We measured the differences in R=σ_L/σ_T and the cross-section ratio σA/σD in deep-inelastic electron scattering from D, Fe, and Au nuclei in the kinematic range 0.2≤x≤0.5 and 1≤Q^2≤5 (Gev/c)^2. Our results for R^A-R^D are consistent with zero for all x and Q^2, indicating that possible contributions to R from nuclear higher-twist effects and spin-0 constituents in nuclei are not different from those in nucleons. The European Muon Collaboration effect is reconfirmed, and the low-x data from all recent experiments, at all Q^2, are now in agreement

Dasu, S.

Filippone, B. W.

Jourdan, J.

McKeown, R.

Milner, R.

Potterveld, D.

Walker, R. C.

English

Caltech Authors - Main

VOLUME 60, NUMBER 25 PHYSICAL REVIEW LETTERS 20 JUNE 1988 
Measurement of the Difference in R -aLiar and of aAfa 0 in Deep-Inelastic e-D, e-Fe, 
and e-Au Scattering 
S. Dasu, (I) P. de Barbaro, (I) A. Bodek, (I) H. Harada, (I) M. W. Krasny, (I) K. Lang, (I) E. M. Riordan, (I) 
R. Arnold, <2> D. Benton, <2> P. Bosted, <2> L. Clogher, <2J G. deChambrier, <2J A. Lung, <2J S. E. Rock, <2J 
Z. M. Szalata, <2> R. C. Walker, <3> B. W. Filippone, (J) J. Jourdan, <3> R. Milner, <3> R. McKeown, <3> 
D. Potterveld, <3> A. Para, <4> F. Dietrich, <5> K. Van Bibber, <5> J. Button-Shafer, <6> B. Debebe, <6> R. S. 
Hicks, <6> R. Gearhart,{?) L. W. Whitlow, <s> and J. Alster<9> 
(!)University of Rochester, Rochester, New York 14627 
<2>The American University, Washington, DC 20016 
O>california Institute of Technology, Pasadena, California 91125 
<4> Fermi National Accelerator Laboratory, Batavia, Illinois 60510 
<s> Lawrence Livermore National Laboratory, Livermore, California 94550 
<6>University of Massachusetts, Amherst, Massachusetts 01003 
<?>stanford Linear Accelerator Center, Stanford, California 94305 
<s>Stanford University, Stanford, California 94305 
<9>University ofTei-Avit•, Ramal Avit•, Tei-AL•iv 69978, Israel 
(Received 2 February 1988) 
We measured the differences in R-adar and the cross-section ratio aA/a0 in deep-inelastic electron 
scattering from D, Fe, and Au nuclei in the kinematic range 0.2::5x::50.5 and I ::5Q 2 ::55 (GeV/cV 
Our results for RA- R 0 are consistent with zero for all x and Q 2, indicating that possible contributions 
to R from nuclear higher-twist effects and spin-0 constituents in nuclei are not different from those in 
nucleons. The European Muon Collaboration effect is reconfirmed, and the low-x data from all recent 
experiments, at all Q 2, are now in agreement. 
PACS numbers: 25.30.Fj, 12.38.Qk, 13.60.Hb 
The discovery of the difference in the deep-inelastic 
cross sections for iron and deuterium targets, 1- 4 known 
as the European Muon Collaboration (EMC) effect, has 
sparked considerable activity in the theoretical study of 
deep-inelastic lepton scattering from nuclear targets. 
There are numerous models 5 for the EMC effect which 
are built on a variety of ideas (a swelling of nucleons 
bound in a nucleus, the presence of tightly bound pions, 
~ isobars, multiquark clusters, etc., in nuclei, and others) 
which result in a change of quark distributions in nuclei 
compared with those in free nucleons. The less drastic 
models attribute the EMC effect to nuclear-binding 
corrections alone. To compare the theoretical predic-
tions for the structure-function ratio with the experimen-
tal results on the cross-section ratio, it is essential to 
measure the differences in R -=rrdrrr, the ratio of longi-
tudinal (aL) and transverse (rrr) virtual-photon absorp-
tion cross sections. Some models 6 predict a large 
difference in the quantity R for deuterium and iron 
(RFe_R 0 =0.1-0.15). Others, 5•7 including those 
based on quantum chromodynamics (QCD), predict a 
