Copyright 1972. All rights reserved
DEEP INELASTIC ELECTRON SCATTERING 5526 JEROME I. FRIEDMAN HENRY W. KENDALL Massachusetts Institute of Technology Laboratoryfo r Nuclear Sciencel Cambridge, Massachusetts
CONTENTS
I. INfRODUcnON...... 204 METHOD...... •. . . •••... ..••• ...... 205 II. EXPERIMENTAL Equipment...... 205 207 Radiative corrections......
III. PROTON AND DEUTERIUM CROSS SECfIONS...... 209
IV. KINEMATICS AND VARIABLES...... 213
V. SCALE INVARIANCE AND SCALING VARIABLES...... •...... 218 VI. SEPARATION OF AND FOR THE PROTON AND DEUTERON ...... 219 <1', <1'1
VII. EXTRACfION OF NEUTRON STRUCTURE FUNcnONS...... 222
VIII. VALIDITY OF SCALE INVARIANCE ...... 225
Proton ...... 225 229 Deuteron...... Ne utron...... 231
CoMPARISON OF ELECfRON AND MUON SCATIERING . 235 IX. REsULTS...... CoMPARISON THEORETICAL MODELS.•••...... 235 X. WITH The parton model...... 235 Sum rules...... 238 Vector dominance models...... 240 242 Regge models......
by University of Kentucky on 08/31/10. For personal use only. Duality ...... 244 246 Resonance models...... 246 Mo dels that predict deviations from scaling......
RELATED PHySICS...... 247
Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org XI. 247 Neutrino-hadron scattering...... 248 Electron-positron colliding beams...... 248 Inelastic Compton scattering ...... 248 Polarization effects...... 249 Lepton pairs fr om hadronic interactions...... Electromagnetic mass differences 249 of hadrons...... 249 Relationships between inelastic e-p and p-p scattering...... 250 Photoproduction......
CoNCLUSIONS...... 250 XII. . ..
S. 1 Work supported in part through funds provided by the U. Atomic Energy Commission under Contract AT (11-1)-3069.
203 204 FRIEDMAN & KENDALL
I. INTRODUCTION Electron scattering has been a powerful tool in the study of nucleon and nuclear structure. Because the interaction of the electron is well undertstood in terms of quantum-electro-dynamics (1), the scattering of electrons can be used to probe unknown structure of hadronic systems. In this review we will concern ourselves exclusively with electron-nucleon scattering. Historically, elastic scat tering produced the first extensive body of information about the structure of the nucleon, starting with the work of Hofstadter & collaborators (2). Since then substantial additional programmatic work on elastic and inelastic scattering has been carried out at various accelerators. The inelastic studies concentrated mainly on measurements of electroproduction of nucleon resonances, a topic initially in vestigated by Panofsky & Allton (3). With the advent of the two-mile electron accelerator at the Stanford Linear Accelerator Center (SLAC) (4), with its higher energies and larger intensities, a new region of inelastic scattering-commonly referred to as the "deep inelastic" region-could be extensively investigated. This region corresponds to the excitation of the continuum well beyond the nucleon resonances. Studies of elastic electron-proton scattering, electroproduction of resonances, and deep inelastic scattering from the proton and neutron have been carried out by an MIT-SLAC collaboration since 1967, using electrons of energies up to 21 GeV from the SLAC accelerator. Initial measurements of deep inelastic electron proton scattering (5) showed that the continuum cross sections were larger than had been previously expected. There were theoretical conjectures, prior to the first experimental measure ments, that suggested that the inelastic spectra might decrease rapidly with in creasing four-momentum transfer squared, q2, perhaps as rapidly as elastic electron-proton scattering. The first measurements established that the inelastic cross sections had only a weak dependence on q2 in addition to the q-4 dependence arising from the photon propagator. The measurements established, in addition, that the scattering could be characterized in a particularly simple manner, now by University of Kentucky on 08/31/10. For personal use only. known as "scaling" or scale invariance. The MIT-SLAC collaboration program of inelastic electron scattering has covered a wide range of four-momentum transfer and missing mass of the recoil Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org ing hadronic system. In these experiments only the scattered electron was de tected. The reactions that have been studied are inelastic electron scattering from the proton, deuteron, and a number of different nuclei (6-8). Experimental work on inelastic electron scattering has also been carried out at DESY See (9) and earlier references therein , and there has been a program of inelastic[ muon scat tering at SLAC (10). ] The purpose of this article is to review and bring up to date the large amount of experimental information from singles measurements of deep inelastic scattering from the proton and neutron. Some of the results on the electroproduction of nucleon resonances willbe briefly discussed, but only insofar as the results provide a comparison of interest with the deep inelastic data. The range and validity of
scaling for the neutron and proton will be treated in detail. Here, we will em- DEEP INELASTIC ELECTRON SCATTERING 205
phasize primarily the experimental measurements from the MIT-SLAC col laboration.2 The inelastic electron-nucleon scattering results have generated an extensive amount of theoretical work. While this article is not intended to provide a de tailed review of the theory, there will be some discussion of the main thrusts of the theoretical effort. The theoretical advances have led to useful and important insights into the experimental results even though there is presently only a partial understanding of the implications of the measurements. Our discussion of the theoretical effort is aimed both at giving a sense of the theoretical understanding of the results and at pointing out the relevance of the measurements to the present theories. In the remainder of this review we will give a brief summary of the experi mental equipment and techniques, followed by a qualitative description of the electron-proton and electron-deuteron scattering results. The scattering for malism, scaling variables, and the problems of separating the transverse and longitudinal contributions to the measured cross sections and of determining the electron-neutron cross sections are then treated. This is followed by a discussion of the range and validity of scaling behavior for the proton, deuteron, and neutron. The next sections are devoted respectively to theoretical models, a com parison of muon and electron scattering, sum rules results, and collateral experi ments related to deep inelastic electron scattering.
II. EXPERIMENTAL METHOD
Before proceeding to the results, a brief description of the experimental method (11) is in order. A relatively monochromatic electron beam from the linear accelerator was passed through a liquid hydrogen or deuterium target and then through a series of beam monitors. The scattered electrons were momentum analysed by one or the other of a pair of magnetic spectrometers installed at the scattering site (see Figure 1). In separate experiments the SLAC 20 GeV and 8 GeV spectrometer were used to cover different kinematic regions. Downstream of the magnetic elements of the spectrometers were placed scintillation counter by University of Kentucky on 08/31/10. For personal use only. hodoscopes which registeredthe momentum and scattering angle of each scattered electron. In conjunction with the hodoscopes there were particle identification counters which were employed to identify electrons amid a background of pi Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org mesons. These consisted of a gas Cerenkov counter, a total absorption counter for electromagnetic cascades, and a few counters used to sample early shower de velopment in the total absorption counter.
Equipment.-This section outlines the principal elements of the SLAC scat tering facility (4). The primary beam of energy in the range 4.5-20 GeV, with tlEjE typically
• The people who have participated in the work reported here are: E. Bloom,
Bodek, Br ide , A. M. e nbach G. Buschorn, L. Cottrell, D. Coward, H. De Staebler, R. Ditzler, J. Drees, J. Elias, J. 1. Friedman, G. Hartmann, C. Jordan, H. W. Kendall,
G. Miller, L. Mo, H. Piel, J. S. Poucher, E. Riordan, M. Sogard, R. E. Taylor, and R. Verdier. 206 FRIEDMAN & KENDALL
Exit Beam
o 25 SO 75 ''--_.1.. ' ---', _-.L'_ FEET
FIGURE 1. Plan view of the SLAC experimental area in which the MIT-SLAC deep inelastic electron scattering measurements were carried out.
from 0.002 to 0.005, was fo cussed on liquid hydrogen or deuterium condensa tion targets, 3 inch thick. The beam was pulsed for approximately 1.6 J.l.sec at repetition rates up to 360 cps. The targets were vertical cylinders with aluminum or stainless steel windows. In the later experiments forced circulation of the liquid gave assurance that beam induced target-density changes were negligibly small. In addition, recoil proton yields were measured in a 1.6 GeV spectrometer, otherwise unused in the pro
gram, to give a direct measure of relative target density, and in all experiments series of measurements at different beam currents were made to establish the effects of beam heating. Residual uncertainties in target densities were about by University of Kentucky on 08/31/10. For personal use only. ± I %. Target temperatures were monitored with hydrogen vapor-pressure thermometers. Beam monitoring was carried out by a pair of toroid beam monitors upstream Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org of the target. Throughout the experimental program, their calibrations were fre quently checked against a Faraday cup. The calibrations agreed in general to better than 1 %. The two spectrometers were capable of determining the momenta of particles up to 20 GeV and 8 GeV. Because of the amount of data at constant angle re quired to correct the measured cross sections for radiative effects, only a limited number of angles were employed in the inelastic program. The 20 Ge V spectrome
ter was used to measure the scattering at 6° and toO, and the other instrument, with its larger solid angle, was employed in the determination of the generally smaller cross sections at angles of 18°, 26°, and 34°. Both spectrometers employed hodoscopes that determined 40 momentum intervals each of fractional mo- DEEP INELASTIC ELECTRON SCAITERING 207
mentum acceptance of There were 55 and 32 angle counters in the 8 GeV and 20 GeV spectrometers10-3• which spanned angular acceptances of 16 mr and 7
mr respectively. Additional hodoscopes were employed in the 20 GeV spectrom eter in a portion of the program to determine the azimuthal scattering angle and the longitudinal position in the target of the scattering event. Precise values of the momentum resolutions and solid angle acceptances for the instruments were determined both from precision measurements of the fields of the magnetic elements and by electron-beam studies of the assembled spectrometers. The solid angleacceptances were approximately 0.75 and 0.06 millisteradians for the 8 GeV and 20 GeV instruments respectively. Cross calibrations were carried out using measurements of elastic scattering. The uncertainties in the solid angles were typically about ± 2%. At many kinematic points, especially at lower scattered electron energies, ap preciable pion contamination of the scattered electron yields was observed. Pion rejection was accomplished primarily through the use of lead-Iucite total electromagnetic shower absorbers, useful at all but the lowest particle energies, and by measurements of the incipient shower formed in the first radiation length of the total absorption detector. A threshold gas Cerenkov counter operated near atmospheric pressure served to reject pions of momenta below about 4 GeV. The only background which could not be rejected by the particle discrimina tion arrays arose from electrons from the Dalitz decay of photoproduced or electroproduced neutral pions. Electron yields from this source increased sharply as the detected particle energies were decreased. The increasing yields were one of the major factors that set lower limits to the scattered electron en ergies that could be usefully measured. Dalitz decays produce equal numbers of positrons and electrons of the same energy. The Dalitz electron contaminations were determined by making appropriate positron measurements. Data from the spectrometer detectors were processed in an array of fast electronic equipment, and candidate events were read into an SDS-9300 on-line computer and onto magnetic tape for subsequent analysis. A sample of the events were processed on-line to provide immediate information on the operation of the apparatus and to allow evaluations of the progress of the runs. by University of Kentucky on 08/31/10. For personal use only. A detailed description of the off-line analysis developed in connection with the MIT-SLAC inelastic electron-proton scattering has been given by Breiden bach (12) and Miller (13). Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org
Radiative corrections.--Corrections must be applied to the measured cross sections to eliminate the effects of the radiation of photons which occurs during the scattering process and during traversals of material before and after scat tering. These corrections also remove higher order electrodynamic contributions to the electron-photon vertex and the photon propagator. The largest correction has to be made for the radiation during scattering, described by diagrams (a)
and (b) in Figure 2. A photon of energy k is emitted in (a) after the virtual photon is exchanged, and in (b) before the exchange. Diagram (c) is the cross section which is to be recovered after appropriate corrections for (a) and (b) have been FRIEDMAN & KENDALL 208 E' E� ):;4 �'
(0 ) (b) (e)
Final Energy "Elastlc -Threshold
Initial Energy
(d) FIGURE 2. Diagram showing radiation in electron scattering after exchange of virtual photon (b) before exchange of virtual photon. Figure (c) represents(a) the diagram for inelastic scattering with all radiative effects removed. Figure (d) is the kinematic plane which is relevant to the radiative corrections program. See text for further discus sion.
