Proton and deuteron F2 structure functions in deep inelastic muon scattering
N e w M u o n Collaboration
Bielefeld University, CERN, Freiburg University, Max Planck Institut f'tir Kernphysik,
Heidelberg, Heidelberg University, Mainz University, Mons University, Neuchatel University, NIKHEF-K, Oxford University, Saclay D A P N I A / S P P , University of California, Santa Cruz, Paul Scherrer Institute, Torino University and I N F N Torino, Uppsala University,
Institute for Nuclear Studies, Warsaw, Warsaw University, Wuppertal University P. Amaudruz a,l M. Arneodo b, A. Arvidson c, B. Badelek d, G. Baum e, j. Beaufays f.z, I.G. Bird g.3, M. Botje a,4, C. Broggini h,5, W. Briickner 8, A. Brtill i, W.J. Burger a.6,
J. Ciborowski f,7, R. van Dantzig f, H. D6bbeling g,8, j. D o m i n g o a,9, j. Drinkard 5, D. Dyring c, H. Engelien i, M.I. Ferrero b, L. Fluri h, p. Grafstr6m c, lO, T. Granier k, D. von Harrach 8,11, M. van der Heijden f,4, C. Heusch j, Q. Ingram a, K. Janson-Prytz c, M. de Jong f,11,
E.M. KabuB 8,11, R. Kaiser i, T.J. Ketel f F. Klein ~, B. Korzen m, U. Kruner m, S. Kullander c, K. Kurek d, U. Landgraf i, F. Lettenstr6m i, T. Lindqvist c, G.K. Mallot n,~, C. Mariotti b.~2, G. van Middelkoop n,f, A. Milsztajn k, y . Mizuno g,13, j. Nassalski o, D. N o w o t n y 8.14, J. Oberski f, N. Pavel m.15, C. Peroni b, H. Peschel m.16, B. Povh g'P, R. Rieger ~, K. Rith 8,
d d o g a 1 8
K. Rbhrich ~''7, E. Rondio , L. Ropelewski , A. Sandacz , C. Scholz , R. Schumacher ' , U. Sennhauser a,,9, F. Sever e,20, T.-A. Shibata P, M. Siebler e, A. Simon 8, A. Staiano b, G. Taylor q,21, M. Treichel 8,22, M. Virchaux k, J.L. Vuilleumier h, T. Walcher Q, R. Windmolders r and F. Zetsche ~
a Paul Scherrer Institute, CH-5234 Villigen, Switzerland b Istituto di Fisica, Universitd di Torino, 1-10125 Turin, Italy
c Department o f Radiation Science, University o f Uppsala, S-75121 Uppsala, Sweden d University o f Warsaw, PL-O0681 Warsaw, Poland
• Physics Department, Bielefeld University, W-4800 Bielefeld, FRG 23 f NIKHEF-K, P.O. Box 4395, NL- 1009 A J Amsterdam, The Netherlands 24 8 M a x Planck InstitutJ~r Kernphysik, W-6900 Heidelberg, FRG 23 h UniversitO de Neuch~tel, CH-2000 Neuchdtel, Switzerland
Physics Department, Freiburg University, W-7800 Freiburg, FRG 23
J Institute for Particle Physics, University o f California, Santa Cruz, CA 95064, USA k DAPNIA/SPP, CE Saclay, F-91191 Gif-sur- Yvette, France
Institut fur Kernphysik, Mainz University, W-6500 Mainz, FRG 23 m Physics Department, Wuppertal University, W-5600 Wuppertal, FRG 23
CERN. CH-1211 Geneva 23, Switzerland
o Institute for Nuclear Studies, PL-O0681 Warsaw, Poland P Heidelberg University, W-6900 Heidelberg, FRG z3
q Nuclear Physics Laboratory, University o f Oxford, Oxford OX1 3RH, UK Facultd des Sciences, Universitk de Mons, B- 7000 Mons, Belgium
Volume 295, number 1,2 Received 29 July 1992
PHYSICS LETTERS B 26 November 1992
The structure functions F2 p and/z 2 ~ measured by deep inelastic muon scattering at incident energies of 90 and 280 GeV are presented. These measurements cover a large kinematic range, 0.006 ~< x ~< 0.6 and 0.5 ~< Q2 ~< 55 GeV 2, and include the first precise data at small x, where large scaling violations are observed. The data agree with earlier results from SLAC and BCDMS but exhibit differences with respect to those of EMC-NA2. Extrapolations to small x of recent phenomenological parton distributions are shown to disagree with the present results.
I. Introduction
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 F 2 ( x , Q2) reflects t h e m o m e n t u m d i s t r i b u t i o n o f q u a r k s in t h e n u c l e o n , an i m p o r t a n t aspect o f its i n t e r n a l structure. T h e Q2 Present address: TRIUMF, Vancouver, Canada, BC V6T 2A3.