negligible difference (R Fe-R 0 = 0.002). Some au-
thors 8 have conjectured that higher-twist effects might 
be different for different nuclei, and yield an atomic-
mass (A) dependence of R. The quantity R is a sensitive 
measure of pointlike spin-0 constituents (e.g., tightly 
bound diquarks) of the nucleus. Therefore an A depen-
dence of R could alter our view of nuclear structure in 
terms of spin- t quarks and vector gluons. The large ini-
tial discrepancy at low x between rrAfrr 0 as measured 
at CERN 1 (European Muon Collaboration) and at 
SLAC 2-4 at different angles and energies could have 
been due to either a Q 2 dependence, a value 9 of R Fe 
- R 0 = 0.15, or an experimental uncertainty. There 
were indications in previous data 3 (SLAC El39) that 
such a difference in R may have been observed. 
We have undertaken precision measurements of deep-
inelastic electron-scattering cross sections on deuterium, 
iron, and gold targets, to resolve these questions. The 
differential cross section for scattering of an unpolarized 
charged lepton with an incident energy E, scattering an-
gle 8, and final energy E' can be written in terms of 
structure functions F 1 and F 2 as 
d 2rr(E,E',8)/d f1 dE'= (4a 2E'2/Q 4)cos 2( t e)[F2(x,Q 2)/v+2tan 2( t 8)F1 (x,Q 2)/M] 
-=rrrr(x,Q 2Hl +tR(x,Q 2)], (I) 
where a is the fine-structure constant, M is the nucleon mass, v = E - E' is the energy of the virtual photon which medi-
ates the interaction, Q 2 =4EE'sin 2(t8) is the invariant four-momentum transfer squared, and the variable x=Q 2/ 
2Mv is a measure of the longitudinal momentum carried by struck nucleon constituents. In Eq. (1) the differential 
© 1988 The American Physical Society 2591 
VOLUME 60, NUMBER 25 PHYSICAL REVIEW LETTERS 20 JUNE 1988 
cross section is also related to R, with 
and E=[I +2(1 + v2/Q 2han 2( tO)] -I representing the 
virtual-photon flux and polarization, respectively. R can 
also be expressed as R =Fd2xFJ, where the longitudinal 
structure function FL=(1+4M 2x 2/Q 2)F2-2XFI is 
proportional to aL. Within the parton models and QCD, 
contributions to FL originate from gluon emission, target 
mass effects, 10 and pointlike spin-0 constituents. The 
structure function 2xF1 (x) is equal to l:;e/[xq;(x,Q 2) 
+xq;(x,Q 2)], where xq;(x,Q 2) and xq;(x,Q 2) are 
quark and antiquark momentum distributions, and e; is 
the quark electric charge for the ith flavor. In this paper 
the differential cross sections per average nucleon (in-
cluding the correction for neutron excess in Fe and Au) 
are represented as aA for Fe and Au and a 0 for D. 
The electron beams and the 8-GeV spectrometer facil-
ity, at the Stanford Linear Accelerator Center (SLAC), 
are uniquely suited for a measurement of R, because 
deep-inelastic cross sections can be measured to better 
than ± I% over a wide range of E at various x and Q 2. 
In this experiment the SLAC beam was tuned over a 
broad energy range (between 3.75 and 19.5 GeV) with a 
precision of ± 0.1 %. A single spectrometer with fixed 
acceptance was used to detect electrons by varying scat-
tered momenta and angles between l and 8 GeV, and 
II o and 46°, respectively. The kinematic region was 
limited by the background levels, counting rates, and the 
size of radiative corrections to the x, Q 2 range of 0. 2 
<x<0.5 and I <Q 2 < 10 (GeV/cV Cross sections 
were measured, for each (x,Q 2) point, at up to five 
different values of E (with a typical E range of 0.35) on 
targets of liquid D2 [2.6% radiation lengths (r.l.)J, Fe 
(2.6% and 6% r.l.), and Au (6% r.U. Values of R for 
each target have been extracted from these measure-
ments and will be presented in a future communication. 
The results for the difference RA- R 0 and the ratio 