made. A measured cross section at fixedE, E', and 0 willhave contributions from (a) and (b) for all values of k which are kinematically allowed. The lowest value of k is zero, and the largest occurs in (b) for elastic scattering of the virtual elec tron from the target particle. Thus, to correct a measured cross section at given values of E and E', one must know values of the cross section over a range of incident and scattered energies. To an excellent approximation, the information necessary to correct a cross section at an angle 0 may all be gathered at the same value of O. Diagram (d) of Figure 2 shows the kinematic range in E and E' of
by University of Kentucky on 08/31/10. For personal use only. cross sections which can contribute by radiative processes to the cross section at
point S, for fixed e. The range is the same for contributions from bremmstrahlung processes of the incident and scattered electrons. For single hard photon emis
Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org sion, the cross section at point S will have contributions from elastic scattering at points U and L, and from inelastic scattering along the lines SL and SU, starting at inelastic threshold. If two or more photons are radiated, contributions can arise from line LU and the inelastic region bounded by lines SL and S U. The cross sections needed for these corrections must themselves have been corrected for radiative effects. However, ifuncorrected cross sections are available over the whole of the "triangle" LUS, then a one-pass radiative correction procedure may be employed, assuming the peaking approximation (14), which will develop the approximately corrected cross sections over the entire triangle, including the point S. The application of radiative corrections requires the solution of another DEEP INELASTIC ELECTRON SCATIERING 209 difficulty, as it is generally not possible to take measurements sufficiently closely spaced in the E-E' plane to apply them directly. Typically five to ten spectra, each for a differentE, are taken to determine the cross sections over a "triangle." Interpolation methods must be developed to supply the missing cross sections and must be tested to show that they are not the source of unexpected error. The radiative tails from elastic electron-proton scattering in practice are sub tracted from the measured spectra before the interpolations are carried out. In the MIT-SLAC radiative correction procedures, the radiative tails from elastic scat tering were calculated using the formula of Tsai (15), which is exact to lowest
order in lX. Included in the calculation of the tail were: the effects of radiative energy degradation of the incident and final electrons, the contributions of mul tiple photon processes, and radiation from the recoiling proton. After the sub traction of the elastic peak's radiative tail, the inelastic radiative tails were removed in a one pass unfolding procedure as outlined above. The particular form of the peaking approximation used was determined from a fit to an exact calculation of the inelastic tail to lowest order which incorporated a model that approxi mated the experimental cross sections. The formulas and the procedures are de scribed by Miller et al (8, 13). The measured cross sections were also corrected in a separate analysis using a somewhat different set of approximations (16). Compari sons of the two gave corrected cross sections which agreed to within a few per cent. Figures 3 and 4 show the relative magnitude of the radiative corrections as a function of W for two typical spectra with hydrogen and deuterium targets. While radiative corrections are the largest corrections to the data, and involve a considerable amount of computation, they are understood to a confidence level of 5% to 10% and do not significantly increase the total error in the measure ments.
III. PROTON AND DEUTERWM CROSS SECTIONS The range of kinematics covered in the published MIT-SLAC measurements of electron proton scattering is given in Table 1. The range of missing mass covered was M $ W $5.7 GeV and the range of the square ofthe four-momentum transfer was 0.3 - = 2M + M2 W2 (E - E') q2 Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org where E is the incident electron energy, E' is the scattered electron energy, and M is the mass of the target nucleon. The quantity q2 is given by = cos q2 2EE' (1 - fJ) where 0 is the electron scattering angle. In the kinematic relations shown the electron mass is neglected. In general, the measurements were made at closely spaced values of the scat tered energy E', for constant scattering angle 0, and constant incident energy E. For each scattering angle spectra were measured at a number of incident en ergiesin order to be able to make radiative corrections to the data. 210 FRIEDMAN & KENDALL 1.5 PROTON (a) E • 10.029 e·5':988 1.0 � Scale ' 8.5 2.0 (b) .. Q 1.5 " 1;; , > J.O !I ....t'? I i!! :g 5 80. i n: • I � 2.0 (c) �.!l 1.0 . _------.-- --. . o 0.5 1.0 2.5 3.6 3.5 4.0 W in GeY FIGURE3. Spectra of 10 GeV electrons scattered from hydrogen at 6°, as a function of the finalhadronic-state energy Figure shows the spectrum before radiative correc by University of Kentucky on 08/31/10. For personal use only. W. tions. The elastic peak has been reduced in(a) scale by a factor of 8.5. The computed radia tive tail from the elastic peak is shown. Figure (b) shows the same spectrum with the elastic peak's radiative tail subtracted and inelastic radiative corrections applied. Figure Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org (e) shows the ratio of the inelastic spectrum before, to the spectrum after, radiative cor rections. Typical spectra for hydrogen and deuterium are shown in Figures 3, 4, 5, and 6. Bumps in the spectra at lower q2.-Figures 3 and 4-are seen at the .1.1236 and N*1518, and the region of the N*1688; in a number of spectra there is also a small bump near the .1.1920. No clear-cut evidence is seen for the excitation of the Roper Pu resonance. In addition to these bumps there is a broad continuum of large cross section. This continuum dominates the scattering as q2 increases as shown in Figures 5 and 6. These spectra have a qualitative similarity to those observed in inelastic electron-nuclear scattering. DEEP INELASTIC ELECTRON SCATIERING 211 The general dependence of the measured spectra on laboratory energy and angle and momentum transfer squared can be seen in Figures and 9, in which some of the measured spectra (17) are sketched or displayed.7, 8,In Figure 9 the data at q2=O were determined by extrapolation from measurements made at 8 = 1 0.5 (18). These figures show that the excitation of discrete states is domi nant for smaller angles and lower incident energies, but at larger angles and higher incident energies the continuum channels dominate the scattering. This is equivalent to the statement that the continuum becomes increasingly large com pared to the observed resonance excitations as q2 increases. The Mott cross sec- 3.0 DEUTERON (a) E·10.029 e· 5�9BB -: 2.0 SeQlo • 1.5 � , (bl -: 2.0 w '" "- c 1.0 2 8 f I by University of Kentucky on 08/31/10. For personal use only. Ii 2.0 Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org (el o 1.0 .�'" - -- --.--._ -.--- - o 0.5 1.5 2.0 2.5 3.0 3.5 4.0 W in GoV FIGURE4. Spectra of 10 GeV electrons scatteredfr om deuterium at 6°. See caption 3. of Figure The quasi-elastic peakhas been reduced in scale by a factor of 1.5. 212 FRmDMAN & KENDALL TABLE 1. KINEMATIC RANGE-ELECTRON·PROTON SCATTERING DATA Angle RangeE RangeE' Rangeq2 Max. W 6° • 7.0-16.0 3.25-13. 2 0.25- 2. 31 4.8 too. 7.0-17.7 3.0 -12.46 0.80- 6.7 5.2 18° b 4.5-17.0 2.0 - 8.0 1.0 -14.0 5.1 26° b 4.5-18.0 1.75- 5.5 1.5 -20.0 5.0 34° b 4.5-15.0 1.2 - 3.25 2.0 -16.7 4. 3 GeV GeV (GeVjc'f GeV • E. D. Bloom et a1 1969. Phys. Rev. Lett. 23:930 M. Breidenbach et at 1969. Phys. Rev. Lett. 23 :935 b G. Miller et a11972. Phys.Rev. D 5:528 tion (without the kinematic correction for target recoil) is given for each energy and angle to serve as a scale for the scattering cross sections. The nature of electron scattering from the nucleon cannot be completely de termined without studies of electron-neutron scattering. A comparison of neutron and proton cross sections is a sensitive probe for the presence of a non diffractive component in the scattering process, since a differencein the two cross 4.0 .. (0) PROTON 0 -: 3.0 E·19.350 e 'IO�OOO � Scale' 1.0 � 2.0 � " .. " t t .8 . 8 1.0 0:: by University of Kentucky on 08/31/10. For personal use only. .. Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org 2 ': .0 (b) m 2 .. 1 � t j , t 1.0 . t , I �" .. "E 8 0:: .""'''''� 2.0 3.0 .5 4.0 4.5 5.0 55 6.0 0 0.5 1.0 15 2.5 3 Win GeV FIGURE 5. Spectra of 19. 3 GeV electrons scattered from hydrogen at too. See caption to Figure 3. DEEP INELASTIC ELECl'RON SCATfERING 213 7.0 6.0 (0) DEUTERON Q E·19.350 " 5.0 e· ICf.OOO • � 4.0 Scole 1.0 > " 3.0 �� c: E 2.0 8 a: 1.0 . 5.0 Q (b) " 4.0 " � 3.0 > ! ! I ! �"- 2.0 I • � .8 1.0 8 a: o 0.5 1.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 EiO Win GeV FIGURE 6. Spectra of 19.3 GeV electrons scattered fr om deuterium at 10°. See caption to Figure 3. sections would establish the existence of some isotopic spin exchange. Moreover the question of scaling of the neutron results can also be investigated. In order to determine the electron-neutron scattering in the absence of a free neutron target one is forced to employ deuterium or heavier nuclei as targets. Its simple structure and low binding energymake deuterium the material of choice. A series of measurements of inelastic scattering from deuterium has been by University of Kentucky on 08/31/10. For personal use only. carried out covering the same kinematic regions as the previous work on the proton, but with some extensions both to higher incident energies and lower scat tered energies (see Table 2). Measurements at 6° and 10° (6, 16, 49) were carried 20 18°, 26°, Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org out using the Ge V spectrometer and were carried out at and 34° using the 8 GeV spectrometer. Measurements of scattering from the proton were made simultaneously in order to reduce possible systematic errors in a comparison of the scattering from the two targets. Some new but still preliminary results (19, 25) on the deuterium and hydrogen cross sections at 18°, 26°, and 34° are available although the final analyses are not complete. A number of representative deu terium spectra are shown in Figures 4 and 6. IV, KINEMATICS AND VARIABLES To extract the effects of the nucleon structure in the scattering process it is useful to separate out the pure Q.E.D. dependence of the scattering cross section. RADlATIVELY CORRECTED SPECTRA = 10° e = 4.88 GeV = 3750 E nb (dct;)MOTT (D.E.S.Y.) 0 250 '" 1820 nb U. K)MOTT = 7.00 GeV E 0 5 0 z � = 740 0.... nb MOTT £-< u = 10.98 GeV (dctg) � E en ,I en Bt:r: Q ....u 25 £-< en = 488 -< nb ...:l MOTT � (d�) = 13.51 GeV ...z E 0 = 389 nb 10 (ddK)MOTT '" 15.15 GeV E by University of Kentucky on 08/31/10. For personal use only. OL£�____ L- ____� ______-l ______-L __ __ Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org = 286 nb ':,��"17� (d�)MOTT 3.0 4.0 LO 2.0 5.0 MISSING MASS (GeV) 142705 FIGURE 7. Visual fitsto spectra showing the scattering of electrons from hydrogen at 10"for primary energies, E, from 4.88 GeV to 17.65 GeV. The elastic peaks have been subtracted and radiative corrections applied. The cross sections are expressed in nano barns per GeV per steradian. The spectrum E=4.88 GeV was taken at DESY; Bartel, W. et al1968. Phys. Lett. B 28:148. DEEP INELASTIC ELECTRON SCATIERING 215 RADIATIVELY CORRECTED G.ROSS SECTIONS E"'13.5 GeV 5 5 5XI0 8=1.5" =9.25xI0 nb g-)MOTT 0 z Q I- u 'C0 w U) � 8=6· '" gj =3780 nb U) I 250 MOTT U) � 0 (!) 