2 Present address: Trasys, Brussels, Belgium.
3 Present address: DAPNIA, Saclay, F-91191 Gif-sur-Yvette, France.
4 Present address: NIKHEF-H, NL-1009 AJ Amsterdam, The Netherlands.
5 Present address: INFN, Laboratori Nazionali del Gran Sasso, 1-67010 Assergi, Italy.
6 Present address: Universit6 de Gen~ve, CH-1211 Geneva 4, Switzerland.
7 Present address: University of Warsaw, PL-00681 Warsaw, Poland.
s Present address: GSI, W-6100 Darmstadt, FRG.
9 Present address: CEBAF, Newport News, VA 23606, USA.
~o Present address: CERN, CH-1211 Geneva 23, Switzerland.
1~ Present address: University of Mainz, W-6500 Mainz, FRG.
12 Present address: INFN-Istituto Superiore di Sanita, 1-00161 Rome, Italy.
13 Present address: Osaka University, 567 Osaka, Japan.
14 Present address: SAP AG,W-6909 Walldorf, FRG.
~5 Present address: DESY, W-2000 Hamburg 52, FRG.
~6 Present address: Gruner und Jahr AG & CoKG, W-2210 Itzhoe, FRG.
~7 Present address: IKP2-KFA, W-5 170 Jiilich, FRG.
~s Present address: Carnegie Mellon University, Pittsburgh, PA 15213, USA.
19 Present address: EMPA, W-8600 Diibendorf, Switzerland.
2o On leave from Jozef Stefan Institut, Ljubljana, Yugoslavia;
present address: NIKHEF-K, NL-1009 AJ Amsterdam, The Netherlands.
2~ Present address: University of Melbourne, Parkville, Victo- ria, Australia.
22 Present address: Universit6 de Neuch~tel, CH-2000 Neuch~- tel, Switzerland.
23 Supported by Bundesministerium f'tir Forschung und Technologie.
24 Supported in part by FOM, Vrije Universiteit Amsterdam and NWO.
d e p e n d e n c e o f F2 can be u s e d to d e t e r m i n e t h e scale p a r a m e t e r o f Q C D a n d t h e m o m e n t u m d i s t r i b u t i o n o f t h e gluons. In a d d i t i o n , t h e v a l u e o f F2 at l o w x d e t e r m i n e s t h e r e a c t i o n rates to be e x p e c t e d at v e r y high e n e r g y c o l l i d e r s such as L H C a n d SSC. K n o w l - edge o f the structure f u n c t i o n o f the p r o t o n ( F ~ ), a n d t h e d e u t e r o n ( F ~ ) has s t e a d i l y i m p r o v e d in r e c e n t years, d u e to d e e p i n e l a s t i c e l e c t r o n a n d m u o n scat- t e r i n g e x p e r i m e n t s [ 1 - 5 ], b u t s i g n i f i c a n t d i s c r e p a n - cies b e t w e e n s o m e o f these results r e m a i n . In this let- ter we p r e s e n t n e w precise results f o r t h e s t r u c t u r e f u n c t i o n s , F 2 p a n d F 2 d, m e a s u r e d in a d e e p i n e l a s t i c m u o n s c a t t e r i n g e x p e r i m e n t .
In t h e d e e p i n e l a s t i c s c a t t e r i n g o f a m u o n f r o m a n u c l e o n , t h e d i f f e r e n t i a l cross s e c t i o n for o n e - p h o t o n e x c h a n g e c a n be w r i t t e n in t e r m s o f 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 , F2 (x, Q 2 ) , a n d t h e r a t i o o f longi- t u d i n a l l y to t r a n s v e r s e l y p o l a r i s e d v i r t u a l p h o t o n ab- s o r p t i o n cross section, R (x, Q 2 ) , as
d20.(x, Q2) 4/r0~2
F2(x '
Q2)d x d Q 2 - Q2 x
( Q2 y2+Q2/E2 )
× 1 - y - - - ~ + 2 [ l + R ( x , Q2)]. ,
( 1 )w h e r e - Q 2 is t h e f o u r - m o m e n t u m t r a n s f e r s q u a r e d a n d E is t h e e n e r g y o f the i n c i d e n t m u o n . T h e t w o scaling v a r i a b l e s x a n d y are d e f i n e d as x =
Q2/2Mv
a n d y =
u/E,
w h e r e u is the e n e r g y o f t h e v i r t u a l p h o - t o n a n d M t h e p r o t o n mass.2. The experiment
T h i s e x p e r i m e n t ( N M C - N A 3 7 ) was p e r f o r m e d at t h e M 2 m u o n b e a m line o f the C E R N SPS. T h e d a t a p r e s e n t e d h e r e w e r e t a k e n d u r i n g 1986 a n d 1987 at n o m i n a l i n c i d e n t m u o n energies o f 90 a n d 280 GeV.
The spectrometer was an upgraded version of the EMC apparatus [6,7]. Improvements relevant to this analysis are described below; further details can be found in refs. [8,9].
The proton and deuteron structure functions were measured simultaneously using two similar pairs of 3 m long targets exposed alternately to the beam. In one pair the upstream target was liquid hydrogen and the downstream target liquid deuterium, while in the other pair the order was reversed. The acceptance of the spectrometer was significantly different for the upstream and downstream targets, giving two sepa- rate determinations of the structure function for each material. The simultaneity of the measurements greatly reduced the uncertainty of the relative nor- malisation between the proton and deuteron struc- ture functions.
