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Z. Phys. C Particles and Fields 52, 361-387 (1991)

Zeitschrift P a r t i c l e s

ffir Physik C

and Fields

9 Springer-Verlag 1991

Forward produced hadrons in pp and pd scattering and investigation of the charge structure of the nucleon

E u r o p e a n M u o n C o l l a b o r a t i o n

J. A s h m a n 12, B. Badelek 1 s,,, G. B a u m

17,b

j. Beaufays 2"c, C.P. Bee 7, C. B e n c h o u k 8, I.G. Bird 4,a, S.C. B r o w n v,e, M.C. C a p u t o iv'f, H . W . K . C h e u n g l~ J.S. C h i m a 11'h, J. C i b o r o w s k i aS'a, R. Clifft 11, G. C o i g n e t 6, F. C o m b l e y 12, G. C o u r t 7, G. d ' A g o s t i n i 8, J. D r e e s 16, M. Dilren 4, N. D y c e w 5, A.W. E d w a r d s 16,i, M. E d w a r d s 11, T. E r n s t 3, J. F a v i e r 6, M.I. F e r r e r o 13, D. F r a n c i s 7, E. G a b a t h u l e r 7, R. G a r n e t 7, V. G i b s o n l o,j, j. Gillies x0,k, p. G r a f s t r 6 m 14,j, K. H a m a c h e r 16 D. v o n H a r r a c h 4,~, p. H a y m a n 7, J.R. H o l t 7, V.W. H u g h e s 17, A. J a c h o l k o w s k a

2,m

T. J o n e s 7,k, E.M. K a b u s s 4'1, B. K o r z e n 16, U. K r f i n e r 16, S O K u l l a n d e r 14, U. L a n d g r a f 3, D. L a n s k e 1, D. L a u t e r j u n g 16, F. L e t t e n s t r 6 m 14'n, T. L i n d q v i s t ~4, J . L o k e n , M. M a t t h e w s 7, Y. M i z u n o 4'~ K. M 6 n i g 16, F. M o n t a n e t 8, E. N a g y 6,p j. N a s s a l s k i 15,q T, N i i n i k o s k i 2, P.R. N o r t o n 11, F.G. O a k h a m 11,r, R.F. O p p e n h e i m 17,~

A.M. O s b o r n e 2, V. P a p a v a s s i l i o u x v, N. Pave116,t, C. P e r o n i 13, H. Pesche116,,, R. Piegaia 17,f, B. Pietrzyt 8, U. P i e t r z y k 16,v, B. P o v h 4, P. R e n t o n lo, J.M. R i e u b l a n d 2, K. R i t h 4, E. R o n d i o 15,a, L. R o p e l e w s k i 15,,,

D. S a l m o n xz'k, A. S a n d a c z 15,q, A. S c h l a g b 6 h m e r 3,w, A. Schneider 16, T. S c h r 6 d e r 3, K.P. Schiller 17, K. Schultze 1, T.-A. S h i b a t a 4, T. Sloan 5, A. S t a i a n o 13 H.E. Stier 3, j. Stock 3, G . N . T a y l o r l O,x, J.C. T h o m p s o n 11, T. W a l c h e r 4'~, J. T o t h 6,p, L. U r b a n 1, L. U r b a n 6'p, H. W a h l e n 16, W. W a l l u c k s 3, M. W h a l l e y 12"z, S. W h e e l e r tz'k,

W.S.C. Williams lO, S.J. W i m p e n n y 7'~, R. W i n d m o l d e r s 9, j. W o m e r s l e y lo,~', K. Z i e m o n s 1 a III Physikalisches Institut A, Physikzentrum, RWTH, W-5100 Aachen, Federal Republic of Germany z CERN, CH-1211 Geneva 23, Switzerland

3 Fakultfit fiir Physik, Universit/it Freiburg, W-7800 Freiburg, Federal Republic of Germany

* Max-Planck Institute for Kernphysik, W-6900 Heidelberg, Federal Republic of Germany 5 Department of Physics, University of Lancaster, Lancaster LA1 4YB, UK

6 Laboratoire d'Annecy-le-Vieux de Physique des Particules, B.P. 110, F-74941 Annecy-le-Vieux, Cedex, France 7 Department of Physics, University of Liverpool, Liverpool L69 3BX, UK

8 Centre de Physique des Particules, Facult6 de Sciences de Luminy, F-13288 Marseille, France 9 Facult6 de Sciences, Universit~ de Mons, B-7000 Mons, Belgium