aAfa0 have smaller systematic errors and are presented 
here. 
Accurate determination of cross sections demanded 
careful monitoring of the apparatus during data taking. 
For the aAfa0 and RA- R 0 measurements, the stability 
of data-taking conditions and the differences between 
running conditions for the liquid D2 a_nd Fe targets were 
crucial. Extensive measures were taken to minimize sys-
tematic errors (summarized in Table 0. The beam posi-
tion and angle were continuously monitored and con-
trolled. The total incident charge was measured with 
two precision toroidal charge monitors, which were fre-
quently calibrated during the experiment. Errors arising 
from any time-dependent fluctuations were reduced by 
the accumulation of the data in small runs alternating 
between various targets. The liquid target assembly con-
2592 
TABLE L Typical systematic errors on a.A/a0 and 
RA-RD. 
Uncertainty Error(±) 
Source A or D aA/aD RA-RD 
Beam steering 0.003° 0.1% 0.004 
Incident energy 0.1% 0.3% 0.014 
Charge measurement 0.1% 0.1% 0.004 
D target density 0.2% 0.2% 0.010 
D acceptance 0.1% 0.1% 0.004 
e + /e- background 0.1% 0.1% 0.004 
A neutron excess 0.2% 0.2% 
Total point to point 0.4% 0.019 
Target length error 0.5%-1.5% 1.0% 
Radiative corrections 0.5% 0.5% O.Dl5 
sisted of an aluminum tube through which liquid D2 
flowed continuously. The liquid-D2 pressure and temper-
ature (and hence average density) were measured con-
tinuously. A new detector package was used to attain an 
electron-detection efficiency of 99.5% while maintaining 
pion misidentification level below 10 -s. It included an 
upgraded hydrogen-gas Cherenkov counter, a ten-plane 
proportional wire chamber system, a new five-layer 
lead-glass shower-counter array, and three planes of 
plastic scintillation counters. The ratio of yields n/e was 
less than 120 (n contamination < 0.1%) and was the 
same within a factor of 2 for Fe and D targets, at all the 
kinematic settings. The flux of electrons from process-
es 11 other than deep-inelastic scattering was measured 
and subtracted. 
Radiative corrections to deep-inelastic electron 
scattering can be separated into two distinct contribu-
tions. 12 The corrections to high-momentum-transfer 
scattering process due to vacuum polarization, vertex 
correction, and photon emission are called "internal." 
The corrections due to electron energy loss in traversing 
the target material due to bremsstrahlung and ionization 
are called "external." The "internal" corrections were 
calculated with the prescription of Bardin. 13 These did 
not differ by more than 1% between the deuterium and 
solid targets. The "external" effects, calculated in ac-
cord to the prescription of Mo and Tsai, 12 are strongly 
dependent on the target radiation lengths and hence are 
different for the Fe and D targets. Significant improve-
ments 14 have been made by use of the complete formal-
ism rather than the energy-peaking approximation ex-
pressions derived by Tsai. The cross sections and the 
values of R obtained for targets of different radiation 
lengths were compared to test the calculations of the ra-
diative corrections. The values of R extracted from the 
2.6% and 6% Fe-target data of this experiment were the 
same within statistical errors ( (R Fe6 - R Fe2·6) = -0.040 
± 0.042). The average ratio of the cross sections 
aFe6/aFe2·6 was 1.017 ± 0.005 ± 0.020. In addition, radi-
VOLUME 60, NUMBER 25 PHYSICAL REVIEW LETTERS 20 JUNE 1988 
TABLE II. Values of RA- R 0 , and aA/a0 averaged over t with statistical (stat.) and point-to-point systematic (syst.) errors. 
There is an additional error of ± 0.015 in RA- R 0 because of radiative corrections and an overall normalization error (!1) in aA/a0 