0::: '- U .0 .5 S:2 0 I- U) <[ '""0 "0 c: ...J w � 25 � bl 8=10" =488 nb (�g�MOTT 0 8=18° (d 0-) =48 nb 25 dil MOTT by University of Kentucky on 08/31/10. For personal use only. 0 5 2 3 4 Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org MISSING MA SS W(GeV) T4"i1"Ci" FIGURE8. Visual fits to spectra showing the scattering of electrons from hydrogen at a primary energy E of approximately 13.5 GeV, for scattering angles fr om 1.5° to 18°. 1.5° (18), The curve is taken fr om the MIT-SLAC data, used to obtain photoabsorption cross sections. 216 FRIEDMAN & KENDALL 600 T 500 q2 =O(GeV/c) 2 400 jl!\ 300 200 t ••• • •••• • • 100 I I ! 0 j�\� = q2= (GeVlc)2 160 8 10° I � 120 "J5 II �::l en b 80 III + . 40 ;\� I I I I b" 0 rJ- I "'- 8=10° q2=2 (GeVid - 40 w -0 � Cl -0 30 I "'- 'I f I " I b IN; C\J 20 I I -0 I I 10 i 0 I 8=10° (GeVid q2=4 - I , 12 I I - - - by University of Kentucky on 08/31/10. For personal use only. 8 �W - 4 0 I Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org I. o I 2.0 3.0 4.0 5.0 6.� 1 TWO PION THRESHOLD W (GeV) i"421:i '-IONE PION THRESHOLD FIGURE 9. Spectra of electrons scattered from hydrogen at momertum transfers 4 2 =0 =0 squared up to (GeV/C) . The curve for q2 represents an extrapo!ati.m to q2 of electron scattering data acquired at e = 1.5° (18). DEEP INELASTIC ELECTRON SCATIERING 217 KINEMATIC RANGE-ELECTRON PROTON AND ELECTRON DEUTERON DATA' fABLE 2. Angle RangeE RangeE' Range q2 Max. W 6° 4.5-19.5 2.5-17.5 0.10- 3.7 5.7 10° 4.9-19.3 2.5-14.7 0.30- 8.6 5.6 18° 4.5-17.0 1.5-8.75 0.44-14.6 5.2 26° 4.5-18.0 1.5- 5.5 0.91-20.1 5.3 34° 4.5-15.0 1.5- 3.25 1.54-16.7 4.3 GeV GeV (GeV/c)2 GeV 25). • Kendall, Cornell Conference (6). See also (16,19, and ::>n the assumption of one photon exchange, the laboratory differential cross sec tion (20) for unpolarized electrons scattering from unpolarized nucleons, with Jnly the scattered electron detected, is: 1. Nhere e4 cos28/2 4E2 sin48/2 fhe functions W1 and W2 depend on the properties of the target nucleon and :an be represented as functions of two invariants, q2 and v=E-E'. The above �xpression is the analog of the Rosenbluth cross section. There is another expres lion (21) that is often used to describe inelastic electron scattering and which is the malog of photoproduction. In this description the cross section for inelastic ;cattering is given by: d2 u 2. by University of Kentucky on 08/31/10. For personal use only. -- = rt[Ut(v, q2) + EU.(V, q2) ] dQdE' Nhere Ut and u. are the absorption cross sections for virtual photons with trans Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org rerse and longitudinal polarization components respectively, and the virtual )hoton spectrum rt is given by: a K 2 r t = h2 E'[ - ] q; Ii 1 E [he quantity K equals (W2-W)j2M where M is the nucleon rest mass and e :quaIs ( :n the limit q�O, gauge invariance requires that u.� and Ut v, q2)-U""(P(V) 218 FRIEDMAN & KENDALL where is the photoabsorption cross section for real pho,tons of energy II, The twoU"(p(II) descr iptions are equivalent and it follows that 3, In order to make separate determinations of WI and W2 (or Us and 0'1), it is neces· sary to measure the inelastic cross section at different angles for the same valuel of q2 and Appropriate changes in the values of both E and E' are required. The resultsII. of the separation are, for convenience, expressed in terms of th« parameter R=u,/ul' The experimental values of WI and W2 are given by: d2u -1 1 dr:J R) q2 2 tan28/2 = --,J [(-) J { + + - WI an M (1 ---2+ II } dfldE ''''p q 2 }- 4 . + 1 = -- 1 -- W2 d2u [(-du) 1{ + 2 ( --) q2 112 tan28/2 M J-1 + R dndE'J up dn 1 q2 where d2u 6"'1' dfldE'J is the experimental inelastic cross section. In practice it was convenient to determine values of and from straigh UI u. line fits to differential cross sections as functions of E. R was determined from the values of u. and Ue, and WI and W2 were, as shown above, determined from R. V. SCALE INVARIANCE AND SCALING VARIABLES On the basis of investigation of models that satisfy current algebra, Bjorker (22 ) had conjectured that in the limit of q2 and II approaching infinity, with the ratio w=2Mv/q2 held fixed, the two quantities vW and become functions of" by University of Kentucky on 08/31/10. For personal use only. 2 WI only. That is: Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org = W1(II, q2) F1(W) ;::j = w fixed IIW2(V, q2) F2(W) It is this property that is referred to as "scaling" inthe variable w in the "Bjorker limit." As we shall see, scaling holds over a substantial portion of the ranges of I and q2 that have been studied. The question naturally arises as to whether ther« are other scaling variables that converge to w in the Bjorken limit, and that pro, vide scaling behavior over a larger region in v and q2 than does the use of w A number of such variables have been proposed. Among these are the variable! proposed by suri (23) DEEP INELASTIC ELECfRON SCATTERING 219 W2 w.=- q' by Rittenberg & Rubinstein (24) by the MIT-SLAC group (8, 13) 2Mv a2 w'= + q2 and a variable by Breidenbach & Kuti (26), based on the physics of the light cone M The applicability of some of these variables is discussed in later sections of the text. Since Wl and W2 are related by VW2/W1 = (1 + R)(1/v + w/(2M)) it can be seen that scaling in Wl accompanies scaling in v W2 only if R has the proper functional form to make the right hand side of the equation a function of w (or some other variable). In the Bjorken limit, it is evident that vW2 and Wl will both scale if R is constant or is a function of w. VI. S:El'AnATION OF V, AND Vt FOR THE PROTON AND DEUTERON Separation of v, and v, for the proton was carried out (8, 13) over the kinema tic region where data were available at three or more values of e, either from direct by University of Kentucky on 08/31/10. For personal use only. measurements or from interpolation between measurements at fixed angle. Actual data points at different angles for the same values of q2 and W2 existed only for q2=4 (GeVjc)2 and W=2, 3, and 4 GeV. However, interpolations of adequate precision could be carried out for fixed points in the q2, W plane. The Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org kinematic regionwhere data were available and the subregionin which separation was carried out are shown in Figure 10. In this region Wi and W2 may be sepa rately determined without assumptions about R. The heavy line bounds all data points measured at the five angles 6°, 10°, 18°,26°, and 34°. Determinations of v, and v, were carried out at twenty-three points in the q2, W2 plane. Figure 11 shows four examples of these separations. The assumption of one photon exchange which underlies the definition of the electromagnetic structure functions implies the linear dependence of cPvj dQdE' jr I on E for a particular point (q2, II), as is displayed in the equation that relates v, and v, to the measured cross sections. The data are everywhere consistent with 220 FRIEDMAN & KENDALL 25 20 N � � 15 � N 0" 10 5 0 5 10 15 20 25 30 W2 (GeV2) FIGURE 10. The kinematic plane in q2 and W2. The heavy line bounds all data point for scattering of electrons, described in (7) and (S), measured at 6°, 10°, ISo, 26°, and 34° The "Separation Region" includes all points where data at three or more angles exist = =0 Various values of ware indicated with w 00 coinciding with the q2 abscissa and w=: (W2=O.SS). corresponding to elastic scattering Region I indicates the region where thl data are consistent with scaling in w. Region II indicates the extension of the scalinl region if the data are plotted against w'. The ranges A, B, C in the variable", indicated iI the figure are employed in the discussion in the text. this requirement. The measured values of R are in the range 0 to 0.5, and nc striking kinematic variation is apparent. On the assumption that R is a constan in this kinematic range, the average value of R for the proton is O.l8±0.1O where the quoted error includes an estimated systematic error of 0.06. The yalue� by University of Kentucky on 08/31/10. For personal use only. R R = 0.0 5q R of are also compatible with 3 2 and with =q2/p2. Various other form would also be compatible with the results. In Figure 12, the measured values oj R are shown as a function of q2. The results of the separation show that qtis domi· Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org nant in the kinematic region that was investigated, roughly given by q2 from I.e 11.0 2.0 to (GeV/C)2 and Wfrom to about 4 GeV. The experimental uncertaintiel in the measurements of R preclude a definite statement that (J', is significantl) different from zero. The new body of electron-proton data taken in conjunction with the deu· terium measurements, whose kinematic range is shown in Table 2 has not yel R i� been fully analyzed. A preliminary analysis shows that the average value of consistent with the results just quoted. An average value of R=O.l2±O.lO wa! found (25). Again no clear dependence of R on any kinematic variable was found. Preliminary results for R, for hydrogen, and for deuterium, as functions of q2 are DEEP JNELASTIC ELECfRON SCATIERING 221 BEST FIT o 8= 18° A 8=6° • 8= 26° • 8= 10° o 8=34° 15 15 10 10 ....- .... -� 2 2 2 2 �� q =4 (GeVlc) q = 4(GeV/c) Ll W=2 GeV W=3 GeV 8 18 R = 0.23 t 0.23 R = O. ! 0. ----::l.. l ..... w 5 5 "0 c: 40 5 �I:) C 1'1 "0 30 4 2 2 2 2 q = 1.5(GeV/c) q =8(GeV/c ) W=3 GeV W=3 GeV R=0.20tO.14 R=0.37!0.20 20 3 o 0.5 1.0 0 0.5 1.0 1617C) E E FIGURE11. Typicalexam ples illustrating the separate determination of u, and Ut. The straight solid lines are best fitsto Equation 2. The dashed lines indicate the one standard deviation values of the fits.The assumption of one-photon exchange made in calculating u, and Ut implies that linear fits should be satisfactory. For the two upper graphs mea by University of Kentucky on 08/31/10. For personal use only. sured data exist at each angle. For the two lower graphs the data were interpolated. Effects of systematic errors are not included. Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org shown in Figure 13. The preliminary studies of the separation of CT. and CTt for deuterium suggest that the average value of R is about the same as R for the pro ton. A value of R equal to O.14±O.08 was found (25). As for the proton, no clear dependence of R on any kinematic variable was established. Figure 14 shows the cross sections CT. and O't for the proton (8,13) plotted for constant q2 as functions of W2. The dashed lines indicate the W2 dependence of 0' 'Y'P' For q2<3 (GeVjC)2 the cross sections are consistent with a constant or a slowly falling energy dependence similar to the behavior of CTt. For larger q2, CT, shows rising energy dependence resembling a threshold-type behavior. This rising be havior of 0', at high energy is unique among the various total cross sections that -O.4�----�------�------�------�------L------�----� 4 8 o 2 6 10 12 14 q - Squared (GeV 1c)2 FIGURE 12. Ratio R=u,/ul for scattering of electrons from hydrogen as a fUnction of q! taken from (8) and (13). Data from a range of WI are averaged for each value ofql. have been measured. The q2 dependence of fTt shown in Figure 15 displays no pure power law behavior, but varies in the region of the present data between 1/ft2 and llq-6, as indicated by the straight lines. The energy and q2 depen dences of fT, may be correlated with the behavior of vW2 that is described in de tail in Sec. VIII. VllI. VALIDITY OF SCALE INVARIANCE The impulse approximation is used to extract the neutron cross section from the deuteron cross section. Thus, to a first approximation, the scattering from the by University of Kentucky on 08/31/10. For personal use only. neutron may be found by subtracting from the deuteron scattering the scattering from the proton; however a number of corrections have to be considered. Especially important are corrections that must be made before the subtraction is Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org carried out to account for the internal motion of the constituent particles within the deuteron. These corrections have come to be known as "smearing" correc tions. Other effectsare the Glauber correction See correction to photoproduction [ in (27)] which is estimated to be less than one percent, the effects of mesonic currents in the deuteron which are assumed on the basis of elastic electron deuteron studies (28) to be small, and the effects of a final state interaction which likewise are assumed to be small. There are also presumably small uncertainties due to possible off-mass shell effects in the nucleon structure functions. None of the latter three effects can be well estimated at present. The corrections for internal motion have been studied by West (29) who in- DEEP INELASTIC ELECTRON SCAlTERING 223 0.4 R - PROTON 0.2 o -0.2 � R - DEUTERON 0.4 0.2 cr 0 __ lJJ_ll_l_ll -0.2 --I 0 2 4 6 8 10 .12 q2 (GeV1c)2 FiGURE 13. Ratio R=u.!u, for scattering of electrons from hydrogen and from deuterium. Unpublished preliminary data from (16) and (25). Data from a range of by University of Kentucky on 08/31/10. For personal use only. W' are averaged for each value of q2. Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org cluded effects arising from the requirement of gauge invariance in the interaction with the deuteron. The variation of the "smearing" correction for different well known deuteron wavefunctions has been found to be small, provided that the wavefunctions are consistent with the observed elastic electromagnetic form factor of the deuteron (28). The variation in the correction for such consistent wavefunctions is less than a few percent. In the initial procedure employed to extract the neutron cross sections, the internal motion effects were not taken out of the deuteron cross section, but were instead inserted into the proton cross section, since this is a good deal easier to do. The smearing procedures of West (29,130,131) with small modifica tions were employed to calculate H" the hydrogen cross sections which include 224 FRIEDMAN & KENDALL 9 CT + CJr S 2 4 6 v 2 4 6 8 10 1 50 ,. 25 3 40 (0) f' 20 (b) q2 = (GeV/c)2 :0 30 15 ::l... - j -t..-l + ---f--t 20 CTy p/57 10 7----'------b'" CTy p/IO 10 q2=1.5 (GeV/c)2 5 b 0 I ? ? 0 ? LI ? � i -10 t -5 0 5 10 0 5 10 15 4 6 8v 5 7 9 II v 6 10 I- (c) :0 4 ::l... 5 btl) I 2 o t o by University of Kentucky on 08/31/10. For personal use only. o 5 10 o 5 10 15 FIGURE a Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org 14. Values of fI. and fItfor hydrogen from (7) and (8) shown at constantqS as function of W2 (and v) for q2 = 1.5, 3, 5, and 8 (GeV /C)2. The dotted curves show the v-dependence of the total photoabsorption cross section tr�v(v). the internal motion effects characteristic of the deuteron. In the evaluation of the data carried out so fa r, the quantity D-H., the deuterium cross section minus the "smeared" hydrogen cross section, will be assumed to represent the smeared neutron cross section. Values of (D/H.) -l represent, with the above limitations, values of the smeared neutron cross section divided by the smeared proton cross section. The data for (DjH.)-l corrected for smearing in this way accordingly have a value at a given w which is the ratio of the cross sections averaged over a DEEP INELASTIC ELECTRON SCATIERING 225 W=2 GeV W = 2.5 GeV W= 3 GeV CTyp =150fLb CTyp =138fLb CTy p=130fLb 100 50 (0) (b) - (c) 20 :c 10 • '-"::l... , - 5 \ \ b \ 2 \\ I 0.5 't, 2 5 10 20 2 5 10 20 2 5 10 20 FIGURE 15. The values of Uj for hydrogen fr om (7) and (8) shown at constant Wasa unction of q2 for W=2, 2.5 and 3.0 GeV. The solid line indicates a l/q2 dependenceand he dashed line represents a l/qB variation with q2. mall region of w around the given value. Computational models show that the lifference between the ratio of the smeared cross sections and true ratio increases lS w approaches unity and is sensitive to the w dependence of nip. A computa ional program is presently underway to remove the effects ofthe internal motion rom the deuteron data. The quantity (2-D/H.) (H./H) "W2P represents the quantity ,,(WzP- WIN) smeared) on the assumption that the values of R.. equal those of Rp. This differ N nce is used as a first approximation to represent ,,(WzP -W2 ) in comparison vith theoretical models. The measured values of (D/H.)-1 and ,,(WzP - WiN) by University of Kentucky on 08/31/10. For personal use only. smeared) are displayed and discussed in the next section. Included is some addi ional information on the size of the smearing correction to (D/H.)-l as a func ion ofw. Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org VIIT. VALIDITY OF SCALE INvABIANCE Proton.-The validity of scaling of "Wz for the proton has recently been tudied (8,13) at laboratory angles of 6°, 10°, 18°, 26°, and 34° over the kinematic ange available to the SLAC accelerator. Over a portion of this range (shown as he separation region in Figure 10) it was possible to determine separately the ontributions of u, and Ut. In this region the scale invariance of the structure unctions can be tested. Outside the indicated separation region, only consistency nth scaling can be studied, as a test of scale invariance requires values of R that an only be found by extrapolation of the measured values. The conclusions that ave been drawn regarding consistency with scaling for " Wz are independent of 226 & FRIEDMAN KENDALL the choice for extrapolation among the three parameterizations of R mentione( above. To test for scaling it is useful to plot IIW2 for fixed w as a function of q� Constant scaling behavior is exhibited in such a plot ifII W2 is independent of q2 2 Values of IIW2 for various ranges of w are shown as functions of q in Figure 16 calculated from interpolations at each angle of radiatively corrected spectra a 60, 10°, and in Figure 17 at 6°, 100, 18°, and 26°. In Figure 18 experimental value: of IIW2 are plotted as functions of w for various ranges of q2. A constant value 0 R=O.l8 has been assumed in calculating IIW2• Scaling behavior is not expectec where there are observable resonances, because resonances occur at fixed W, no at fixed w, nor is it expected for small q2, because IIW2 cannot depend solely on � in this limit. Aninspection of a number of similar plots leads to a group of con clusions regarding the validity of scaling in several kinematic regions : 1. For 4 2. For w <4 (Region A of Figure 10): The experimental values of IIW2 scal, for W>2.6 GeV, but "W2 appears to increase as W decreases below 2.6 GeV This region covers kinematic ranges of W between 2.6 GeV and 4.9 GeV, and 0: (GeV/c)2. q2 between 2 (GeV/C)2 and 20 3. For w> 12 (Region C of Figure 10): There are relatively few points abov( q2 =1 (GeV/c)2 and no points above q2=2 (GeV/c)2, making it difficult to de, termine any variation of IIW 2 with changingq2. There are no measurements of ], in this region, and the values of vW2 are especially sensitive to variations of R The large angle data have a maximum w of 9 and influence the values of II W2fOJ 0.4 0.4 0.4 1* I (01 (b) (c) tHtI 11 1 1, 'N�� i 0.3 0.3 0,3 II II .W2 l by University of Kentucky on 08/31/10. For personal use only. ttfltt • 02 0.2 0.2 4,,,, '6 8.",sI2 12s",018 • 0 0 0 4 0 3 4 0 3 4 5 . 0 3 Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org q2 (GeV/c)� q2(GeVlc)2 q2 (GeVlc)2 0.4 0.4 (d) (e) 0.3 0.3 R= 0. 18 .W2 I� I x = /I!I� 10° I 02 0.2 \ .::60 16s",s24 24 s",s36 0 0 I 3 4 0 0 3 4 5 q2 (GeVlc1 2 q2 (GeVlc1 2 16. The quantity for the proton for various ranges of Cd plotted agains1 FIGURE JlW. (7). q2. JlW. is kinematically constrained to zero for q·=O. Results fr om DEEP INELASTIC ELECTRON SCATIERING 227 ° ° + 6 o 18 x ° ° 10 l:;. 26 0.5 I I I 0.4 I- 4 0 9 0* t� 0.3 l- f 1 * r l/W2 - 0.2 I- i w=4 - 0.1 f- 0 I I I I I I I 0 2 4 6 8 2 (GeV/c )2 q iii1iii FIGURB 17. "WI for the proton as a function of q' for W>2 GeV, at w=4. Results fr om (7, 8, and 49). R·0.18 W.2 GeV 0.35 0.35 (a) THEOREnCAL SlGMFlCANCE. (b) I {�����TE�T:�:ON.HO I I 1 0.30 0.30 T I v W2 � 0.25 H t t 0.25 t 2 t 0.5 < q2 < 0.75 0.75 by University of Kentucky on 08/31/10. For personal use only. 0 0 10 15 20 25 30 35 10 15 20 25 30 35 (c) (d) Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org 0.35 0.35 I 0.30 1 il ! vW2 1 II I 0.30 II I j 2 0.25 0.25 • 1.5 00>12 only through the values of R determined in the low 00region. Scaling can not be tested critically in this region since the uncertainity in R prevents the large 00behavior of II 2W from being known with assurance. IfR=0. 18 is assumed when q2>0.8 (GeVjC) 2, IIW2 decreases slightly as w increases. However, for larger values of R consistent with the extrapolated values, II W2 is constant. Preliminary analysis of more recent data does not resolve these questions (16, 49). A falling v W2 with increasing 00would indicate a nondiffractive component of v W2• One of the most remarkable aspects of the above results is that scaling be havior, presumed to be a property asymptotically reached in the Bjorken limit, 2 sets in at such low values of q and II. The theoretical significance of this is presently not well understood. Tests of scaling in 00' carried out by the MIT SLAC experimental group have shown that the use of 00' extends the scaling region from W = 2.6 GeV down to W = 1.8 GeV, shown as Region II in Figure 10. The 2 constant a was determined to be 0.95 ± 0.07 (GeVjC) by fitting that portion of the data with W� 1.8 GeV and q2> 1 (GeVjC) 2. The statistical significance of a is greatly reduced in a fit to the data for W> 2.6 GeV, implying that functions of either 00or 00'give satisfactory statistical fits in this kinematic range. In the follow ing discussion, the value of a willbe chosen to be equal to M2=0.88 which gives ' w = w + -=-M2 W2 + 1 q2 q2 Figure 19 shows 2MW1 and vW2 for the proton as functions of 00for W>2.6 ' GeV, and Figure 20 shows these quantities as functions of w for W> 1.8 GeV. The data presented in both figures are for q2> 1 (GeVjc)! and use R=O.18. The experimental results for both structure functions scale in 00 and 00' within the errors of measurement over a large kinematic range. We have noted that if v W2 scales in the Bjorken limit then scaling of 2MW1 is expected provided R is constant or is a function of w. As we have seen, the measured values of R are small and are not sufficiently precise to determine any possible functional depen dence of R. by University of Kentucky on 08/31/10. For personal use only. 2 It is of interest to examine the explicit q dependence of W2 at constant Win the scaling region. Since for 00>4which corresponds to (W2-M2)jq2>3 the quantity IIW 2 is approximately constant, we find that Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org 1 W2 ,....."------1 + q2j(W2 -M2) which is a relatively weak dependence on q2. For 1 ::::;00 ::::;2, vW2 is found to be proportional to (1 -1jw)3 and the dependence of W2 is 1 2 """" 3 W2 - M2 _ 2 2 W + q [ q [W 2 M2 J J It is thus evident that for (W2-M2)jq2«1, W2 has approximately the same ql dependence as the square of the elastic form factor. The q' dependence is clearly intermediate between these extremes for intermediate values of w. DEEP INELASTIC ELECI'RON SCATIERlNG 229 70 R=0.18 6.0 W>2.6 GeV 5.0 4.0 3.0 2.0 1.0 o 0.6 R=0.18 W>2.6 GeV 0. 5 0.4 0.3 0.2 0. 1 by University of Kentucky on 08/31/10. For personal use only. o 2 4 6 10 20 8 W FIGURE 19. 2MW1 and "W. for the proton as functions of fo r W>2.6 GeV, Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org w q2>1(GeVIe)' , and using R=0.18. Data from (8). Deuteron.