~o Nuclear Physics Laboratory, Unversity of Oxford, Oxford OX1 3RH, UK

~ Rutherford and Appleton Laboratory, Chilton, Didcot OX1 0QX, UK 12 Department of Physics, University of Sheffield, Sheffield $3 7RH, UK x3 Istituto di Fisica, Universitfi di Torino, 1-10125, Italy

~'~ Department of Radiation Science, University of Uppsala, S-75121 Uppsala, Sweden

5 Physics Institute, University of Warsaw and Institute for Nuclear Studies, PL-00681 Warsaw, Poland 16 Fachbereich Physik, Universit/it Wuppertal, W-54600 Wuppertal, Federal Republic of Germany x7 Physics Department, Yale University, New Haven, CT 06520 USA

Received 14 March, 1991; in revised form 7 August, 1991

" University of Warsaw, Poland, partly supported by CPBP.01.06 b Permanent address, University of Bielefeld, Bielefeld, FRG c Now at TRASYS, 1040 Brussels, Belgium

a Now at NIKHEF-K, 1009 AJ Amsterdam, The Netherlands e Now at TESA S.A., Renens, Switzerland

f Now at City University, 1428 Buenos Aires, Argentina g Now at University of Colorado, Boulder, CO 80302, USA h NOW at British Telecom, London, UK

i Now at Jet, Joint Undertaking, Abingdon, UK J Now at CERN, Geneva, Switzerland

k Now at R.A.L., Chilton, Didcot, UK 1 Now at University of Mainz, Mainz, FRG m NOW at L.A.L., Orsay, France

Now at University of California, Santa Cruz, CA 950-64, USA o Now at RCNP, Osaka University, Ibaraki, Osaka, Japan

P Permanent address, Central Research Institute for Physics, Hun- garian Academy of Science, Budapest, Hungary

q Institute for Nuclear Studies, Warsaw, Poland, partly supported by CPBP.01.09

r NOW at NRC, Ottawa, Canada

s Now at AT&T, Bell Laboratories, Naperville, Illinois, USA Now at DESY and University of Hamburg, II Institute of Experi- mental Physics, FRG

u Now at Gruner & Jahr, Itzehoe, FRG

v Now at MPI for Neurologische Forschung, K61n, FRG w Now at GEI, Darmstadt, FRG

x Now at University of Melbourne, Parkville, Victoria, Australia Y Now at University of Durham, Durham, UK

z Now at University of California, Riverside, USA z, Now at University of Florida, Gainesville, USA

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Abstract. Final data measured with the EMC forward spectrometer are presented on the production of forward charged hadrons in #p and ~d scattering at incident beam energies between 100 and 280 GeV. The large sta- tistic of 373000 events allows a study of the semi-inclu- sive hadron production as a function of z, p~ and (p~) in small Q2, xB i and Wbins. Charge multiplicity ratios and differences as a function of z and x~ i are given for p, d and n-targets. From the differences of charge multip- licities the ratio of the valence quark distributions of the proton

d~(x)/uv(x)

is determined for the first time in charged lepton scattering. The Gronau et al. sum rule is tested, the measured sum being 0.31_+ 0.06 stat. _+

0.05 syst., compared with the theoretical expectation of 2/7~0.286. The measured sum corresponds to an abso- lute value of the ratio of the d and u quark charge of 0.44-t-0.10 stat._0.08 syst.

1 Introduction

During the period 1977 to 1985 the European Muon Collaboration (EMC) took data to perform a detailed series of measurements of deep inelastic muon nucleon scattering. In these experiments both the scattered muons and the hadronic final states have been measured.

The NA2 (NAT) phase of the experiment in 1977-1980 (1983-1985) concentrated on high statistics measure- ments of forward produced hadrons in addition to mea- surements of inclusive muon scattering. The NA9 phase (1981-1982) also included the backward region and pro- vided powerful particle identification. This paper pres- ents final results on the semi-inclusive distributions of forward produced charged hadrons from the NA2 and NA2' phase for muon scattering from proton and deu- teron targets. It is based on 154000 events from #p- scattering and 219000 events from #d-scattering. The incident beam energies were 120, 200 and 280 GeV for the #p- and 100 and 280 GeV for the/~d-scattering. The large statistics available from these measurements enable detailed studies of the hadronic final states in small kine- matic bins and allow detailed comparisons between the two targets.

