M E A S U R E M E N T OF T H E RATIOS
OF D E E P INELASTIC M U O N - N U C L E U S C R O S S S E C T I O N S O N VARIOUS N U C L E I C O M P A R E D TO D E U T E R I U M
European M u o n Collaboration
Aachen, CERN, Freiburg, Heidelberg, Lancaster, LAPP (Annecy), Liverpool, Marseille, Mons, Oxford, Rutherford, Sheffield, Turin, Uppsala, Warsaw, Wuppertal, Yale
J. A S H M A N a, B. B A D E L E K b,l, G. BAUM c,2, j. BEAUFAYS d, C.P. BEE ~, C. B E N C H O U K f I.G. BIRD g,3, S.C. B R O W N ~.4, M.C. C A P U T O c, H.W.K. C H E U N G h, j. C H I M A i,5,
J. C I B O R O W S K I bA, R.W. C L I F F T i, G. C O I G N E T j, F. C O M B L E Y a, G. C O U R T ¢, G. D ' A G O S T I N I f, J. D R E E S k, M. D O R E N ~, N. D Y C E g, A.W. E D W A R D S k,6, M. E D W A R D S i, T. ERNST m,
M.I. F E R R E R O ", D. F R A N C I S e, E. G A B A T H U L E R ¢, J. G A J E W S K I b,l, R. G A M E T ~, V. G I B S O N h,7,
J. GILLIES h, p. G R A F S T R O M o,7, E. H A G B E R G o, K. H A M A C H E R k, D. V O N H A R R A C H P, P. H A Y M A N e, J.R. H O L T ¢, V.W. H U G H E S c, A. J A C H O L K O W S K A d,8, T. JONES ~,9, E.M. KABUSS m.3, B. K O R Z E N k, U. K R O N E R k, S. K U L L A N D E R o, U. L A N D G R A F m, D. LANSKE ~, F. L E T T E N S T R O M o, T. L I N D Q V I S T °, M. M A T T H E W S ¢, Y. M I Z U N O p, K. M O N I G k, F. M O N T A N E T f.7, j. NASSALSKI b,10, T. N I I N I K O S K I d, P.R. N O R T O N i, G. O A K H A M i, l l, R.F. O P P E N H E I M c.t 2, A.M. O S B O R N E d, V. PAPAVASSILIOU c, N. PAVEL k, C. P E R O N I n, H. P E S C H E L k, R. P I E G A I A ~, B. P I E T R Z Y K f, U. P I E T R Z Y K k,13, B. P O V H P, P. R E N T O N h, J.M. R I E U B L A N D d, K. R I T H m'3, E. R O N D I O hA, L. R O P E L E W S K I b'l, D. S A L M O N n,9, A. SANDACZ b, lO, M. S C H E E R ~, T. S C H R O D E R m, K.P. S C H O L E R ~, K. S C H U L T Z E ~, T.-A. SHIBATA P, T. SLOAN ~, A. STAIANO p,14, H.E. STIER m, j. S T O C K m, G.N. T A Y L O R h,l 3, J.C. T H O M P S O N i, T. W A L C H E R a,16, S. W H E E L E R a, W.S.C. WILLIAMS h, S.J. W I M P E N N Y e, 17, R. W I N D M O L D E R S q and W.J. W O M E R S L E Y h,~ 8
a DepartmentofPhysics, UniversityofSheffield, SheffieldS3 7RH, UK b Physicslnstitute, UniversityofWarsaw, PL-00681 Warsaw, Poland
and Institute for Nuclear Studies, PL-00681 Warsaw, Poland c Physics Department, Yale University, New Haven, CT 06520, USA d CERN, CH-1211 Geneva 23, Switzerland
e Department o f Physics, University o f Liverpool, LiverpoolL69 3BX, UK
f Centre de Physique des Particules, Facult~ des Sciences de Luminy, F-13288 Marseille, France g Department o f Physics, University o f Lancaster, Lancaster LA 1 4YB, UK
" Nuclear Physics Laboratory, University o f Oxford, Oxford OXI 3RH, UK Rutherford-Appleton Laboratory, Chilton, Didcot, Oxon 0 X l l OQX, UK i LaboratoiredePhysiquedesParticules, IN2P3, F-74019Annecy-le-Vieux, France k Fachbereich Physik, Universitiit Wuppertal, D-5600 Wuppertal, Fed. Rep. Germany
IIL Physikalisches lnstitut A, Physikzentrum, D-51OO Aachen, Fed. Rep. Germany m Fakultiitfar Physik, Universitiit Freiburg, D- 7800 Freiburg, Fed. Rep. Germany n Istituto di Fisiea, Universitfl di Torino, 1-10125 Turin, Italy
o Department o f Radiation Science, University o f Uppsala, S-751 21 Uppsala, Sweden P Max-Planck Institutffir Kernphysik, D-6900 Heidelberg, Fed. Rep. Germany q Facultb des Sciences, Universitb de L'Etat ~ Mons, B- 7000 Mons, Belgium
Received 22 December 1987
For footnotes see next page
0 3 7 0 - 2 6 9 3 / 8 8 / $ 03.50 © Elsevier Science Publishers B.V.