-The final analysis of the larger angle measurements on deuterium is not yet complete so that separations of the scalar and transverse contributions to the inelastic e-d scattering are preliminary and of limited scope. However, on the assumption that RD =RP, a result consistent with the preliminary determina tions of RD as discussed in Sec. VI, values of II W2D may be derived from the measured results. These values are shown in Figure 21(a) and (b), where (a) displays the values for 6= 6° and 10° (16), and (b) the values for 6= 18°, 26°, and 34° (19, 25), as functions of w. The values of IIW2P measured in the same series of experiments are included also. It appears that within the errors of measurement 6 R=O.IS W>1.S GeV 5 4 2MpWJ 3 2 � 0.4 0.3 0.2 by University of Kentucky on 08/31/10. For personal use only. Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org 0. 1 o ��.•., __� __ �-L�-L�� __ _L- __ I 2 3 4 5 6 7 S 9 10 20 FIGURE 20. 2MWl and " Wz for the proton as fu nctions of Ill' for W> 1.80 GeV. ql > l(GeVje)1 andusing R=O .18. Data from (8). DEEP INELASTIC ELECTRON SCATIERING 231 e ; 18?00 . 26?OO and 34?00 0.4 STRUCTURE FUNCTIONS = 0.8 9 5�988 and 10�00 o Proton • Deuteron 0.6 , hv� /1I I ' I, " iijj� I C\I 5 0.4 4' � "If\!\ t. ++ 4"'\1 � f. tJi � , � 0.2 I•. I, .. 1.0 5.0 9.0 13.0 17.0 21.0 25.0 w 2Mv/q2 by University of Kentucky on 08/31/10. For personal use only. FIGURE 21. The quantity "W, for the proton and the deuteron separately displayed for 18°, 26°, and 34° (top) from (6, 19, 25) and for 6° and 10° (bottom) as functions of w, from (6, 16). The data are for W>2 GeV (top), W>2.25 (bottom),q2> 1 (GeVjc)2, and Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org use R=0.18. the preliminary deuteron results exhibit scale invariance with about the same un certainties as the proton. The data displayed are subject to the restrictions that W�2 GeV and q2 �1 (GeV/C) 2. Ne utron.-Values of (D/H.) -1 which represent-within the limitations de scribed in Section VII-the values of the smeared neutron cross sections divided by the smeared proton cross sections are plotted in Figure 22 against X= 1/CI/. The points shown are preliminary and represent data (19) having values of 232 FRIEDMAN & KENDALL 1.0 0.9 l- I j , 0.8 e- l i 1 1 0.7 I r- t f f I �0.6 HI!!! ... r- � jlj' E 1!l 0.5 -!!.' e- , I J: I "- a 0.4 � I f j t 0.3 e- 0.2 - 0.1 - � I I I I J I r r 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 'Iw X = FIGURE 22. The quantity (D/H.-l) as a function of x=l/w. Thedata are from (19), and are for W>2 GeV and q2 >I(GeV/C)2. This quantity is approximately equal to the ratio of neutron to proton scattering cross sections. The ratios shown are averages over small intervals of x. See also Figure 23. by University of Kentucky on 08/31/10. For personal use only. q2 �1 (GeVjC)2 and W�2 GeV. Some of the data were reported earlier (6). Fur Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org ther analyses have not made significant changes in the ratio of neutron to proton cross sections except for the two smallest w points which increased on the average by 1.5 standard deviations. These results indicate sizable differences between the neutron and proton cross sections, and thus provide evidence for a significant nondiffractive component in the scattering process. The values of the neutron proton cross section ratio are consistent with a single function of w. Thus within the errors the neutron cross section exhibits scaling. With the expected reduction in the presently shown errors fr om further data analysis a more stringent test for scaling behavior of the neutron will soon be available. DEEP INELASTIC ELECTRON SCATTERING 233 Figure 23 shows the effect of the smearing correction, as calculated, on the plot of (D/H)-l versus w. The dashed line represents a curve drawn through the corrected points shown in Figure 22. The solid curve represents the dashed curve before smearing corrections were made. The "smearing" effects for the points shown are thus smaller than the errors in the experimental points for w>1.5, and cannot account for the differences between the proton and neutron observed in Figure 22. The smearing correction is much larger for w < 1.5, and the value of nip in this region is more dependent on the assumptions in the smearing procedure. West (29) has found that, relatively independent of the deuteron model, there is no smearing correction inthe neighborhood of w = 1.5, because of a crossover of the corrected and uncorrected curves. Since there is a sizable difference in the uncorrected yields for the proton and neutron at this point, this firmly establishes the neutron-proton difference. It should be em phasized again that the corrected curve shown in Figure 23 is the ratio of the 1.2 0.9 Uncorrected --. , *::r: 0.6 '-.... a ',... Corrected 0.3 / ...... by University of Kentucky on 08/31/10. For personal use only. Limit of Data - Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org o 0.2 0.4 0.6 1.0 X= l/W FIGURE 23. This figure displays the magnitude of the correction for internal motion On the measurements of (DIH- l) as a function of x=l/",. The solid curve in the presentfigure, Un corrected, represents a curve drawn through the uncorrected points of (DIH- l), i.e. H* =H. The dashed curve, Corrected, represents the data of Figure 22, (DI H. -1), i.e., H*= H•. The line, Limit Of Data shows the highest value of x for which data of significant statistics exist. 234 FRIEDMAN & KENDALL � !! ..:!: � ..... 'C � S eo ...... �II) � zt\l 8 3::I .. o.. t\I c �I!:0. 8c g � 0.10 0.211 0.30 O.1iO O.SO 0.60 0.70 0.10 O.W 1.00 '0.00 X=lIOHEGA FIGURE 24. Preliminary values of (W2P- W2N) (smeared) as a function of x=l/", derived from the points of Figure 22 with the assumption that R" = Rp. This data is dis cussed further in the text. by University of Kentucky on 08/31/10. For personal use only. neutron to proton cross sections where both include the effects of internal motion. Figure 24 represents v( W2P -W N) (smeared) a function of (19). There is a Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org 2 as x maximum of this quantity at about x= 1/3. Inelastic muon scattering measurements carried out at SLAC (10) have yielded information on the ratio of the neutron and proton cross sections in the deep inelastic region, and on the comparison of electron and muon scattering. The comparison is discussed in Sec. IX. The ratio of neutron and proton cross sections was developed from measurements of the scattering of a 12 GeVIc muon beam from hydrogen, carbon, and copper targets. Measurements of in elastic scattering were made for 0.3 5:.q2 5:.2 (GeVIc) 2 and 0.6 5:.v�6 GeV. In order to extract the ratio of neutron to proton cross sections, data were analysed in kinematic regions where possible shadowing effects arising from a p-domi- DEEP INELASTIC ELECTRON SCATIERING 235 nance mechanism would be minimized. In these regions, the minimum mo mentum transfer for p production tmi,, ==(q2+Wp)2j4v2 was large. With this re quirement the A dependence found was AO.99±Ol showing that there was no detect able shadowing. This data yielded an average ratio of neutron to proton cross section of 0.91 ± 0.06. Since the range of w for this data is w> 5, the electron and muon scattering results are consistent. COMPARISON OF ELECTRON MUON SCATTERING RESULTS IX. AND The SLAC muon scattering group has made a detailed study (10) of the com parison of the muon and electron scattering results in the regions of kinematic overlap. Figure 25 shows a comparison of the results. The agreement is excellent. Since the radiative corrections for muon scattering are about a factor of four smaller than fo r electron scattering, this comparison is consistent with the conclu sion that the radiative corrections are not introducing an appreciable error into the electron scattering results. One further conclusion arises from this com parison. The muon scattering group has used these results to put a limit on any possible difference in interactions of the muon and the electron. Using the con ventional form for a breakdown parameter 1 1 1 A 2 jA they find that AD >4.1 GeV at the 98% confidence level for data with q2 <4.0 (GeVjC) 2 and v<9 GeV. COMPARISON WITH THEORETICAL MODELS X. Many different attempts have been made to understand the experimental re sults in deep inelastic electron-nucleon scattering (30a-e). The main theoretical lines of approach that have been followed are the parton model, the vector domi nance model, dual resonance models, Regge pole models, and studies of current commutators on the light cone. by University of Kentucky on 08/31/10. For personal use only. The parton model.-In the parton model, developed by Feynman (31) and Bj orken & Pa schos (32), the proton is conjectured to consist of point-like con Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org stituents, called partons, from which the electron is scattered incoherently. This model is implemented in the infinite momentum frame of reference, in which the relativistic time dilation slows down the motion of the constituents nearly to a standstill. The incoming electron thus "sees," and incoherently scatters from constituents which are essentially real and which are noninteracting with another during the time the virtual photon is exchanged. In this frame, the impulse ap proximation is assumed to hold, so that the scattering process is sensitive to the properties and motions of the constituents. Consider a proton of momentum P, made up of partons, in a frame approach ing the infinite momentum frame. The transverse momenta of any parton is negligibleand the ith parton has the momentum Pi = xoP,where Xi is a fraction 250 • This Experiment f • e-p (SLAC) 200 • yp 150 (0) K= 1.5-2.5 (b) (GeV) ::0 100 100 � b x �. ·x ."x 50 x 50 • + + x + .. x 0 1.0 2.0 3.0 4.0 0 1.0 2.0 3.0 4.0 150 + K=2.5-3.5 (c) 150 + K=3.5-5.o (d) (GeV) (GeV) 100 100 b� * ++ + 50 fl. 50 ..+ + x ( Xx Ix + t + +< 0 a 150 + K=5'o-7.0 (e) 150 K=7.0-8.3 (0 (GeV) (GeV) by University of Kentucky on 08/31/10. For personal use only. ::0 100 100 � b + .. + .+ + 50 • 50 f. Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org t * ,x + 0 0 o w w � � 0 M � � � Iq2J (GeVlc)2 FIGURE 25. Comparison of cross sections for p.pand ep scattering as fu nctions of qt. The incident muon momentum for these measurements was 12 GeVIe. The electron data was taken fr om (7) and the figure and the muon data are from (10). The quantity p isthe ratio of the inelastic muon to the electron inelastic cross sections and K, defined in the text, equals(W2- MJ)/2M. DEEP INELASTIC ELECTRON SCATIERING 237 of the proton's momentum. Assuming the electron scatters from a point-like parton of charge Q;, leaving it with the same mass and charge, the contribution to W2 (v, q2) from this scattering is . Q� W2(')(v, q2) = Q;20(v - q2/2Mx) = q2/2Mv) --v o(x - The expression for vW2 for a distribution of partons is given by vW2(v, q2) = peN) E Q;2 = F2(x) � ( ) XfN(X) where x = q2/2MII = l/w and where P (N) is the probability of N partons occurring. N (Qi)2N 1:i=l is the sum of the squares of the charges of the N partons, and !N (X) is the distribu tion of the longitudinal momentum of the partons. This, with the assumption of point-like constituents in the parton model automatically gives scaling behavior. The quantity F2(x)/x gives the weighted average of !N (X), the distribution of longitudinal momenta for the N parton system. The current applications of the parton model have identified partons with bare nucleons and pions (33, 34), and also with quarks (32, 35). Parton models incorporating quarks have provided the most extensive quantitative comparisons with the data. Quark parton models require strong final state interactions to account for the fact that these con stituents have not been observed in the laboratory. There may be some problem (36) in making the "free" behavior of the constituents during photon absorp tion compatible with a strong final state interaction. This question is avoided in by University of Kentucky on 08/31/10. For personal use only. parton models employing bare nucleons and pions because the recoil constituents are allowed to decay into real particles when they are emitted from the nucleon. Drell, Levy & Van (33) have derived a parton model, in which the partons Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org are bare nucleons and pions, from a canonical field theory of pions and nucleons with the insertion of a cutoffin transverse momenta. The calculation shows that the free point-like constituents which interact with the electromagnetic current in each order of perturbation theory and to leading order in logarithms of 2Mv/q2 are bare nucleons making up the proton and not the pions in the pion cloud. This result is consistent with the conclusions of Callan & Gross (37) that a small value of R=cr./crt at large q2 and II requires that constituents responsible for the scattering have spin 1/2. The experimental results for R most likely (25) rule out pions as constituents, but, of course, are consistent with the possibility that the proton is composed of quarks. The field theoretic parton model shows that vW2 and W1 should scale in the Bj orken limit and indicates that the original parton 238 FRIEDMAN & KENDALL model is consistent with some of the requirements of field theory. One of the re sults ofthis calculation is the suggested connection between the elastic form factor and the behavior of p W2 in the neighborhood of w = 1. If the elastic form factor 2 2 2 G(q2) has the dependence (l/q )n/ as q -+oo , then the predicted behavior for II W2 is IIW2-t{1 -1/w)n-l as w-tl . This relation was also pointed out by West (34) using a different approach. For either w or w' <2, the experimental values of pW2 can be satisfactorily fit with a single cubic term, a result which is consistent with this prediction. The field theoretic parton model also relates deep inelastic scattering to colliding beam processes, such as e++e--tP+anything. The original parton model has also been formally derived fr om the behavior oflocal fieldtheory in the equal-timelight cone limit (38, 39, 88, 89). A detailed description of a quark-parton model has been given by Kuti & Weisskopf(35). Their model of the proton contains in addition to the three valence quarks, a sea of quark-antiquark pairs, and neutral gluons responsible for the binding of the quarks. The momentum distribution of the quarks corresponding to large w is given in terms of the requirements of Regge behavior. The model is compatible with the measurements of pW2for the proton and neutron for values of w>2. It has difficulty at smaller values of w as it predicts p W2N/11 W 2P =2/3 in this region whereas the measured result appears to fall to as Iow a value as 0.35 ± 0.07 at w=1.25. As this model is a simple impulse approximation descrip tion, it has been pointed out that the presence of two-particle correlations could account for the observed ratio in the neighborhood of w= 1. The quark model and, more generally, the light cone algebra based on the quark model, are not compatible with a ratio less than 0.25 even with the inclusion of such correlations (40). A recent calculation by Lee & Drell (41) provides a fully relativistic generali zation of the parton model that is no longer restricted to infinite momentum frames. This theory obtains bound state solutions of the Bethe-Salpeter equation for a bare nucleon and bare mesons, and connects the observed scale invariance with the rapid decrease of the elastic electromagneticform factors. by University of Kentucky on 08/31/10. For personal use only. Sum rules.-Excellent tests of applications of the parton model are provided by sum rule evaluations. From weighted integrals of IIW2(W) with respect to w, sum rules can be derived on the assumption that the nucleon's momentum Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org is, on the average, equally distributed among the partons. Two important sum rules, which can be evaluated for neutrons and protons, are: where /2 is the weighted sum of the squares of the parton charges and is the /1 DEEP INELASTIC ELECTRON SCATTERING 239 mean square charge per parton. The sum 12 is equivalent to a sum rule derived by Gottfried (42) who showed that for a proton which consists of three nonre1a tivistic point-like quarks /2P equals 1. The experimental value of the integral when integrated over the range of the SLAC-MIT data gives : dw 20 - == = f 0.78 ± 0.04 12P 1 w "W2P where the integral is cut offfor w>20 because of insufficient information about R. Since the experimental values of I'W2 at large w do not exclude a constant value, there is some suspicion that this sum might diverge. This would imply that in the quark model the scattering has to occur from an infinite sea of quark-antiquark pairs as well as from the three valence quarks. Table 3 gives a summary of the comparison of the experimental values of the sum rules with the predictions of various models. Unlike the previous sum, the experimental value of 11 is not very sensitive to the behavior of" W2 above w > 20. The experimental value is about one TABLE 3. SUM RULE RESULTS-THEORY AND MEASUREMENTb Expected Value" Measurement "'m q2(GeV/c)1 3 Quark 3 Quark + 'Sea' 0.159± .005 20 1.0 hP 1 0.165 ± .005 20 1.5 1/3 2/9+- 0.172± .0090 200 1.50 3(N) 0.154± .005 12 2.0 0.120± .008 20 1.0 hN 2/9 2/9 0. 115± .008 20 1.5 0.107 ± ;009 12 2.0 0.739±.029 20 1.0 liP 1 1/3+2(N)/9 0.761 ± .027 20 1.5 0.780± .040 20 1.5· by University of Kentucky on 08/31/10. For personal use only. 0.607 ± .021 12 2.0 0.592± .051 20 1.0 2/3 2(N)/9 O.584±.050 20 1.5 Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org I.N 0.429± .036 12 2.0 O. 147±.059 20 1.0 U'_I.N 1/3 0. 177± .057 20 1.5 0. 178 ± .042 12 2.0 • (N) expectation value of number of quarks, N. b Data fr om Kendall (6), and (16) and (19), except where noted. • E. D. Bloom et al 1969. Phys. Rev. Lett. 23 :930 M. Breidenbach et a1 1969. Phys. Rev. Lett. 23:935 G. Miller et al I972. Phys. Rev. D 5:528 240 FRIEDMAN & KENDALL half the value predicted on the basis of the simple three-quark model of the proton, and it is also too small for a proton having three valence quarks in a sea of quark-antiquark pairs. The Kuti-Weisskopf (35) model which includes neutral gluons in addition to the valence quarks and the sea of quark-antiquark pairs predicts a value of It that is compatible with this experimental result. The difference 12P -/2N is of greatinterest because it is presumed to be sensi tiveonly to the valence quarks in the proton and the neutron. The values of neither 12P nor 12N depend on the properties of gluons, and assuming that the quark antiquark sea is an isotopic scalar, the effects of the sea cancel out in the above difference, giving 12P -12N = 1/3. Unfortunately it is difficult to extract the correct value fr om the data because of the importance of the behavior of v W2 at large w. w-+oo w> If one extrapolates vW.p - W.N toward for 12 with the asymptotic dependence expected on thev basis of Regge theory (l/W)1/2, one obtains a rough estimate of 12P -/2N=O.22 ± O.07. This is not incompatible with the expected value. However, it is not clear that the form of extrapolation is correct nor at what value of w the leading Regge term becomes dominant if it is correct. A P light cone model by suri & Yennie (43) predicts the difference v W2 - V W2N to -1 be proportional to w • Such a dependence would not permit l2P -12N to reach 1/3. On the basis of a formal study of quark models, Llewellyn-Smith (44) has shown that when the interactions between quarks are due to scalar or pseudo scalar fields there is an upper bound This upper bound appears to be experimentally satisfied unless some unexpected behavior occurs in unexplored regions of w. Bj orken (45) pointed out that the Adler sum rule for inelastic neutrino scat tering derived from the commutaior of the two time components of the weak current leads to the following constant q2 inequality for inelastic electron scat tering. by University of Kentucky on 08/31/10. For personal use only. 2 � dv[W2P(v, q2) + W2N(v, q )] � ! fq2 /2M inequality is satified at w=5. Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org This Vector dominance mode/s.-An early dynamical description of the process was given by Sakurai (46) in terms of the vector dominance model (VDM). This model gives for large v: M ' 2 Ut(q W) . 2, = .2 2 U'YP(W) and [M + q ] (q W) us 2, R = = HW) W) M. - 2Mv (Tt(q2, (.t-.)[1 L] DEEP INELASTIC ELECfRON SCATTERING 24 1 where M. is the mass of the vector meson, taken to be the p meson ; �(W) is the ratio of the total cross sections for vector mesons with helicity states 0 and ± 1 respectively incident on nucleons. This result implies scale invariance for " W2 in w the large 11, fixed limit and gives the characteristic diffractive limit that IIW2 w--+ • equals a constant as 00 This prediction of a strong dependence of R on q2 is in gross disagreement with experiment in the kinematic region in which u. and Ut have been separately determined, as shown in Figures 12 and 13. This difficulty would disappear if �(W) were zero ; however, such a constraint produces the wrong q2 dependence for "W2 and would be surprising fr om general considera tions. Cho & Sakurai (47) have suggested that this model should only have va lidity in the pure diffractive region, say for w�to, where R is not yet measured. However, R has been measured up to about w�9 with no q2 dependence apparent. The role of p dominance in inelastic electron scattering has been further studied by an experimental investigation of the A dependence of the process by the MIT-SLAC group (48). Electron scattering fr om Be, Cu, and Au was studied for 8=60 at incident electron energies E= 4.5, 7, to, 13.5, 16, and 19.5 GeV, for values of E' at and above 2.5 GeV. OVer this span of data v varied from 0.1 GeV to 17 GeV, and q2 varied from 0.10 (GeV jC)2 to 3.7 (GeVjC) 2. Very gen eral considerations of VMD suggests that at low q2 (here meaning q2 :5,W), and large v, the "hadronic" cloud associated with a physical photon should manifest itself as a cross-section dependence on A less than linear. A comparison is made of the results with a simple p-dominance calculation by Brodsky & Pumplin (50). They assume a p-nucleon total cross section that is independent of energy. To facilitate the comparison a shadow factor S is defined : NUn) S = U nudeus/(Z by University of Kentucky on 08/31/10. For personal use only. than 3% in the kinematic region considered here. The values of S, for two bands about q2 =0.5 and 1.0 GeV2, are shown in Figures 26, 27, and 28 as functions of v. The appropriate predictions of Brodsky Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org & Pumplin are shown as solid lines. There is no consistent deviation of any of the data from S = 1 and in particular there is substantial disagreement with the predictions (50). A model by Yennie, suri & Spital (51) inserts into the calculation of Sa non-VDM and VDM part each of unknown strength. A fit to the data gives a ratio of VDM to non-VDM contributions to the interaction amplitude of 0-0.10. This requires a drastic reduction in the forward p electroproduction am plitude predicted by a vector dominance model which fits the real photo-absorp tion cross section. These results are equivalent to the statement that an evaluation ofthe neutron proton cross section ratios deduced fr om the heavy target data with the assump tions just mentioned are the same as those displayed in Figures 5(a) and 5(b) from 242 FRIEDMAN & KENDALL Be 1.2 s 5 5 -0'"8. 1( 0'"o -O'"HI ! 