeV beam energy.

Any improvement of our existing knowledge of the nucleon spin in this kinematic region requires both improved statistics and energy resolution. This region of physics can be explored with a high precision using the 6 GeV electron beam and the associated equipment in Halls B and C at TJNAF (CEBAF).

Polarization measurements are an essential part of the program for the study of nucleon structure and transition functions at TJNAF (CEBAF). New information about nucleon structure in the form of two spin structure functions, and , can be obtained from inclusive scattering of polarized electrons from polarized nucleons. In addition to the measurement of these two functions, the CLAS detector in Hall B is ideally suited to the measurement of many exclusive reactions over large kinematic regions of the final states. These studies will provide a wealth of information on the quark-gluon structure of the ground state and excited state of nucleons. The interferences between different amplitudes are obtained with polarization measurements, so that a small amplitude need only compete to first order with large amplitudes. Approved experiments for the TJNAF (CEBAF)-CLAS program include both inclusive and exclusive polarization measurements.

The differential cross section for inclusive scattering of polarized electrons off polarized protons can be expressed as

where and are the electron and target polarizations, respectively, is the angle between and the direction of the virtual photon, and is the azimuthal angle between the electron scattering plane and the target polarization vector. The quantity is a kinematical parameter giving the ratio of longitudinal to transverse polarization of the virtual photon. The functions and depend on two variables, the invariant four-momentum transfer of the electron , and the invariant mass W of the hadron system after absorption of the virtual photon, and they can be related to the cross sections for absorption of virtual photons.

In typical spectrometer experiments the two structure functions are separated by making two sets of measurements, one with along the beam ( ) and one with perpendicular to the beam. In the CLAS we will polarize the target along the beam only, and vary kinematical parameters to separate and . Measurements will be made over the full range of incident energies (1.2 to 6 GeV), so that for fixed and W there will be a range of values of the kinematical factors that appear in the definitions of the cross section asymmetry. We will cover the ranges, .

The structure functions are intimately related to the nature of the quark-gluon interactions in the nucleon. Two particularly interesting features are discussed below.

1. The possibility that gluonic excitations may play a role in the spectrum of nucleon states is an open question. It has been suggested [11] that the Roper resonance at W=1440 MeV might be a hybrid state including both quark and gluonic excitations. One consequence [12] is that the transition form factor will decrease much more rapidly with increasing . In the region of the Roper mass, the structure function is determined largely by the tail of the and the Roper itself. For pure Roper excitation whereas for pure excitation . As a result the measured will be sensitive to a small admixture of the Roper.
2. Gerasimov [13] and Drell and Hearn [14] independently derived on very general grounds a sum rule for the photo-absorption cross sections:

   

   where is the photon energy, and are the absorption cross sections for total helicity and , M is the mass of the nucleon, and k is the anomalous magnetic moment of the nucleon. This sum rule has never been tested experimentally.

The interpretation of the EMC results at high on the polarized proton structure functions in terms of the Bjorken [1] sum rule suggests [15]

This not only diverges as but it has the wrong sign to agree with the GDH sum rule. The integral must change sign in the region of . Calculations [16] using existing data combined with resonance models indicate that the zero point is at . Results of the EMC extrapolation as well as various calculations showing the expected cross-over in sign for the integral as a function of are shown in Figure 1. Also shown are the expected errors in the TJNAF (CEBAF) measurements for Experiment E91-023 as well as for a requested extension to make use of 6 GeV beam.

 
Figure 1: Various estimates for the generalized GDH integral. The band that rises toward infinity at small is the extrapolation from the EMC measurements. Also shown are some model calculations, as well as expected errors from TJNAF (CEBAF) measurements.

Although the integral is taken over an infinite range in , the factor of and the expected high energy behavior of the absorption cross sections indicate that the integral is nearly saturated by the contribution from the resonance region. Our measurements will extend to over a range . Experiment E91-023 at TJNAF (CEBAF) (spokespersons: Burkert, Crabb and Minehart) based on the preceding discussion has been accepted by the TJNAF (CEBAF) Program Advisory Committee. The experiment will use a polarized NH target polarized along the beam. A similar experiment to measure neutron structure functions using a polarized neutron target (ND ) has been proposed and accepted by TJNAF (CEBAF).