of ± 1.1%. 
Target r.l. X Q2 llt' Value 
Fe 2.6 0.20 1.00 0.24 -0.040 
Fe 6.0 0.20 1.00 0.24 -0.084 
Au 6.0 0.20 1.00 0.24 -0.042 
Fe 6.0 0.20 1.50 0.23 -0.140 
Fe 6.0 0.20 2.50 0.33 0.141 
Fe 6.0 0.35 1.50 0.20 0.037 
Fe 6.0 0.35 2.50 0.28 0.104 
Fe 6.0 0.35 5.00 0.28 0.023 
Fe 2.6 0.50 2.50 0.37 0.040 
Fe 6.0 0.50 2.50 0.37 0.021 
Fe 6.0 0.50 5.00 0.39 -O.D18 
ative corrections for SLAC El39 data with 12% (unpub-
lished), 6% and 2% r.l. Fe targets 3 were calculated. The 
cross sections for 12% r.l. data agreed with 2% and 6% 
data at all kinematics only after the application of the 
improved radiative corrections. We have therefore ap-
plied the improved radiative corrections to the SLAC 
El39 data as well. These SLAC El39 results are higher 
than the peaking approximation results 3 by about I%. 
The improvements in "external" corrections did not 
affect the aFefaD results of SLAC E87 2 and SLAC 
E61 4 data, since those experiments used D and Fe tar-
gets of equal radiation lengths. 
The difference RA- R D was determined by our mak-
ing linear fits, weighted by the statistical and point-to-
point (t-uncorrelated) systematic errors, to the ratio of 
cross sections, 
aAfaD=F1/FP[l +t'(RA- RD)], 
versus t' = tf( 1 + tR D). The RA- R D results are thus 
independent of absolute normalizations of target length, 
spectrometer acceptance, beam intensity, and energy 
scale. They are also insensitive to changes in acceptance 
with t, offsets in beam energy, spectrometer angle, sur-
vey errors, long-term charge-monitor drifts, and "inter-
nal" radiative corrections. The values of RA- R D for all 
(x,Q 2) points are shown in Table II. The average X2 per 
degree of freedom for the goodness of fit was 0. 7 indicat-
ing that the estimate of systematic uncertainty is conser-
vative. The results are also plotted against x for various 
Q 2 values in Fig. 1 (a). Our results for RA- R D show 
no x or Q 2 dependence, and are consistent with zero at 
all measured values. The average value is (RA - R D) 
=0.001 ±0.018 (statistical) ±0.016 (systematic). 
The results for the ratio aAfaD averaged over various 
t points are also shown in Table II. The overall normali-
zation error (~) in aA I aD of ~ = ± 1.1% is dominated by 
the errors in target length 15 measurement and radiative 
corrections. Our results for aAfaD averaged over Q 2 
RA-RD aAJaD 
Stat. Syst. Value Stat. Syst. 
0.059 0.021 1.006 0.005 0.004 
0.058 0.020 1.022 0.005 0.004 
0.060 0.021 1.021 0.005 0.004 
0.057 0.018 1.028 0.004 0.002 
0,075 0.025 1.023 0.006 0.002 
0.080 0.027 1.000 0.005 0.002 
0.055 0.019 0.995 0.005 0.002 
0.059 0.016 0.981 0.005 0.002 
0.059 0.016 0.923 0.009 0.005 
O.Q38 0.014 0.933 0.005 0.002 
0.050 0.017 0.939 0.006 0.004 
and t are compared with data from SLAC El39 (with 
improved radiative corrections, ~ = ± 1.3%), 3 SLAC 
E87 (~=±l.l%), 2 and SLAC E61 (~=±4.2%) 4 in 
(a) E140 (this expt) 
Au Fe 0 2 
0 • 1.0 
0.2 t • 
1.5 
1 • 2.5 Cl ~ + ~ 5.0 0: 0 - - ------
<( 
0: 
-0.2 
1 .1 
Cl 
10 1.0 
<( ..... 
10 
0.9 
0.8 
1.1 
Cl 
lt'1>M .. r T·1------10 < 
10 
0.8 
0 0.4 0.8 
X 
FIG. I. (a) The results for R- R 0 are plotted as functions 
of x; 2.6% and 6% Fe, and Au (open symbol) targets are plot-
ted separately. Statistical and systematic errors are added in 
quadrature. (b),(c) The results for aA/a0 are plotted as func-
tions of x and are compared with other (b) electron and (c) 
muon experiments. Our data from Fe and Au (x =0.2) targets 
are each averaged over t and Q 2• Statistical and point-to-point 
systematic errors are added in quadrature for all experiments. 
The overall normalization errors (!1) are discussed in text. 
2593 
VOLUME 60, NUMBER 25 PHYSICAL REVIEW LETTERS 20 JUNE 1988 