Volume 202, number 4 PHYSICS LETTERS B 17 March 1988 Results are presented on the ratios of the deep inelastic muon-nucleus cross sections for carbon, copper and tin nuclei to those measured on deuterium. The data confirm that the structure functions of the nucleon measured in nuclei are different from those measured on quasi-free nucleons in deuterium. The kinematic range of the data is such that (Q2) ~ 5 GeV 2 at x ~ 0.03, increasing to (Q2) ~ 35 GeV 2 for x~ 0.65. The measured cross section ratios are less than unity for x £ 0.05 and for 0.25 £ x < 0.7. The decrease of the ratio below unity for low x becomes larger as A increases as might be expected from nuclear shadowing. However, this occurs at relatively large values of Q 2 ( ~ 5 GeV 2) indicating that such shadowing is of partonic origin.
1. Introduction
Prior to the p r e s e n t a t i o n by the E u r o p e a n M u o n Collaboration [ 1 ] o f a c o m p a r i s o n between the n u - cleon structure f u n c t i o n F2 m e a s u r e d o n iron a n d d e u t e r i u m , it h a d generally b e e n a s s u m e d that the deep inelastic cross section o n a heavy nucleus would be given by the i n c o h e r e n t s u m of the cross sections o n the c o n s t i t u e n t nucleons, apart from the effects of the F e r m i m o m e n t u m of the nucleons. The cross sec- tion ratio o ' F e / o " D m e a s u r e d in ref. [ 1 ], where a ve a n d a D are the cross sections per n u c l e o n for iron a n d d e u t e r i u m respectively, showed deviations from u n - ity which could not be interpreted in terms o f the c o n v e n t i o n a l prescription for F e r m i m o t i o n . This ef- fect (which is n o w generally referred to as the E M C
From University of Warsaw, PL-00681 Warsaw, Poland.
z Permanent address, University of Bielefeld, D-4800 Bielefeld, Fed. Rep. Germany.
3 Present address: Max Planck Institut far Kernphysik, D-6900 Heidelberg, Fed. Rep. Germany.
4 Present address: TESA S.A., Renens, Switzerland.
5 Present address: British Telecom, Ipswich, UK.
6 Present address: Jet, Joint Undertaking, Abingdon, UK.
7 Present address: CERN, CH- 1211 Geneva 23, Switzerland.
8 Present address: Laboratoire de l'Acc616rateur Lin6aire, F- 91405 Orsay, France.
9 Present address: Rutherford-Appleton Laboratory, Chilton, Didcot, Oxon OX11 0QX, UK.
m From Institute for Nuclear Studies, PL-00681 Warsaw, Poland.
~ Present address: NRC, Ottawa, Ontario, Canada K1A 0R6.
~2 Present address: AT&T, Naperville, I1, USA.
~3 Present address: Max-Planck Institut fir Neurologische For- schung, D-5000 Cologne, Fed. Rep. Germany.
,4 Present address: INFN, I- 10125 Turin, Italy.
,5 Present address: University of Melbourne, Parkville, Victoria 3052, Australia.
~6 Present address: University of Mainz, D-6500 Mainz, Fed. Rep.
Germany.
,7 Present address: University of California, Riverside, CA 92521, USA.
~s Present address: University of Florida, Gainesville, FL 32611, USA.
effect) was subsequently c o n f i r m e d by data from SLAC [2,3] a n d from the B C D M S Collaboration at C E R N [4]. T h e data show that the nuclear m e d i u m influences the deep inelastic scattering process. A re- cent account of the status o f theoretical models of the effect can be f o u n d in ref. [ 5 ].