The integrated incident muon flux was measured by two different methods. In addition to the method of the EM Collab. [ 10] which used a random trigger to sample the beam, a new trigger was installed. The total numbers of counts in two planes of the scintil- lator hodoscopes used to determine incident beam tracks were recorded, and prescaled to form this trig- ger. In both methods the beam tracks present in the triggers were reconstructed off line, in the same way as for scattered muon triggers, in order to determine the integrated useable flux. In this way hodoscope and reconstruction efficiencies were taken into account.
A statistical precision of 1% could be achieved with the second method in a few hours of data taking.
Uncertainties in the incident and scattered muon momenta are important sources of systematic error.
The beam momentum measurement system (BMS) was calibrated to an accuracy of + 0.2% at both 90 and 280 GeV, using a purpose built spectrometer [ 11 ]. At both energies, the main spectrometer mag- net (FSM) was calibrated against the measured masses of the J / ~ and K ° mesons to an accuracy of _+ 0.2%. The relative calibration of the BMS and FSM for the 280 GeV data was checked in a series of ded- icated runs with a system of specially installed silicon microstrip detectors.
During four periods of data taking at 280 GeV, 11.5 × 106 triggers were recorded, whilst at 90 GeV, 5.8 x 106 triggers were taken during one period. The following selections and cuts were applied to the data.
The longitudinal position of the reconstructed inter-
action vertex was required to be within one of the tar- gets. Since beam defining veto hodoscopes had aper- tures of 3 cm radius, whilst the target cells were 5 cm in radius, the beam was well contained laterally within the target material. To eliminate muons from ~ and K decays, the scattered muon was required to have a momentum larger than 15 (40) GeV/c in the 90 (280) GeV data set. In order to remove regions of rapidly varying acceptance, minimum scattering an- gles were imposed of 13 mrad in the upstream and 15 mrad in the downstream targets. Events with z, less than 7 (30) GeV in the 90 (280) GeV data were re- jected to ensure good resolution in z,. A requirement o f y < 0.9 removed kinematic regions where radiative contributions are large. For a given x bin, those
O2
points whose acceptance was less than 30% of the maximum in that bin were removed.
It was found that some of the large drift chambers used to reconstruct the tracks of the scattered muon suffered inefficiencies due to large event-related background. These chambers (W45, quoted in ref.
[6] ) were not used in the results presented here be- cause these inefficiencies are not fully understood.
The spectrometer's acceptance is then limited by the size of the smaller proportional chambers at the same position (P45, quoted in ref. [ 7 ] ).
After all cuts there remained 270000 (131 000) events on hydrogen, and 561 000 (267 000) events on deuterium at 90 (280) GeV. It was checked that imposing more restrictive kinematic cuts did not change the final F2 values significantly. The kine- matic region covered is 0.006~<x~<0.6 and 0.5~<
Q2 ~< 55 GeV 2. The use of tracks reconstructed in P45 rather than W45 limits the high Q2 range of each data set; consequently, at present there is no overlap be- tween the results from the two energies.
3. Structure function analysis
An iterative method was employed to extract the structure functions. In this method the spectrometer acceptance was determined with a Monte Carlo sim- ulation; each accepted Monte Carlo event was weighted with the inclusive cross section, i.e. the one- photon exchange cross section together with contri- butions from radiative and other higher order pro- cesses. These weights were computed from an initial
Volume 295, number 1,2 PHYSICS LETTERS B 26 November 1992 choice o f
F2
and a fixed parametrisation o f R [ 12 ].A comparison o f the normalised yields of data and accepted Monte Carlo events permitted new values of
F2(x,
Q2) to be determined. Parametrisations of the new F2 values were used to recompute the one photon cross section and the radiative contributions for use in the subsequent iteration. The procedure was repeated until the values o f F2 changed by less than 0.2% - typically after two or three iterations.The initial F2 and the form o f the parametrisation was that of Appendix A in ref. [8]. In its use here only the 8 parameters describing the deep inelastic region were fitted, while the parametrisation of the resonance region was kept fixed. To check that the results did not depend on the initial values o f the pa- rameters, the procedure was repeated starting from a markedly different F2; using that of calcium arbitrar- ily multiplied by 0.9 gave structure functions that differed by less than 0.1% after three iterations. The sensitivity of the results to the form of the parame- trisation was checked by repeating the procedure us- ing the 15 parameter function of ref. [ 13 ]. The dif- ferences in the resulting F2 due to the functional form were negligible everywhere except in the lowest x bin where they were up to 2%. The differences were used point by point as an estimate of this systematic error.