Forward produced hadrons are the key to understand the fragmentation of the struck quark (current fragmen- tation). High statistical and systematic precision of the data is needed to measure subtile QCD effects such as scaling violations and factorisation breaking of the scaled energy distributions, especially because these ef- fects are further distributed by residual target mass ef- fects. Another, probably more direct, access to QCD ef- fects is via the study of the transverse momentum

Pt

of the produced hadrons. Here charged lepton scattering experiments have the advantage with respect to e § e- annihilation that the reference direction of the process, the virtual photon direction, is directly measured. How- ever, the study of QCD effects in Pt spectra is complicated by the intrinsic transverse momentum of the quarks in- side the nucleon and by a contribution usually assigned to the (nonperturbative) fragmentation process. There-

fore precise measurements of the kinematic dependences are needed to determine the dominant variables and to disentangle the contributions from the different sources.

As leading hadrons predominantly contain the struck quark, information about the quark (charge) composi- tion of the nucleon can be obtained from their distribu- tions. The data allow a study of this aspect in a large range of xBj; superior to those of previous experiments.

Comparison of data on muon scattering from protons and deuterons gives information on the charge structure of the neutron. The ratio of the valence quark distribu- tions of the proton

d~(x)/uv(x)

can also be determined from this comparison. These data are complementary to neutrino scattering data and give important input and constraints to phenomenological quark distribution and structure function parameterisations needed for the anal- ysis of hadron collider data. Finally, a sum rule derived by Gronau, Ravndal, and Zarmi [1], which is related to the (square of the) ratio of the u and d quark charge, can be tested. Using the measurement of the average squared valence quark charge from the comparison of the muon-nucleon and neutrino-nucleon structure func- tions, the absolute charges of the u and d quarks can be determined.

This paper is organised as follows:

In Sect. 2 we give briefly definitions of the variables and cross-sections. We describe how neutron rates have been extracted and introduce some other theoretical as- pects.

Section 3 describes the apparatus, target setups, data analysis, and data sets, as well as cuts and corrections applied to the data. Sources of systematic errors are dis- cussed and final systematic errors for semi-inclusive cross-sections and @2) are given.

Section 4 contains the physics results. First we present semi-inclusive scaled energy and transverse momentum distributions of charged hadrons. Here we restrict our- selves mainly to the presentations of final data and do not repeat the detailed analysis presented in several pre- vious papers [2]. The complete presentation of the data allows versatile phenomenological studies, fitting of models etc. Then charge multiplicity ratios for protons, deuterons and neutrons are discussed in detail. The dif- ferences of charge multiplicities are shown and the ratio of the

d~(x)/uv(x)

valence quark distributions are extract- ed. Finally we present the first significant test of the Gronau et al. sum rule and the determination of the quark charges. The latter two subsections also include the necessary formulae, their derivation and a detailed discussion of the systematic errors.

In Sect. 5 we give a brief summary of the results of this paper.

2 Definition of variables and cross-sections

Throughout this paper we use standard variables rele- vant to deep inelastic scattering [3] which are

Q2(v),

the virtual photon squared four momentum (energy) transfer; x~j or simply x, the Bjorken scaling variable;

y, the fraction of the muon energy transfer in the labora-

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363 tory frame; and W 2, the mass squared of the hadronic

system recoiling against the muon; i.e.:

Q 2 _ - _ q 2 = _ ( k - k ' ) 2 ~ 4 EE' sin 2 ~-, 0 q . P

v - - E-- E', M

Q~

x 2 M y ' q . P v Y k . P E '

W 2 = ( p + q)2 = M 2 + 2 M v - Q 2.

k(k'), E(E') are the four momenta and energies of the incoming (scattered) muon respectively. P and M are the four momentum and mass of the target nucleon and 0 is the muon scattering angle in the laboratory frame.

To describe the hadron kinematics we use the scaled hadron energy

P. h Ea

Z - -

P . q v

and the square of the hadron transverse momentum with respect to the direction of the virtual photon, p2, where h is the four momentum of the hadron and Ea its energy.

In the quark-parton model (QPM) the structure func- tion of the nucleon can be expressed as

FzN (X) = x" Z e 2 qi(x),

i = u , d , . . .

where ei are the quark charges and qi(x) the quark distri- bution functions; the probability densities to observe a quark i with momentum fraction x inside the nucleon.

They obey relationships due to isospin and charge con- jugation symmetries. For the distributions of the valence quarks, which define the quantum numbers of the nu- cleon, the following hold:

. - - p r o t o n n e u t r o n . U v ( X ) . - - U v a 1 .. . .