T h e differential cross section per nucleon, for one p h o t o n exchange, can be expressed as follows:
d2o "y 8na2ME~
d x d y - 0 4 F 2 N (x, a z )
f
X ( 1 - y + 2 [ I + R N ( x ' Q 2 ) I ) .
I n this expression Q 2 = _ q2, where q is the four-mo- m e n t u m carried by the virtual photon. The usual Bjorken scaling variables a r e x = Q2/2pN'q= Q2/2Mv a n d y = q'pN/p'pN = v/E~,, where p a n d PN are the four- m o m e n t a o f the i n c i d e n t lepton a n d target n u c l e o n respectively a n d M is the p r o t o n mass. T h e final expressions for x a n d y are the values in the frame where the target is at rest, a n d in this frame the en- ergy transferred is v a n d the i n c i d e n t lepton energy is Eo. T h e cross sections d e p e n d o n the n u c l e o n struc- ture f u n c t i o n F 2 N (x, Q2) a n d o n the ratio RN(x, Q2) =aL(X, Q2)/aT(X, Q2); that is, the ratio o f the l o n g i t u d i n a l to transverse virtual p h o t o n cross sections.
M e a s u r e m e n t s o f R N ( x , Q2) at high Q2 [6], indi- cate that R N is small a n d shows n o strong depen- dence o n the a t o m i c n u m b e r A o f the target nucleus [ 7 ]. I f R N is i n d e p e n d e n t o f A, then the ratio o f the cross sections per n u c l e o n for different nuclei A ~ a n d A2 is equal to the ratio o f the structure f u n c t i o n s per nucleon, A F2,/F22. A
The original E M C data [ 1 ] were o b t a i n e d from separate m e a s u r e m e n t s of the absolute values of the n u c l e o n structure f u n c t i o n F2 with iron a n d deuter- i u m targets. These m e a s u r e m e n t s were taken u n d e r
different experimental conditions (beam energy, b e a m intensity, target arrangement and trigger) and at different times. In consequence, the systematic er- rors on the F N ratios were rather large. In addition to the point-to-point systematic errors there was a further overall normalisation uncertainty of _+ 7%.
In order to decrease the systematic errors, a new experiment was designed to measure directly the ra- tios of the nucleon structure functions from nuclear and deuterium targets. Thin targets of carbon, cop- per and tin and a liquid deuterium target were used.
The geometry of the targets was similar and they were interchanged at intervals of a few hours in order to average out the effects of time dependent inefficien- cies in the spectrometer and the beam intensity mon- itoring apparatus.
2. Apparatus and data taking
The experiment was performed in the M2 muon beam line at the CERN SPS using the EMC forward spectrometer to detect the scattering muons and the fast forward hadrons produced from deep inelastic scattering events. The data were taken in several ex- perimental runs, with incident m u o n energies of 100,
120, 200 and 280 GeV.
Fig. 1 shows a diagram of the apparatus. It was de- signed to measure simultaneously the spin depen- dent structure functions using a polarised target and the structure function ratios from the downstream targets. The nuclear and deuterium targets, each of thickness of ~ 8 g / c m 2, were suspended from motor driven booms which allowed them to be inter- changed frequently. The carbon, copper and tin tar- gets were each in the form of four thin discs distributed over the same region in space as the 60 cm long deuterium target, in such a way that the acceptance was the same for each of the targets.
The forward spectrometer was similar to that de- scribed in ref. [8 ] but modified to allow data to be taken at higher incident beam intensities than here- tofore. To achieve this, the drift chambers upstream of the magnet described in ref. [ 8 ] were replaced by the multiwire proportional chambers labelled PVI and PV2 in fig. 1. Each of these chambers had the central region deadened to avoid background from the incident beam. Particles from deep inelastic scat- tering events in this region were detected by several small multiwire proportional chambers placed in the beam region which were specially designed to work in a high intensity environment. These chambers are labelled P0 in fig. 1.
EMC FORWARD
/ / V1.S V3 V2.1
/ / / / / / I \ J
~ nVl (Vl.3)
\ H l l
~.,.~_.v, U" i , I 0 t_~i , Ii~J~qll
II
uU
BHA BHA'
I ~ Fe
SPECTROMETER
P4A
PI, C I P/.B PSA (BHE/F} /MWPC~
\ \ I / I v''J
iO,,
, , , , , . . . . ....,_,,
, i , , ,n
"''"JP~L~ \P"
E H3V XBHB' BHB POC PV2 POD H1H H1V W~.A WSA W5B
W/.8 H4. MS
Fig. 1. Schematic diagram o f the EMC forward spectrometer used to measure the polarised target asymmetries a n d the structure function ratios from various nuclear targets.