With the present data a determination o f R is not possible and it was taken to be that given by the par- ametrisation o f ref. [ 12 ], which includes the low x data o f C D H S W [ 14 ]. The Q2 behaviour of the par- ametrisation at low x is consistent with a calculation based on a model due to Nikolaev and Zakharov [ 15 ]. To calculate the radiative contributions to the cross section, rife parametrisation o f R which is valid down to Q 2 = 0 . 3 5 GeV 2, has to be extrapolated to lower values of Q2. We assumed it to be constant with an uncertainty of 100%.
The radiative contributions to the cross section were calculated using the method of Akhundov, Bar- din and Shumeiko [ 16 ]. This procedure contains the most complete treatment o f higher order corrections available. The inputs to the calculation were taken from recent descriptions of available data as dis- cussed in ref. [8 ]. In the kinematic range o f the pres- ent measurement the largest radiative contributions to the cross section are less than 35%.
For the proton the calculation o f the radiative ef- fects at low x has been checked by Bardin against a
calculation developed for H E R A [ 17 ] and found to be in good agreement. The procedure was compared with that o f Mo and Tsai [ 18 ] with the inclusion of v a c u u m polarisation by quark and r loops and elec- troweak interference terms. The differences between the results from the two schemes were always less than 2% [ 19 ]. The change o f radiative correction scheme has a negligible effect on the previously published nu- cleon structure function ratio [8,20] where the Mo and Tsai approach without the above mentioned terms was used.
In order to determine the systematic error on
i;2
due to the inputs to the radiative contribution calcu- lation, the prescription described in ref. [ 8 ] was fol- lowed. The contributions were recalculated with all inputs m o v e d to the limits of their uncertainties in the direction that maximised the change in the cor- rection and the structure functions redetermined. The d o m i n a n t contributions to the error are the uncer- tainty on
R(x,
Q2), the parametrisation of the pro- ton form factor and the suppression factor for deuter- ium. The value of R was changed both in the calculation of the one-photon exchange cross section (eq. ( 1 ) ) and in the calculation o f the radiative con- tributions. The resulting difference in the structure functions was about 3% (1.5%) for F p (F~) at the lowest x, becoming negligible above x = 0 . 0 5 . The difference at each (x, Q2) point was taken as the con- tribution to the systematic error.In the Monte Carlo simulation used to determine the acceptance only the incident and scattered muons (but no hadrons) were tracked, and hits in the detec- tor were generated using parametrisations o f the measured efficiencies o f the trigger hodoscopes and tracking chambers. A sample o f Monte Carlo events equivalent in size to that o f the data was generated and passed through the reconstruction programs. In the extraction o f the structure functions, differences between data and Monte Carlo are attributed to the difference between the true and assumed structure functions. Therefore, we have checked that the acceptance is well described by the simulation. This was done by comparing distributions o f data and Monte Carlo events in variables not, or only weakly, related to x and
Q2,
for example the azimuthal angle of the scattered muon. The account for changes in the detector, the acceptance was determined separately for each period of data taking.Reconstruction losses correlated with multiplicity in the chambers were determined with a further de- tailed Monte Carlo simulation in which the genera- tion of the complete final state was made. The L U N D hadron generator [21 ] was used to generate the pri- mary hadrons. These were allowed to decay and in- teract, and the full development of hadronic and electromagnetic showers produced in the apparatus was simulated with the GHEISHA program [ 22 ]. The reconstruction inefficiencies were determined by comparing events reconstructed both with and with- out the inclusion of the simulated backgrounds and were evaluated independently for the 90 an 280 GeV data. No significant difference was observed between the inefficiency for the upstream and the down- stream target events, or for hydrogen and deuterium events. The inefficiency was observed to be strongly correlated with the total multiplicity in the cham- bers. The multiplicities observed in the detectors were well reproduced by the simulation, except for those
in the W45 drift chambers. For this reason these chambers were not used in the present analysis. The reconstruction inefficiencies were parametrised as a function of y and the data corrected. The correction was zero for y<0.2, rising linearly to 5% (8%) at y = 0 . 8 5 for the 90 (280) GeV data. The small differ- ences observed in the multiplicities between the data and Monte Carlo event samples were used to esti- mate the uncertainty on the correction. The conse- quent systematic error on F2 decreases from 1% (1%) ofF2 at the lowest x for the 90 (280) GeV data, to 0.5% (0.8%) for x>0.03.
The accuracy of the acceptance determination was estimated from a comparison of structure functions measured separately in the upstream and down- stream targets. They were fitted independently with the 8-parameter functional form described above. The differences between the fits were up to 4% at the low- est x and between 1% and 2% elsewhere. At each (x, Q2) point half of the difference between the two fit
?D proton / × = 0 008 NMC NMC
- • 90GeV ,~ (x 4.0] t" f ~ ¢::::~'~:~ × = 009 ( x 7 5 )
L" O 280 OeV / ~ ~ = 0.0125 9
= 0 1 1
% ( x ~ 2 ) ~ ~ × 5 2 )
~ ~ O I11 X = 0 ] 4
X ~ 0 0 1 7 5 o O
J " ( X 2 5 ) ~ ( X 3 7 )
x 0 . x = 0 1 8
× = 0 2 2 5
x 5 ( x 1 7 )
0 x = 0 2 7 5
o ~ ( x 1 2 )
.