0.25 deuterium after appropriate smearing. A direct comparison indicates this is in deed the case within the errors. Attempts to save the vector dominance point of view have been made by Tung (52) and Wataghin (53) who have introduced generalizations of the VDM. Other approaches (54, 55) have been to apply the model withthe extension of the vector meson spectral function to higher masses. While a number of different by University of Kentucky on 08/31/10. For personal use only. approaches can be taken to patch up the VDM theory, it isclear that the simple theory is in difficulty. Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org Regge mode/s.-Another approach relates inelastic scattering to virtual for ward Compton scattering which is described in terms of Regge exchange. In the Regge limit v--+ 00,with q2 fixed, this gives v -t 002 2 W1.--(q , ) f31(q )Va(O) JI -t W 2p (q__ 2OO, ) f32(q2)Jla(O)-2 where a(t) is the leading trajectory. It is expected that the leading trajectory is that of the Pomeron with a(O) = 1. Abarbanel, Goldberger & Treiman (56), and also DEEP INELASTIC ELECTRON SCATTERING 243 I 1.2 Cu s ! 1.0 --..."....= NO -- SHA DOWING 4 5 5 5 5 = OCu1(3 . CT"o - . CT"H I O.25< q2 Q --�---- 5�-- -�---�--�----��--��----��---�--� O 2 4 6 8 I O 1 2 14 � 18 ENERGY LOSS V 27. FIGURE The shadowing factor S, for inelastic electron scattering from copper. See caption to Figure 26. Harari (57) have conjectured that the leading Regge pole at finite q2 continues to dominate as q2...400 with v/ q2 fixedand very much greaterthan unity. The require ments of scale invariance makes the following constraints: � and � by University of Kentucky on 08/31/10. For personal use only. fh(q2) (q2)-a(O) fJ2(q2) (q2)1-a(Ol in this limit. Since a{O)= 1 for the leading trajectory it follows that W1(w) is pro portional to w and v W�w) is a constant. An investigation of a simple model by Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org Abarbanel, Goldberger & Treiman (56) produced residue functions which were sufficientlyclose to this requirement to lead to the hope that it would be obtained in a more complete model. In the detailed application of the Regge theory to this process, discussed by Moffat & Snell (58), Pagels (59), Akiba (60) and Breiden bach & Kuti (26), scale invariance is inserted into the theory by choosing the residue functions to have the required behavior. The following functional be havior is obtained for large w: VW2 = 2: b;Wa,-l ·p,p' ,At " · . 244 FRIEDMAN & KENDALL 1.2 Au s f ------1 .0 - �- --flI- SHADOWING IL ----- 5 = erA . I( 118ero-39CTH ) J 0.25< q2 < 0.75 GeV'1c2 0.75 < q2 < 1.50 GeV2/c2 O.5 �--�-- � � L- � �� L � ! --�L------0 2 4 6 8 10 12 14 I 6 '8 ENERGY LOSS v FIGURE 28. The shadowing fa ctor S, for inelastic electron scattering fr om gold. See caption to Figure 26. where the sum includes all trajectories that couple to the photon, such as the Pomeron, the p', and A2 trajectories. The quantities a, are the intercepts of the trajectories at 1=0, and the quantities hi are unknown constants that can be determined from the measurements. The A2 trajectory is required since isospin by University of Kentucky on 08/31/10. For personal use only. exchange must be included to account for the observed difference between struc ture functions of the proton and neutron at small w. An important consequence of v(1/w) this approach is that v -v N is predicted to be proportional to for Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org W2P W large w. Unfortunately the data 2 are not sufficiently precise at large w to test this prediction. Duality.-The observed difference between W2P and W2N points to the exis tence of significant nondiffractive contributions to the forward Compton ampli tude for virtual photons. This leads to the application of the concept of duality to inelastic electron scattering. In the usual "two component" duality picture, diffractive scattering at high energies is related to the low energy background, while nondiffractive t-channel exchanges are connected to low energy resonances. Finite energy sum rules have been proposed by Leutwyler & Stern (61) to test this connection. DEEP INELASTIC ELECTRON SCATI'ERING 245 Bloom & Gilman (62) have pointed out that low energy resonance electropro duction has a behavior which is correlated with that of the deep inelastic scatter ing. Qualitatively they expect that fits in w' to vW2 for values of Wabove 1.8 GeV, Fiw'), representing the scaling limit of vW2 should, on the average, follow the resonances and their associated low energy background, at least for values of q2> 1. Bloom & Gilman have quantitatively tested their assertion with a constant q2 finite energy sum rule: Vmu 1+lVma:2/q2 -M 2 = dw'F {w') 2 2 f dv vW2{v, q ) f 2 q 0 1 where Wma� has been chosen above the region of prominent resonances and Villa", = 2M The evaluations (25) of this sum rule with interpolated experimental values at 2 10% 2 fixedq indicate that it is satisfied to better than for a range of q from 1 to 4 (GeV/C)2 and for W"""" from 2.2 to 2.5 GeV. The authors, on the assumption of local duality, suggest that: The ratio 0.47 is not favored by the recent measurements (see Figure 22) but is also not excluded by them. In an extension of the above work, Briedenbach & Kuti (26) have found that an excellent fit to the data both inside and outside the 2 resonance region for q > 1 can have the form : vW2 = F2{w') [R(W) + BG(W)] where R(W) is the sum of Breit-Wigner forms for the prominent bumps and BG( W) describes a smooth background term added to the resonances. For by University of Kentucky on 08/31/10. For personal use only. W> 2 GeV, R(W) approaches zero and BG(W) approaches unity leaving vW2 equal just to the scaling function Fiw'). To show that the essential physics does not depend on the particular scaling variable used, the fitting procedure was also Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org done with WL. The fit was equally good and also leads to satisfactory finite energy sum rules. While the Bloom & Gilman sum rule is expected to hold only in the region of q2�1, Rittenberg & Rubinstein (24) have proposed a finite energy sum rule that is conjectured also to hold at low q2 and even to the limit of real photons using a different scaling variable, where A2 is a constant chosen to maximize the goodness of fit of the data to the 246 FRIEDMAN & KENDALL scaling curve. The evaluation of this sum rule for the range of 1.0,2:,q2�0.3 GeV gives reasonably good agreement with predictions. [See especially the detailed comparison in (63)]. Resonance models -Attempts have been made to build the structure func tions from direct channel. resonances. While the form factor for the excitation of any specific resonance might be expected to go to zero rapidly for large it has been shown that the scale invariance of v W2 can be achieved in such a q2,model if the total number of resonances excited increases sufficiently rapidly with W. Landshoff & Polkinghorne have constructed a Veneziano-like model which produces scale invariance by(64) incorporating an infinite number of resonances. When combined with the quark-parton model (65), this point of view allows a complete calculation of the nondiffractive contributions to the structure func tions, essentially without free parameters. The predictions for v WzP for w <3 are in reasonable agreement with the data; however the model falls well below the data for larger w, a result which is probably due to the absence of diffractive components in the model. While the calculated difference v W2P - V W2N is in fair agreement with experiment, the prediction that v W2N I(v W2P) = 2/3 disagrees with the measurements near w = 1 where the nondiffractive part of the amplitude might be expected to dominate. Atkinson Contogouris have extended the Lands & (66) hoff & Polkinghorne model to include a diffractive part and get better agree ment with measurements of v WzP at large w. A different type of resonance dominance model has been worked out by Domokos, Kovesi-Domokos & Schonberg (67) who built the structure functions from an infinite series of N* and � resonances. The predictions for v WzP are in good agreement with experiment for values of w�7 but fall below experiment at larger w, probably because of the absence of diffractive contributions to the structure functions. The value of v WzNIv WzP near w = 1 is about 0.70-0.78, which is in disagreement with experiment. Models that predict deviations from scaling.-A number of models predict deviations from scaling, among which are the following. On the basis of a model by University of Kentucky on 08/31/10. For personal use only. which postulates parton clusters, Wilson has conjectured that scaling will break down somewhere in the range of between(68) 8 and 30 (GeVjC) 2. The calcu lation by Cheng & Wu of the high q2energy behavior of scattering amplitudes Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org in quantum electrodynamics(69) when extended to virtual photons show that scale invariance should be violated. The deviation from scaling arises from terms in v W2 like In( j ) where is the mass of the exchanged vector mesons. is I q21 X2 X If A taken to be the p mass, the sizes of these logarithmic terms are large enough to produce observable violations of scaling behavior at SLAC energies. Such viola tions are not observed. A super-eikonal model by Fried & Moreno (70) predicts a weak violation of scaling. The precision of the present measurements is prob ably not greatenough to discern this predicted deviation. Weak violation predic tions also resulted from the work of Fishbane & Sullivan (71) who studied vW2 in fieldtheory model without a transverse momentum cutoff. Ageneral discussion DEEP lNELASTJC ELECTRON SCATTERING 247 of the problems associated with scale invariance has been given by Gell-Mann (72). It should be emphasized that the current measurements are consistent with scale invariance only to within their errors which, with the inclusion of the uncer tainties in the radiative corrections, range from 5 to 10%. Models which intro duce a violation of scale invariance within this range constitute no contradiction with experiment and tests of their validity require measurements at higher energies. RELATED PHYSICS XI. Deep inelastic electron scattering has been related in a number of theoretical investigations not only to other electromagnetic processes but also to weak and strong interaction physics. Neutrino-hadron scattering.-Bjorken (73) has conjectured that the three structure functions which describe inelastic neutrino-nucleon scattering [(74) gives a summary of formalism], v+n-+.u+hadrons, also asymptotically mani fest scale invariance. The doubly differential cross section is described in terms of the structure functions W1± , W2±, Wi , where the + and - correspond to neutrino and anti-neutrino interactions. In the limit in which both v and q2 approach infinity, with w fixed, it was argued that the structure functions approach the following limiting behavior W1± (v, q2) � Fl±(W) by University of Kentucky on 08/31/10. For personal use only. Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org There have not yet been separate experimental determinations of these struc ture functions ; however, there has been some evidence for scaling behavior. On the basis of scale invariance, the total cross section is predicted to rise linearly with energy. a prediction in agreement with current data. The data from the CERN heavy liquid bubble chamber (75) give u=(0.52±0.13)G2 ME/7r per nucleon. A second direct consequence of scaling is that the average q2 is pre dicted to be proportional to v, verifiedin reference (76). The applications of current algebra and the parton model lead to a number of relations (77) between the electromagnetic and weak structure functions in addi tion to relations between the weak structure functions themselves. For example, 248 FRIEDMAN & KENDALL the existence of nondiffractive contributions to the electromagnetic structure functions suggests a difference in the neutrino and anti-neutrino cross sections. In the parton model, Ws, which arises from the interference of the vector and axial vector currents, is a measure of the number of baryon partons minus the number of anti-baryon partons. In general, Wa and (W1•2+- W1•2-) have no diffractive parts and are expected to approach zero in the limit of large w. Electron-positron colliding beams.