Volume 202, number 4 PHYSICS LETTERS B 17 March 1988 3. Data analysis
The raw data were passed through a chain o f pro- grams which performed pattern recognition and geo- metrical reconstruction o f the incident and scattered muons, as well as any charged secondary hadrons which passed through the forward spectrometer mag- net. A vertex fit, using the incident and scattered muons, was also performed. The flux o f muons was determined using a r a n d o m trigger [ 9 ].
In order to avoid regions o f small or rapidly vary- ing acceptance, or where radiative corrections were large, events were only accepted if they passed the se- lection criteria given in table 1. The cuts on y are such that the region at low x and high y, where radiative corrections are large, is thus avoided. The event yields were converted to cross sections using the measured m u o n flux and the appropriate target density and thickness. F o r the deuterium target a small correc- tion ( - 1.4%) was made for events occurring in the mylar walls o f the target. For the heavy nucleon tar- gets a small correction ( - 0 . 9 % ) was made for events occurring in the air between the target discs. The cross section ratios measured from the various experimen- tal runs agreed within errors and were c o m b i n e d in the subsequent analysis.
The measured ratios were corrected for radiative effects, so that they correspond to the single p h o t o n exchange diagram, following the procedures de- scribed in refs. [ 6, l0 ]. The procedure includes cor- rections for the radiative tails o f coherent elastic scattering from the nucleus and o f quasi-elastic scat- tering from the nucleons (the latter includes a
suppression at low
QZ
due to the Pauli exclusion principle), as well as corrections for deep-inelastic radiative scattering. The evaluation o f the deep-ine- lastic radiative corrections requires knowledge o f the absolute value o f the structure functions, both inside and outside the kinematic d o m a i n o f the data. The procedure adopted here was to use a parameterisa- tion o f the measured deuterium F ~ values [ 10] and to evaluate F J f r o m this, using the measured struc- ture function ratios. In this way most o f the uncer- tainty in the radiative correction to the ratio due to the value o f F D in the unmeasured region is can- celled. The radiative corrections were then recalcu- lated and the procedure iterated until convergence was obtained. In practice no significant variation persisted b e y o n d the first iteration. It should be stressed that, after application o f the kinematic cuts described in table 1, the correction factors applied to the cross section ratios are everywhere small. The largest correction factor is at small x, and in the first x b i n (0.02 ~<x~ 0.04) the correction a m o u n t to 3.1%, 7.6% and 11.4% for C / D , C u / D and S n / D respec- tively. The main part o f the radiative correction which does not cancel in the ratios is from the coherent pro- cess. This term is calculated using parameterisations o f the accurately measured nuclear form factors [ 11 ].Uncertainties in the radiative correction procedure are included in the systematic errors, as discussed below.
The measured ratios were also corrected for the unequal numbers o f protons and neutrons in the nu- clear target. The correction was calculated using
F~ (x)/F~
(x) = (0.92 - 0.86x) _+ 0.05, which is con- sistent with the availble data [ 10 ].Table 1
Kinematic cuts applied to the data sample. The quantities p~ and 0p are the momentum and scattering angle respectively of the scattered muon.
Beam energy (GeV)
Q(min)2
(GeV 2) U(min ) (GeV) Ph(min) (GeV)0p(min)
(GeV) 100120 200 280
y~<0.65 for 0.02~<x<0.04 y~<0.75 for 0.04~<x< 0.06 y~<0.85 for x~> 0.06
2 10 20 10
2 10 20 10
3 25 30 10
3 25 40 10
4. Results
T h e final c o r r e c t e d ratios o f the n u c l e o n structure functions o b t a i n e d w i t h C, C u a n d Sn targets relative to those o b t a i n e d w i t h d e u t e r i u m are given in table 2 and plotted in fig. 2. T h e ratios are e x t r a c t e d f r o m the cross section ratios assuming R a = R D. T h e error bars shown in this figure are the total errors, o b t a i n e d by adding the statistical and s y s t e m a t i c errors in q u a d r a t u r e . T h e extent o f the statistical errors is shown by the i n n e r bars. As any v a r i a t i o n w i t h Q2 o f the ratios is relatively small the d a t a f r o m all Q2 are c o m b i n e d for this analysis.