~oo7o
(x 1 0} 0 1t
proton × =o5o( x l 0 )
• 90 Ge~
, ~ 0 2 8 0 GeV
1 10 1 10 100
e ~ (OeV % Q: ( o e v ~)
Fig. 1. The proton structure function F~. In the figure the data in each x bin have been scaled by the indicated factor for clarity. The filled symbols represent the 90 GeV data, the open symbols the 280 GeV data. The errors bars represent the statistical errors, the bands the total systematic error excluding the normalisation error o f 1.6% (2.6%) o f the 90 (280) GeV data.
Volume 295, number 1,2 PHYSICS LETTERS B 26 November 1992 values was taken as a c o n t r i b u t i o n to the systematic
error.
The data from the four 280 OeV periods were found to be consistent, apart from some overall normalisa- tion differences. The structure functions from the in- dividual periods were averaged, a n d the normalisa- tion spread of + 2 % was included in the overall n o r m a l i s a t i o n error. F o r the single period of 90 GeV, the consistency of the data was checked by splitting the period into five parts. A similar n o r m a l i s a t i o n spread of _+ 1% was thus estimated. Hence the rela- tive n o r m a l i s a t i o n u n c e r t a i n t y of the 90 GeV with re- spect to the 280 GeV data is _ 2.2%. The u n c e r t a i n t y in the relative n o r m a l i s a t i o n of F ~ with respect to F 2 d is negligible.
The data were n o r m a l i s e d to the average of the two m e a s u r e m e n t s of the integrated i n c i d e n t m u o n flux.
These were f o u n d to differ by 1.3%, with the r a n d o m trigger m e t h o d systematically measuring a smaller flux t h a n the scaler method. This difference does not
affect the relative n o r m a l i s a t i o n of the 90 a n d 280 GeV data sets; half of it was c o m b i n e d with the above n o r m a l i s a t i o n spreads to give total n o r m a l i s a t i o n er- rors of 1.6% a n d 2.6% for the 90 a n d 280 GeV data, respectively.
The data were corrected for a 3.1% c o n t a m i n a t i o n of the d e u t e r i u m with H D molecules. The N M C m e a s u r e m e n t of
F~/F~
[8] was used to d e t e r m i n e the correction, which varied from 1% at the lowest x, to 0.5% at x = 0.5, with negligible error. The a m o u n t of non-target material within the vertex cuts a n d the subsequent c o n t a m i n a t i o n of the event sample was negligible.4. Results
The structure functions are shown versus Q2 for each b i n in x in figs. 1 and 2 ~. The data clearly ex-
~ The values ofF2 and the errors are tabulated in ref. [23].
i , = o 09
0 2 8 0 G e V ~ j l
x = 0 0 1 2 5
, ) ! 1
/ x - 0 0 1 7 5
, , ~ - - - ( ~ 3 / )
1 , ~ = 0 0 2 5
{ ' 2 b j j J
, ' 7
4 / f ~ - : i : ~ -~: :I' <: ~ _ ~ _ ~_ ~ . . . . , :,:,,
t ", 1 2 ',
, i o ;
+ , ~ o o,o i -
~ g : : : : ~ ( × ! o ) 0 1 d e u t e r c , r~ - ~
[ 0 2 8 0 ,.he',,/ - ~ : ~ I :J
1 1 0 1 I 0 t O 0
O' ( C e v ' ~) O ' , C,<~,~, :)
Fig. 2. The deuteron structure function Y~. In the figure the data in each x bin have been scaled by the indicated factor for clarity. The filled symbols represent the 90 GeV data, the open symbols the 280 GeV data. The error bars represent the statistical errors, the bands the total systematic error excluding the normalisation error of 1.6% (2.6%) of the 90 (280) GeV data.
hibit the scaling v i o l a t i o n s expected f r o m p e r t u r b a - rive Q C D . T h e slopes, d ln F 2 / d l n Q2, are strongly positive at low x a n d b e c o m e negative at larger val- ues o f x. In figs. 1 a n d 2 the error bars represent the statistical errors. The systematic errors due to the ra- d i a t i v e corrections, i n c i d e n t a n d scattered m u o n en- ergy calibrations, r e c o n s t r u c t i o n inefficiency, func- tional form o f the p a r a m e t r i s a t i o n and the acceptance u n c e r t a i n t y were a d d e d in q u a d r a t u r e a n d are shown as the bands. These b a n d s are p l o t t e d relative to the function fitted to the d a t a as d e s c r i b e d above. It should be n o t e d that these errors are c o r r e l a t e d be- tween energies a n d materials, and the r e a d e r is re- ferred to ref. [23] for details. The 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 is not i n c l u d e d in the error bands.