-On the basis of crossing symmetry, the process e-+e+�p (or p)+hadrons has been related to deep inelastic scattering (33). A number of differentapproaches (73, 78, and 79) have suggested that the total cross section for collisions should exhibit a point-like behavior and thus have a 1/£2 energye+ -e dependence.- Results from the Frascati colliding beam measurements appear to confirmthe predicted large cross sections (80). Inelastic Compton scattering.-Inelastic Compton scattering of photons from protons, 'Y+�'Y'+hadrons has been studied by Bjorken & Paschos (32, 81) within the parton model. At large momentum transfers they find that this cross section is related to the inelastic electron cross section by the following expres sion: where the brackets signify mean values. Measurements of this cross section can in principle distinguish between fractionally and integrally charged constituents in a parton model. number of predictions of polarization effectsexpected Polarization effects.-A in deep inelastic scattering of leptons have been made, some of which may be subject to test. Studies have been made by Bjorken (82), in the framework of equal time current commutators, and in the quark-parton model, by Galfi et al by University of Kentucky on 08/31/10. For personal use only. (83), and by Kuti & Weisskopf (35). Nash (84) has completed similar studies in the framework of the quark-parton model of Landshoff, Polkinghorne & Short (85). Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org Sum rules from the light-cone structure of the spin-dependent scaling func tions and studies in cutoff field theories have been reported by Galfi et al (86). Niedermayer (87) has applied the quark light cone algebra of Fritzsch & Gell Mann (88) [see also Cornwall & Jackiw (89)] as have Dicus, Jackiw & Teplitz (90), Wray (91), and Hey & Mandula (92). Domokos, Kovesi-Domokos & Schonberg (93), and Close & Gilman (94) have applied the resonance model to polarized electron scattering. The Regge analysis of spin-dependent forward virtual compton scattering can be found in (86). Kinematic inequalities (86, 95), the application of finite energysum rules to spin-dependent scaling phenomena [for a summary paper see (96)], and a general review of the rapidly growing field(97) is reported by Kuti et al. DEEP INELASTIC ELECTRON SCATTERING 249 Carlson & Tung (98) have shown how simultaneous measurements of the longitudinal and transverse polarization effects in inelastic lepton-hadron scatter ing can be used to determine the two spin-dependent structure functions which in turn may be used to test experimentally the consequences of assuming scale in variance of the leading light cone singularities. The hyperfine splitting (hfs ) in atomic hydrogen is an interesting bridge be tween the usually disconnected fields of high-energy and precision atomic physics. For an excellent survey of the literature see Brodsky & Drell (99). The size of the proton polarizability contribution to the hfs from two-photon ex change (OPOL) was a longstanding problem subject to many discussions (99). Recently, Gnadig & Kuti (100) have shown that positivity conditions when evaluated in terms of the SLAC-MIT data put tight upper and lower bounds on the unknown part of OPOL. A calculation of OPOL in the resonance model was carried out by Jensen, Kovesi-Domokos & Schonberg (101). Lepton pairs fr om hadronic interactions. -The process p +p-'>/ + I + hadrons has been investigated in a number of different models (102). Light cone (103), quark-parton (35, 81) and dual-quark parton models (104) give a qualitatively correct description of data from measurements of p+nuc1eon�JL++JL- + hadrons (105). Electromagnetic mass differences of hadrons.-The electromagnetic mass differences of hadrons are sensitive to the hadronic internal structures, and the deep inelastic results using Cottingham's dispersion integral (106) have been employed to gain some understanding of these differences. A number of theoreti cal difficulties which still persist have so far prevented a full understanding of the origin of these differences (107-9). For a review of the problems see (110). Relationships between inelastic e-p and POp scattering.-Attempts have been made to relate inelastic ep and pp scattering. Following the suggested relationship for elastic scattering by Wu & Yang (111), which was further developed by by University of Kentucky on 08/31/10. For personal use only. Abarbanel, Drell & Gilman (112), Berman & Jacob (113) studied the connection between the ep and pp inelastic cross sections at large momentum transfers and large energy losses, and Low & Treiman (114) and Berman, Bj orken & Kogut Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org (115) have shown that electromagnetic processes may dominate pp scattering at high transverse momentum transfers. Allaby et al (116) have also studied a possi ble relationship. Benecke et al (117), in proposing the hypothesis of limiting frag mentation, provide connections between the two processes, and the general ideas of constituent structure and scaling have been used by Feynman (118) and Bj orken (71) to make speculations about hadron reactions. An application of the fragmentation model to inelastic electron or muon scattering which related hadronic cross sections and electroproduction structure functions has been carried out by Choudhoury & Rajaraman (119). A fragmenta tion model has been studied by Nieh & Wang (120) who predict deviations from scaling, an expectation which will be checked in lepton-proton scattering studies to be carried out at the National Accelerator Laboratory (121). 250 FRIEDMAN & KENDALL Photoproduetion.-]affe (I22) has shown that parton-pair annihilation may contribute to the photoproduction of muon pairs of large invariant mass offpro tons. The contribution can, in principle, be distinguished from background muons from Bethe-Heitler processes and, iffound to scale as is predicted, the measurements can be interpreted in terms of the photon's structure. The production of W bosons may occur through deep inelastic scattering of electrons or muons and through photoproduction where the boson comes from a hadronic vertex. The photoproduction can occur elastically or inelastically, with a number of hadrons in the final state. The elastic production may compare favorably with neutrino induced reactions in the production of this elusive parti cle (123). The deep inelastic electron scattering results we have discussed suggest that the inelastic photoproduction may also contribute. A parton-quark model prediction of the cross sections has been carried out by Mikaelian (124). XII. CONCLUSIONS The deep inelastic electron scattering measurements have established the validity of scale invariance for the proton and neutron over a wide kinematic range, the relative smallness of u. compared to u to and the nature of the differences between the proton and neutron structure functions. These features have sug gested that the nucleon may be composed of point-like constituents, and theories based on this assumption have been offeredas possible explanations of the results. More fundamentally the scattering results have been related to the behavior of the product of two currents at short distances and near the light cone. Both from the point of view of constituent structure and behavior of currents near the light cone, predictions have been made for a wide variety of reactions including neu trino scattering, muon pair production, e+ -e- annihilations, and aspects of hadron-hadron interactions. Only a fraction of these predictions have been tested by comparison with experiment. It is evident that neither the body of experimental results on deep inelastic lepton scattering nor the related theoretical developments can be considered at all complete. In particular, one wishes to know for both the proton and the neu 2 by University of Kentucky on 08/31/10. For personal use only. tron: (a) to what values of v and, independently, q , scale invariance will persist; (b) what is the value of W2N /W2P as x---+1(e) ; the details of how (W2P - W2N) de 2 creases asw---+ oo(d) ; thevalues of RP and RN for large I' and q ; (e) the behavior of Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org spin-dependent effects in deep inelastic scattering; and lastly, (j) what are the particles and their distributions in the final hadronic states. Answers to these experimental questions will help select between the numerous theoretical models presently available. Varied predictions for a, b, and e have been discussed in this review. Some experimental results have appeared for a recent summary of the coincidence electroproduction experiments, see (125)],[ and a number of experi ments are underway to study the nature of the final hadronic states at SLAC (126), Cornell (127), and DESY (128). Extensive discussions and reviews of hadronic final state properties have been presented by Bjorken (71) and by Llewellyn-Smith (129). DEEP INELASTIC ELECTRON SCATfERING 251 In summary, one sees that the deep inelastic results have touched a variety of the unanswered questions in the physics of the weak, electromagnetic, and ha dronic interactions of hadrons and have stimulated substantial theoretical in quiry into the nature of hadronic constituent structure. Many problems have been raised by the theories which have attempted to account for the results. Clarification of many of these problems and additional insights should emerge from the programs of measurements now planned or underway. by University of Kentucky on 08/31/10. For personal use only. Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.org 252 FRIEDMAN & KENDALL LITERATURE CITED 1. Brodsky, S. J., Drell, S. D. 1970. [Final results will be available in Ann. Rev. Nucl. Sci. 20 :147 Riordan, E. M. et al (to be pub 2. Hofstadter, R., Ed. 1963. Electron lished) and Riordan, E. M. 1972. Scattering and Nuclear and Nucleon PhD thesis. MIT] Scattering. New York : Benjamin 26. Breidenbach, M., Kuti, J. 1972. 3. Panofsky, W. K. F., Allton, E. 1958. MIT- CTP-247. In press Phys. Rev. 110:1155 27. Brodsky, S. J., Pumplin, J. 1969. 182:1794 4. Neal, R. B., Ed. 1968. The Stanfo rd Phys. Rev. Two Mile Accelerator. New York: 28. Elias, J. et al 1968. Phys. Rev. 177: Benjamin 2075 5. 14th Int. Conf. High Energy Phys., 29. West, G. B. 1971. Phys. Lett. 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Rev. D 2:2473 presented at 4th Int. ConJ. on Hig h 110. Zee , A Princeton Preprint (Phys. Energy Collisions, Oxford (SLAC Reports In press) 1039) 111. Wu, T. T., Yang, C. N. 1965. Phys. 130. Atwood, W. B., West, G. B. SLA C 137:708 Reo. B 1081 112. Abarbanel, H. D. I., DreIl, S. D., Gil 131. Bodek, A, Friedman, J. I., Sogard, by University of Kentucky on 08/31/10. For personal use only. man, F. I. 1969.Phys. Rev. 177:2458 M. Private communication Annu. Rev. Nucl. Sci. 1972.22:203-254. Downloaded from www.annualreviews.orglO and q'>O.5 (GeVjc)'. A value of 0.18 is used for R. Data fr om (49). The line at "Wz =0.30 is drawn to facilitate comparisons be tween the graphs. Datafor q' below 1.0 (GeVjc)' show deviations from scaleinvariance. 228 FRIEDMAN & KENDALL