T h e systematic errors g i v e n in table 2 were calcu- lated as follows. F o r each source o f possible system- atic e r r o r the c o n t r i b u t i o n to the e r r o r on the ratio was calculated, separately for each b i n o f x a n d for each target ratio. T h e s e i n d i v i d u a l systematic errors
were t h e n a d d e d in q u a d r a t u r e to obtain the total es- t i m a t e d systematic error.
T h e m a i n p o t e n t i a l sources o f systematic e r r o r are the following (a m o r e detailed discussion can be f o u n d in ref. [ 12 ] ):
( i ) R a d i a t i v e corrections. In o r d e r to e s t i m a t e this e r r o r the u n c e r t a i n t y in the m e a s u r e m e n t s o f the nu- clear elastic f o r m factors a n d in the size o f the Pauli suppression factor were considered. Also i n c l u d e d were the errors on the absolute value o f F D a n d on the ratio F 2 / F 2 a D , as well as t h a t on R N ( X ) . T h e c o m - b i n e d u n c e r t a i n t i e s f r o m these effects are largest for small values o f x, a n d a m o u n t to 1.6%, 1.7% and 3.0%
for the bin 0.02 ~< x < 0.04 and to 1.1%, 1.2% and 1.3%
for the bin 0.04 ~< x < 0.06 for C / D , C u / D a n d S n / D respectively. F o r larger x this e r r o r is less t h a n 1%.
( i i ) C o r r e c t i o n s for non-isoscalarity o f the target.
An e r r o r o f + 0 . 0 5 on F~ ( x ) / F p ( x ) was used in or-
Table 2
Values of the ratios of the structure functions per nucleon for carbon, copper and tin, compared to that for deuterium. In addition to the point-to-point systematic errors there are overall normalisation uncertainties of _+ 0.9%.
Nucleus < x> < Q 2 > F2A/FzD Statistical error Systematic error
C 0.031 5.1 0.923 0.043 0.022
0.050 7.8 1.020 0.035 0.020
0.078 11.4 1.002 0.027 0.019
0.123 14.4 1.044 0.032 0.019
0.173 17.3 0.995 0.037 0.018
0.243 20.2 0.957 0.032 0.018
0.343 24.1 0.902 0.045 0.017
0.442 29.8 0.902 0.069 0.017
0.564 33.6 0.874 0.089 0.016
Cu 0.031 4.4 0.940 0.026 0.023
0.050 8.4 0.963 0.021 0.020
0.079 13.5 0.997 0.017 0.019
0.123 17.9 1.042 0.019 0.019
0.173 21.1 1.018 0.023 0.019
0.244 24.4 1.038 0.021 0.020
0.342 29.5 0.945 0.029 0.018
0.443 34.0 0.957 0.046 0.019
0.573 40.4 0.897 0.061 0.018
Sn 0.031 4.0 0.800 0.042 0.033
0.050 7.7 0.873 0.037 0.027
0.079 11.1 0.948 0.031 0.028
0.123 14.6 1.008 0.037 0.030
0.173 17.1 1.030 0.044 0.031
0.246 19.8 1.009 0.041 0.030
0.343 24.8 0.927 0.056 0.028
0.443 32.4 0.841 0.083 0.026
Volume 202, number 4 PHYSICS LETTERS B 17 March 1988
~u_~
u _ N
a) E H C
1 . 1
0.9 0.8
0.7 , , , , , ,
b)
1.1
t.t. 0.8
0.7 , , , , , ,
0 0.1 0 . 2 0 . 3 0~* I).5 0 6 0.7 x
Fig. 2. Ratios of the nucleon structure functions (a) F c / F D, (b)
C u D F2 F2 S n D a function ofx. The ratios are ex-
F2 /F2 and (c) as
tracted from the cross sections assuming R A ---A D, and are cor- rected for radiative effects. The errors shown are the total errors, obtained by adding the statistical and systematic errors in quad- rature. The extent of the statistical errors is shown by the inner bars.
d e r to estimate the uncertainty on this correction. The correction is largest for S n / D a n d a m o u n t s to + 0.4%
at small x, rising to + 0.8% at large x.