The d a t a used in the present analysis are a subset o f those p r e s e n t e d in ref. [8 ] for the m e a s u r e m e n t o f
F~/Fr~(=2F'~/F p -
1). T h e ratioF2/F2
" P from the present analysis is consistent with that p r e s e n t e d in ref. [ 8 ] , albeit with larger statistical errors. In thee v a l u a t i o n o f the G o t t f r i e d sum f r o m the ratio
n P
F2/F2
[ 2 0 ] , we used for F d a fit to the then avail- able world data. I f the presently d e t e r m i n e d F 2 d h a d been used in that analysis, the value o f the G o t t f r i e d sum in the m e a s u r e d range w o u l d be 0.234 + 0.008, where the error is statistical only. This is in agree- m e n t with the p u b l i s h e d value. F u r t h e r m o r e , the G o t t f r i e d sum o b t a i n e d directly f r o m F ~ a n d F 2 d was f o u n d to be consistent with the result given in ref.[ 20 ], over the presently m e a s u r e d range.
In figs. 3 - 5 the d e u t e r o n results are c o m p a r e d to those from p r e v i o u s experiments. The error b a r s shown in these figures are the q u a d r a t i c sums o f the statistical a n d systematic errors o f each e x p e r i m e n t , excluding the n o r m a l i s a t i o n errors.
Fig. 3 shows very g o o d a g r e e m e n t between the present d a t a a n d those o f b o t h SLAC [5] and B C D M S [4 ]. The present d a t a cover part o f the Q2 region o f each o f the other experiments, a n d e x t e n d to m u c h lower x. The curve p l o t t e d in this figure is
x
L2
0 5 / - -
d e u t e r o n x = o . o o 8
• N M C / ~ ( x 4 0 ) "
A S L A C
[] B C D M S
,,.//
x = 0 0 1 2 5/ ~ / ( X 3 2 )
/// /
/, /
-oo,,s, , " ( x 2 5 )
/ - x = 0 025
/ / " # ( X 2 0 )
x -. 0.035 . /
-÷
× = 0 0 0 0 ( ~ 2 )
z - 4 ~ +
. x = 0 0 7 0
i ~ _ ~ J ~ . ~ d ~ ~_~_____~ ,~, L .. . . , , , , ~_~__~
1 1 0
Q 2 (GeV ~)
0 1
× = 0 . 0 9
(x75)
x = O l l
(×52)
x = 0 . 1 4
(x3z)
× = 0 1 8 ( X 2 5 )
× = 0 225 ( X 1 7 )
x = 0 2 7 5
(x~2)
x = 0 3 5 ( x ~ o )
deuteron ~ ~
• N M C x = 0 5 0
A S L A C ( x 1 0 )
, i l l _ _ k k B J I
1 10 1 0 0
O 2 (GeV 2) Fig. 3. The present F2 d (filled symbols) compared with those of SLAC (triangles) and BCDMS (squares). The SLAC and BCDMS data were rebinned to the NMC x bins. The error bars represent the quadratic sum of the statistical and systematic errors. The curve is the result of the fit of the 15-parameter function to all three data sets including data at x> 0.5 not shown in this figure.
Volume 295, number 1,2 PHYSICS LETTERS B 26 November 1992 Table 1
The parametrisation ofF~, F~. This function is strictly valid only in the kinematic range of the NMC, SLAC and BCDMS data.
( ln{Q'/A2))"(~,
(1 +C(x)]
F2{x, Q2)=A(x) \ ~ / Q2 ,],
Q2 =20 GeV2, A=250 MeV,
A(X) =xal(
1 - x)"~[as +a4( 1 - x ) +a~( 1 --x) 2 + a 6 ( 1 - x ) 3 + a 7 ( 1 - - x ) 4] ,B(x) =bl +b2x+b3/(x+b4) ,
C ( X ) =ClX'~'C2X2"~'C3X3"~'C4 x 4 ,
Parameter Proton Deuteron
al -0.1011 -0.0996
a2 2.562 2.489
a3 0.4121 0.4684
a4 -0.518 - 1.924
a5 5.967 8.159
a6 - 10.197 - 10.893
a7 4.685 4.535
b~ 0.364 0.252
b2 -2.764 -2.713
b3 0.0150 0.0254
b4 0.0186 0.0299
c~ - 1.179 - 1.221
c2 8.24 7.50
c3 -36.36 -30.49
c4 47.76 40.23
t h e result o f a fit to t h e three d a t a sets using t h e 15- p a r a m e t e r f u n c t i o n d i s c u s s e d a b o v e (see table 1 ).
T h e E M C - N A 2 d a t a [ 2 ] h a v e r e c e n t l y b e e n re-an- a l y s e d [ 24 ], using t h e Q C D p r e d i c t i o n for R in place o f t h e R = 0 a s s u m e d in the o r i g i n a l analysis ~2. T h e s e d e u t e r o n d a t a are c o m p a r e d w i t h t h e p r e s e n t results as a f u n c t i o n o f x for t w o d i f f e r e n t v a l u e s o f Q 2 in fig.
4. T h e S L A C a n d B C D M S d a t a are also s h o w n for c o m p a r i s o n . S y s t e m a t i c d i f f e r e n c e s w i t h E M C o f up to 20% at l o w x are seen. In the light o f the studies m a d e o f t h e r e c o n s t r u c t i o n losses in the large drift c h a m b e r s ( W 4 5 ) it s e e m s likely t h a t t h e d i s c r e p a n - cies at low x are d u e to such i n e f f i c i e n c i e s a f f e c t i n g the E M C data.