Fig. I (b). There is excellent agreement between all the 
SLAC data. In Fig. l (c) our data are compared with 
high-Q 2 data from CERN muon experiments by the 
Bologna-CERN-Dubna-Munich-Saclay (BCDMS) col-
laboration (~ == ± 1.5%), 16 and the EMC (preliminary 
results,~=± 0.8%). 17 The initiallow-x discrepancy be-
tween EMC and SLAC data is now resolved. 
We conclude that RA- R 0 is consistent with zero, in 
agreement with models which predict no A dependence 
of R (e.g., QCD). We rule out mode!s 6 predicting a 
large difference RA- R 0 . Our data indicate that possi-
ble contributions to R from nuclear higher-twist effects 
and spin-0 constituents in nuclei are not different from 
those in nucleons. The aAfa 0 measurements can now be 
identified with the structure-function ratios F1/FP and 
F?/FP. The EMC effect is confirmed with very small 
errors and all recent data are now in agreement. Thera-
tio aA/a 0 is larger than unity at low x, and is therefore 
inconsistent with models using nuclear-binding correc-
tions only. Because the ratio Ff/FP is equal to the ratio 
of quark distribution functions, we conclude that the 
EMC effect is due to a nontrivial difference in the quark 
distributions between heavy nuclei and the deuteron. 5•7 
We acknowledge the support of Professor B. Richter 
and the SLAC staff, which was crucial for the success of 
this experiment. This research was supported by Depart-
ment of Energy Contracts No. DE-AC02-76ERI3065, 
No. DE-AC02-76ER02853, No. DE-AC03-96SF00515, 
and No. W-7405-ENG-48, and National Science Foun-
dation Contracts No. PHY84-l0549 and No. PHY85-
05682. 
11. J. Aubert eta/., Phys. Lett. 123B, 275 (1983); G. Bari et 
a/., Phys. Lett. 163B, 282 (1985). 
2594 
2A. Bodek et a/., Phys. Rev. Lett. SO, 1431 (1983), and 51, 
534 (I 983). 
3R. G. Arnold et a/., Phys. Rev. Lett. 52, 727 (1984), and 
SLAC Report No. SLAC-PUB-3257, 1983 (unpublished). 
4S. Stein eta/., Phys. Rev. D 12, 1884 (1975). 
5E. Berger and F. Coester, Annu. Rev. Nucl. Part. Sci. 37, 
463 (1987). 
6Bo-Qiang Ma and Ji Sun, Beijing University Report No. 
Print-86-1217, 1986 (unpublished). 
7F. E. Close et a/., Phys. Lett. 129B, 346 (1983) (QCD 
model); R. D. Smith, Phys. Lett. B 182, 283 (1986) (convolu-
tion model). 
BE. V. Shuryak, Nucl. Phys. A446, 259C (1985). 
91. A. Savin and G. I. Smirnov, Phys. Lett. 14SB, 438 
(1984). 
lOA. De Rujula et a/., Ann. Phys. 103, 315 (1977); G. Al-
tarelli and G. Martinelli, Phys. Lett. 768, 89 (1978). 
II L. S. Rochester eta/., Phys. Rev. Lett. 36, 1284 (1976). 
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Y. S. Tsai, SLAC Report No. SLAC-PUB-848, 1971 (unpub-
lished); equation (C. I) from SLAC-PUB-848 was used to cal-
culate the "external" effects·. The shape of the internal brems-
strahlung was approximated by that of the external brems-
strahlung (i.e., the method of equivalent radiators) in the eval-
uation of this double integral. 
13D. Y. Bardin and N. M. Shumeiko, Yad. Phys. 29, 499 
(1979) [Sov. J. Nucl. Phys. 29, 969 (1979)]; D. Y. Bardin et 
a/., Nucl. Phys. B 197, I (1982), and references therein. 
14S. Dasu, Ph.D. thesis, University of Rochester Report No. 
UR-1059, 1988 (unpublished). 
15Uncertainties on the target lengths are ±0.5% forD and 
Fe 6% r.l. targets, and ± 1.5% for the Fe 2.6% r.l. and Au 6% 
r.l. targets. 
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Measurement of the Difference in R=σ_L/σ_T and of σ^A/σ^D in Deep-Inelastic e-D, e-Fe, and e-Au Scattering

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Measurement of the Difference in R=σ_L/σ_T and of σ^A/σ^D in Deep-Inelastic e-D, e-Fe, and e-Au Scattering

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