( i i i ) Vertex selection criteria. T h e v e r t e x d i s t r i b u - tions along the b e a m d i r e c t i o n for d e u t e r i u m a n d the heavy nuclear targets have a somewhat different shape because the d e u t e r i u m target is c o n t i n u o u s a n d the nuclear targets were discrete discs. S o m e u n c e r t a i n t y thus arises in the v e r t e x selection because o f the tails
o f the distributions and from b a c k g r o u n d events. The possible e r r o r on the ratios due to this source was in- vestigated b o t h b y M o n t e Carlo s i m u l a t i o n a n d b y studying the sensitivity o f the ratios for different ver- tex cuts. T h e e s t i m a t e d e r r o r on the ratios F2/F2A D is + 0.6%, a n d is i n d e p e n d e n t o f x .
( i v ) A c c e p t a n c e differences. T h e thicknesses in t e r m s o f r a d i a t i o n a n d i n t e r a c t i o n lengths o f the var- ious targets are different a n d hence the profiles o f the hit d i s t r i b u t i o n s in the wire chambers, a n d p o t e n - tially the r e c o n s t r u c t i o n efficiencies, could be target d e p e n d e n t . This p r o b l e m was i n v e s t i g a t e d in two ways. F i r s t l y a d e t a i l e d M o n t e Carlo s i m u l a t i o n o f the e x p e r i m e n t was carried out. Background hits were a d d e d b y t a k i n g a real event in a s i m i l a r k i n e m a t i c region to the generated event, a n d f r o m the s a m e tar- get, a n d a d d i n g all the hits, plane b y plane, except those which h a d been successfully used b y the recon- struction p r o g r a m s as belonging to a track. The sec- o n d m e t h o d consisted o f c o m p a r i n g the event yields, after the usual selection criteria, in the p o l a r i s e d tar- get (see fig. l ), in the presence o f different h e a v y tar- gets in the b e a m . N o significant v a r i a t i o n o f the r e c o n s t r u c t i o n efficiency with x was f o u n d w i t h i n the s y s t e m a t i c e r r o r ascribed for this effect, n a m e l y + 1.5% for C / D a n d C u / D a n d + 2 . 7 % for S n / D .
I n a d d i t i o n to the a b o v e errors there is a overall n o r m a l i s a t i o n u n c e r t a i n t y (affecting all b i n s o f x in the s a m e w a y ) a m o u n t i n g t o + 0 . 9 % for each o f the m e a s u r e d ratios. This error arises f r o m the statistical e r r o r on the b e a m tracks a c c u m u l a t e d to m e a s u r e the m u o n flux [ 9 ], a n d on the u n c e r t a i n t i e s in the target masses.
T h e integrals
0 . 7
J [ F g ( x ) - F D ( x ) ]
/'A--D= d x
0 . 0 2
Table 3
Values of the integral I A- D for different targets.
Target combination x region i A- D × 103
value statistical error systematic error
C/D 0.02-0.7 - 4 . 7 + 1.8 + 2.3
Cu/D 0.02-0.7 - 1.2 + 1.2 _+ 2.3
Sn/D 0.02-0.7 -3.6 + 2.4 + 3.5
have been evaluated, and the results are shown in ta- ble 3. The value o f F 2 D (x) was taken from ref. [ 10]
and the ratio F~ ( x ) / F D (x) was taken from table 2.
The systematic error given was estimated by calculat- ing the contribution to the integral I A- D separately for each source of systematic error, then adding the resultant errors in quadrature. This integral repre- sents the change in the m o m e n t u m fraction carried by quarks and antiquarks. The results indicate a pos- sible reduction in the visible m o m e n t u m fraction per nucleon for heavy nuclei compared to that for deuterium.
5. Discussion
The main features of the ratios of the nucleon structure functions F 2 / F : A D can be summarised as follows: There is a depletion below unity for values of x>~0.25. The ratio is consistent with unity, or a small rise above unity in the x range roughly between 0.08 and 0.20. For small x (~<0.05), the measured ratios lie below unity, and the magnitude of the de- viation from unity grows with increasing atomic weight.
Taking into account the quoted statistical, system- atic and overall normalisation errors, the measured ratios on C u / D are compatible with the original mea- surements on F e / D [ 1,10], except for a difference in the two lowest x points of 1-2 tr (fig. 3). The present data, extending lower in x, indicate a turning over of the ratio at low x. This effect becomes increasingly apparent at higher atomic weight.