A c o m p a r i s o n w i t h p r e v i o u s l y p u b l i s h e d p r o t o n ,2 In this re-analysis by Bazizi and Wimpenny, additional un-
published EMC data were included [25 ].
2
k
0 4 ~
i
+ + - 6 6
9?6
'32 = 2C, 0e~/2
, i
i ?
h o l
°il
t • NVC 6 ~ v :
£ ,3 C E; k1% ±[
- 3 EMC N A 2 r e a r l a l '
{ ) , J i i
G
8 01 S 1 0 "
Fig. 4. The present F2 a compared with those of the re-analysed EMC-NA2 data, and those of SLAC and BCDMS, at a Q2 of 5 and 20 GeV 2. Only those x points within the measured ranges of each experiment are shown (i.e. with no Q2 extrapolations). The error bars represent the quadratic sum of the statistical and sys- tematic errors.
d a t a [ 1,3,5 ] leads to s i m i l a r c o n c l u s i o n s .
Finally, in fig. 5 t h e d e u t e r o n d a t a are p l o t t e d ver- sus x for several b i n s o f Qz t o g e t h e r w i t h t h e E M C - N A 2 8 l o w x m e a s u r e m e n t [ 7 ] , a n d the S L A C d a t a [ 5 ]. T h e E M C - N A 2 8 d a t a are in fair a g r e e m e n t w i t h the p r e s e n t data. O f i n t e r e s t in this figure is t h e clear x - i n d e p e n d e n c e o f the structure f u n c t i o n s for Q2 < 2.5 G e V z a n d x < 0.1 as e x p e c t e d f r o m a s i m p l e R e g g e theory.
T h e low x b e h a v i o u r o f t h e s t r u c t u r e f u n c t i o n s ( o r t h e p a r t o n d i s t r i b u t i o n s ) is i m p o r t a n t in d e t e r m i n - ing the r e a c t i o n rates to be e x p e c t e d in f u t u r e e x p e r - i m e n t s at h i g h e r e n e r g i e s ( L H C , S S C ) . In fig. 6 t h e p r e s e n t F ~ is s h o w n c o m p a r e d to t h o s e c a l c u l a t e d f r o m r e c e n t p h e n o m e n o l o g i c a l p a r t o n d e s c r i p t i o n s , at Q 2 = 5 G e V 2. T h e c u r v e s s h o w n in t h e figure cor- r e s p o n d to t h e r e c o m m e n d e d p a r a m e t r i s a t i o n s (see ref. [ 2 6 ] ) o f K w i e c i f i s k i et al. ( K M R S - B 0 ) [ 2 7 ] , M o r f i n a n d T u n g ( M T - S 1 ) [28 ]. T h e s e p a r a m e t r i s - ations were c o n s t r a i n e d by precise d a t a a b o v e x = 0.07
,-- d I- 2
0,4
0.2
0.4
0.2
0.4
0.2
Q2 = 0 . 7 5 O e V '
l l I IIIIILI t ~ ~ ~tt~] J
Q2 = 1 . 7 5 O e V 2
A
ZX
t i i i i i J t ] i J i i i i l l i t
Q2 = , 5 . 5 0 O e V 2
/ x
• NMC ~,
o E M C - N A 2 8
,5.
~, SLAC
QZ = 1 . 2 5 0 e V 2
.
Q2 = 2 . 5 0 C e V 2
/ x
t I I J ~ l l l ^ I J I J l l l l l I
02 ~ 4 . 5 0 O e V 2
t "1,,.
8 m
,,x
1 L I k l l l
i i i i l t l l l i J i i ~ l l l ] i i i ~ t l t i J i l l l l ~ ] i i J i i i l l l i ~ i k l l l J
0.01 0.1 0.01 0 !
X
Fig. 5. The present F ~ compared with those of EMC-NA28 and SLAC as a function of x at several values of
Q2.
The error bars represent the quadratic sum of the statistical and systematic errors.b u t fail to describe the low x b e h a v i o u r of the present data. Also shown is the result of a model (in part con- strained by experimental data) due to Gliick et al.
( G R V ) [29]. This gives a fair description of the present data.
5. C o n c l u s i o n s
We have presented new m e a s u r e m e n t s of proton a n d deuteron structure functions over a wide kine- matic range: 0 . 0 0 6 ~ < x 4 0 . 6 a n d 0.54q2~<55 GeV 2.
The data exhibit logarithmic scaling violations clown to small values of x, even at low Q2. In the range of overlap with the previous SLAC a n d BCDMS data
Volume 295, number 1,2 PHYSICS LETTERS B 26 November 1992
(',
o o
o •
Q
- @.
• : M \,
!