A large collaboration called the group will use the CLAS detector at TJNAF (CEBAF) to measure transition form factors for electroproduction of nucleon resonances by studying single meson production reactions. Precise measurements of the angular distribution of the hadronic decay products will allow isolation of the excitations of individual resonance throughout the resonance region, W < 2000 MeV. These reactions are characterized by the existence of a charged hadron in the final state in coincidence with the scattered electron. The resolution of the CLAS will be good enough for missing mass measurements to separate single meson production from more complicated processes. The CLAS will also provide in many cases excellent detection, and neutron detection in the forward angles, which will be useful for studies with polarized neutron targets.

For single meson electro-production there are 11 independent amplitudes, functions of , W and the angle , of the pion relative to the vector in the rest frame of the hadronic invariant mass W. Therefore a complete model independent characterization of the process requires a minimum of 11 independent measurements at each point in the three dimensional parameter space, but in reality even more are required since the observables are bi-linear combinations of the amplitudes. Without a polarized target only five structure functions can be measured, making the interpretation of the data strongly model dependent. Existing exclusive measurements of electroproduction of nucleon resonances are limited to a small part of the three-dimensional parameter space, and no measurements with polarized targets have been made. The first N* polarization measurements can be made simultaneously with the inclusive measurements discussed earlier. Two proposed experiments have been approved by the TJNAF (CEBAF). (R. Minehart is a co-spokesman of both).

In addition to the program studying the spin structure functions of the nucleons we have a specific experiment to study the charge distribution of the neutron.

The form factors of the proton and neutron are fundamental properties of the nucleon, and a critical testing ground for models based on QCD. A detailed knowledge of these form factors is essential to our understanding of the electromagnetic response functions of nuclei. Our present knowledge of the neutron electric form factor is inadequate. The slope of at is known accurately from neutron-electron scattering, but at higher , where has been extracted from elastic d(e,e') scattering, or inclusive quasielastic d(e,e') scattering, the systematic errors are very large. For both of these measurements removal of the proton contribution requires information about the deuteron structure, and large uncertainties are introduced from uncertainties in the theoretical description of the deuteron (mostly from final state interactions and meson exchange current contributions). As a result, is known with a systematic error of about .

At TJNAF(CEBAF) we proposed Experiment 93-026 (Donal Day is the spokesperson, approved for 60 days of running) to extract by measuring the spin-dependent part of the elastic n(e,e') cross section. A measurement of the asymmetry in the quasielastic scattering of longitudinally polarized electrons from polarized deuterium nuclei in deuterated ammonia (ND ) will determine the product . The idea is to measure the part of the elastic cross section that corresponds to the interference between the Coulomb and the transverse components of the nucleon current. The measurement is carried out by observing the asymmetry in the cross section that results when either the beam or the target polarization is reversed.

 
Figure 2: Coordinate system for with orientation of polarization axis shown. The asymmetry is maximized when . The neutron is detected along

The detection of the neutron knocked out of the deuterium nucleus (in coincidence with the scattered electron) will isolate elastic electron-neutron scattering from elastic electron-proton scattering. The neutron detector will consist of a `wall' of plastic scintillators. The coincident detection of a neutron with an electron has been used successfully by the collaboration at a recent experiment at NIKHEF to measure the magnetic form factor of the neutron.

In addition to the measurement of the neutron electric form factor, we have approval for two other experiments in Hall C using the polarized target. The first, a measurement of the deformation of the nucleon which can come about through the presence of D-state contributions to the ground state, would provide an important test of quark models of the nucleon. The experimental signature of this deformation would be L = 2 contributions to the nucleon to delta electromagnetic transition. By measuring the scattering asymmetry when the direction of the nucleon spin is in the scattering plane we can isolate these contributions.

The other experiment is a high precision measurement of the deuteron vector response function which together existing measurements of and allow the separation of the monopole and quadrupole form factors near and diffraction minimum.