A discussion of other experimental data on quark distributions in nuclei, and on the status of models for these effects, can be found in ref. [ 5 ]. Two main classes of models have emerged for the region x ~ 0. l, namely the conventional nuclear physics models which involve a convolution of the contributions of the constituents (n, N, A, multiquark bags, etc.) of the nucleus and the
Q 2rescaling model. This latter model does not include the effects of Fermi motion and is applicable only for x < 0.7. Both these models can be expressed as a change in the scale of either x
o r Q2 ( o r
both) in nuclear matter. Empirically any model with such a scale change can be made to fit the existing data. Furthermore, the data suggest that the distance over which quarks move is larger for bound
, i i
tti EMc cu0
1.2 • EMC (Fe/D)
o B E D H 5 IFe/D}
11 A SLAE {Fe/D)
o~ - [ i * ~ ~
0 8
0.7 , , , I , ! , i
0.2 O.t, 06 08
X
Fig. 3. Ratios of the nucleon structure functions Fc2"/F~ (this experiment) - full circles, F2 /F2 Fe n [10] - full squares (inner errors are statistical, outer are total i.e. combined statistical and systematic), F2 /F2 re o [4] - open circles and F2Fe/F2D [2,3] - open triangles. The error bars shown are the total errors, ob- tained by adding the statistical and systematic errors in quadrature.
than for quasi-free nucleons.
None of the models in these categories can be used to describe the ratios observed at low values ofx. The vector dominance model ( V D M ) [13] partly de- scribes nuclear shadowing phenomena for real pho- tons and for low-Q 2 and low-x virtual photons.
However, any VDM effects are predicted to fall off as ~ 1/Q2, and so will have largely died out in the Q2 range of this experiment. A possible explanation for shadowing at large Q2 is the model of Nicolaev and Zakharov [ 14 ]. In this model the longitudinal extent Az~ 1/Mx of the partons seen by the virtual photon is considered. For x<x~A -~/3, where x c ~ M J M N
~ 0.15, partons from different nucleons are whitin a
c o m m o n volume covering the whole nucleus in the
longitudinal direction. Shadowing below xc is attrib-
uted to the fusion of overlapping partons and, from
m o m e n t u m conservation, a rise in F ' I / F D above un-
ity (antishadowing) is predicted in the region of
x~xc. This model does not explain the large-x behav-
iour of the data, the physics of which may well mod-
ify the low-x predictions of the model. However, the
model is in qualitative agreement with the data ex-
cept that it predicts a stronger A dependence than seen
in the data. The Q2 dependence of nuclear shadow-
ing has been considered by Qiu [ 15 ] using modified
Altarelli-Parisi equations which take into account
parton recombination effects in nuclei. Qiu con-
Volume 202, number 4 PHYSICS LETTERS B 17 March 1988 cludes t h a t s h a d o w i n g will v a n i s h o n l y slowly w i t h
i n c r e a s i n g Q2.
I n s u m m a r y , these i n v e s t i g a t i o n s c o n f i r m p r e v i o u s o b s e r v a t i o n s t h a t t h e n u c l e o n s t r u c t u r e f u n c t i o n s for b o u n d a n d q u a s i - f l e e n u c l e o n s b e h a v e differently.
T h e o b s e r v e d s t r u c t u r e f u n c t i o n r a t i o falls b e l o w u n - ity at large x ( > 0 . 2 5 ) , t e n d s to rise a b o v e u n i t y at m e d i u m x ( ~ 0 . 1 5 ) a n d t h e n falls a g a i n b e l o w u n i t y at s m a l l x ( ~< 0 . 0 5 ) . I n t h e s m a l l - x r e g i o n ( ( Q2 ) ~ 5 G e V 2) this e x p e r i m e n t shows e v i d e n c e for n u c l e a r s h a d o w i n g s i m i l a r to t h a t o b s e r v e d at l o w e r v a l u e s o f Q2 at SLAC [ 16].
Acknowledgement
We w o u l d like to t h a n k all p e o p l e i n t h e v a r i o u s l a b o r a t o r i e s w h o c o n t r i b u t e d to t h e c o n s t r u c t i o n , op- e r a t i o n a n d a n a l y s i s o f this e x p e r i m e n t . T h e s u p p o r t o f t h e C E R N s t a f f i n o p e r a t i n g t h e SPS, m u o n b e a m a n d c o m p u t e r facilities is gratefully a c k n o w l e d g e d .
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