Fig. 6. Recent phenomenological descriptions o f F ~ (KMRS-B0 [27 ], MT-SI [28 ], GRV [29 ] ) compared with the present data.
g o o d a g r e e m e n t is o b s e r v e d b e t w e e n t h e t h r e e e x p e r - i m e n t s . C l e a r k i n e m a t i c s d e p e n d e n t d i f f e r e n c e s w i t h t h e E M C - N A 2 d a t a a r e s e e n . R e c e n t p a r a m e t r i s a - t i o n s o f p a r t o n d i s t r i b u t i o n s fail t o d e s c r i b e t h e x d e - p e n d e n c e o f t h e s t r u c t u r e f u n c t i o n s b e l o w x = 0 . 0 7 . T h e i n t e r p r e t a t i o n o f t h e p r e s e n t d a t a i n t e r m s o f Q C D will f o l l o w i n a f u t u r e c o m m u n i c a t i o n .
A c k n o w l e d g e m e n t
W e w o u l d l i k e t o t h a n k D . Y u . B a r d i n f o r d i s c u s - s i o n a n d c o m p a r i s o n o f t h e r a d i a t i v e c o r r e c t i o n p r o - c e d u r e s , a n d R . H o r i s b e r g e r f o r p r o v i d i n g t h e s i l i c o n s t r i p d e t e c t o r s .
R e f e r e n c e s
[1] EMC-NA2 Collab., J.J. Aubert et al., Nucl. Phys. B 259 (1985) 189.
[2] EMC-NA2 Collab., J.J. Aubert et al., Nucl. Phys. B 293 (1987) 740.
[3] BCDMS Collab., A.C. Benvenuti et al., Phys. Lett. B 223 (1989) 485.
[4] BCDMS Collab., A.C. Benvenuti et al., Phys. Lett. B 237 (1990) 592.
[5] L. Whitlow et al., Phys. Lett. B 282 (1992) 475.
[6] EMC-NA2 Collab., O.C. Allkofer et al., Nucl. Instrum.
Methods 179 (1981) 445.
[7] EMC-NA28 Collab., M. Arneodo et al., Nucl. Phys. B 333 (1990) 1.
[ 8 ] NM Collab., P. Amaudruz et al., Nucl. Phys. B 371 ( 1992 ) 3.
[ 9 ] M. van der Heijden, Ph.D. Thesis, University of Amsterdam (1991);
I.G. Bird, Ph.D. Thesis, Free University (Amsterdam, 1992);
A. Brfill, Ph.D. Thesis, Freiburg University ( 1992 ).
[ 10] R.P. Mount, Nucl. Instrum. Methods 187 ( 1981 ) 401.
[ 11 ] M. Arneodo, Ph.D. Thesis, Princeton University (1992).
[12] L.W. Whitlow et al., Phys. Lett. B 250 (1990) 193.
[ 13 ] A. Milsztajn et al., Z. Phys. C 49 ( 1991 ) 527.
[ 14] CDHSW Collab., P. Berge et al., Z. Phys. C 49 ( 1991 ) 187.
[15] N.N. Nikolaev and B.G. Zakharov, Z. Phys. C 49 (1991) 607.
[16] A.A. Akhundov et al., Sov. J. Nucl. Phys. 26 (1977) 660;
44 (1986) 988;
JINR-Dubna preprints E2-10147 (1976), E2-10205 (1976), E2-86-104 (1986);
D. Bardin and N Shumeiko, Soy. J. Nucl. Phys. 29 (1979) 499.
[ 17 ] H. Spiesberger, invited talk at DESY-Zeuthen Workshop on Deep inelastic scattering (April 1992 );
D. Bardin, invited talk at DESY-Zeuthen Workshop on Deep inelastic scattering (April 1992).
[ 18] L.W. Mo and Y.S. Tsai, Rev. Mod. Phys. 41 (1969) 205;
Y,S. Tsai, preprint SLAC-PUB-848 ( 1971 ).
[19] B. Badelek, D. Bardin, K. Kurek and C. Scholz, in preparation.
[20] NM Collab., P. Amaudruz et al., Phys. Rev. Lett. 66 ( 1991 ) 2712.
[21 ] The LUND Monte Carlo Programs, CERN pool programs long writeup (April 1987 ), and references therein.
[22] Program GHEISHA, H. Fesefeldt, III. Physikalisches lnstitut (Aachen), report PITHA 85/02.
[23] NM Collab., P. Amaudruz el al., preprint CERN-PPE/92- 124.
[24] K. Bazizi and S.J. Wimpenny, preprinl UCR/DIS/91-02.
[25 ] H. Peschel, Ph.D. Thesis, University of Wuppertal (1990).
[26] H. Plothow-Besch, Parton density functions, Proc. third Workshop on Detector and event simulation in high energy physics (Amsterdam, April 1991 );
Program PDFLIB, CERN Program Library Pool W5051 (1991).
[ 27 ] J. Kwieciriski et al., Phys. Rev. D 42 ( 1990 ) 3645.
[ 28 ] J.G. Morfin and W.K. Tung, Z. Phys. C 52 ( 1991 ) l 3.
[29} M. Glfick, E. Reya and M. Vogt, Z. Phys. C 53 (1992) 127.