(X)

= d v a I . . . . ( x ) ,

.__ p r o t o n __ n e u t r o n

dv(x)'-dval . . . . (x)-Uval .... (x).

Further, the distribution of each type of sea quark is identical with that of its anti-quark partner inside the nucleon, so that in total the sea quarks carry the quan- tum numbers of the vacuum.

The naive QPM assumes independence of the actual virtual photon quark scattering and the fragmentation of the struck quark. Thus, if Dh(z) is the probability den- sity that a quark of type i fragments into a hadron h with energy fraction z, the normalised scaled energy dis- tribution can be described as

e 2 qi(x, QZ)'Dh(z, Q2) 1 d f f h _ I . d N h i=~, a ....

ato, d z U. d z ~', e 2qi(x,Q2) ,

i = u , d . . . .

(1)

where N, denotes the number of events and Nn the number of hadrons.

This equation also holds in QCD in the leading log approximation. The explicitly written Q2 dependence is due to QCD scaling violations of either the quark distri- butions or fragmentation functions. Higher order terms such as vertex corrections lead, in principle, to an x de- pendence of the fragmentation functions, thus to a (small) breaking of the factorising QPM ansatz.

Following the basic idea of the QPM we choose to present all hadron cross-sections as normalised differen- tial cross-sections as a function of z or p~. To show dependences on p~ and z simultaneously, we present

1 d N h

Nu" dPt z in z bins. Previous studies of the azimuthal angle distribution in this experiment [4] have shown that it can be understood in terms of the QPM and QCD.

Hence all distributions have been integrated over the azimuthal angle.

We do not show results on the characteristics of event P~/Pt as the apparatus shapes, like Thrust, Sphericity, iu o u t

acceptance is limited to the forward region and thus, only a small part of the tracks can be used to determine such quantities. We refer to results of previous analyses of the EMC [5].

For the derivation of the hadron production rates from neutrons we assumed that scattering from the deu- teron takes place incoherently off the proton and neu- tron, because the deuteron is a weakly bound nuclear system (binding energy ~2.2 MeV). Apart from Fermi motion no evidence for other nuclear effects has been observed so far [6J. The corrections for Fermi smearing have been computed [7] and the influence on the hadron production rates was found to be less than 0.5% in the region x < 0.5 and has therefore been neglected. The had- ron production rates from neutrons have been derived by subtracting the proton rate from the deuteron rate weighted by the cross section ratio equal to F~(x)/Fd(x).

1 d N" / FV\ 1 dNd F~ 1 dNv

N; dTz = I I + F ~ " ) N u ~ dz F; Nf d z " (2) F~(x)/F~(x) was taken from a linear parameterisation of the EMC data [7J. This ratio has been well measured by different experiments (see [8, 9] for a summary). A comparison, especially with the new precise measure- ment of the N M C [9], shows that an x dependent error of 5-10% covers the systematic uncertainty of this para- meterisation for the applied range in x.

The measurement of the structure functions in deep inelastic charged lepton nucleon scattering cannot pro- vide direct information about valence quark distribu- tions. Through F~(x)/F~(x) one can obtain information about the ratio of the distributions of all d and u quarks inside the proton, neglecting s g and heavier quarks, d (x) _ 1 - 4. (F~ (x)/Ff (x))

u (x) (F~ (x)/F~ (x)) - 4 " (3)

For high x this reflects the ratio of the valence quark distributions d~(x)/u,(x), which in this region is less than 1/2 and decreases as x increases. For small x, however, the sea significantly contributes to the cross section. The

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additional measurement of the hadronic final state pro- vides a possibility to separate that part of the cross sec- tion originating from the sea, so that a direct measure- ment of

d,,(x)/u,,(x)

becomes possible. In terms of the standard ideas on quark fragmentation, the h a d r o n pro- duced at the largest values of z will most likely contain the struck quark. Hence the charge and z dependence of the energy distributions are sensitive to the flavour of the fragmenting quark [10]. The difference of the nor- malised scaled energy distributions for positive and nega- tive particles does not depend on sea quark, but only on valence quark distributions. Starting from (1), and using relations between fragmentation functions and be- tween quark distribution functions, it is evident that the ratio

d,,(x)/uv(x)

can be extracted by constructing ratios of differences of charge multiplicities obtained from scat- tering from protons and neutrons. Explicitly we give the formulae in Sect. 4.4.

3 Experiment, data and analysis

The experiment was performed in the M 2 m u o n beam line at the C E R N SPS using the E M C forward spectrom- eter to detect the scattered muons and the fast forward hadrons. The data were taken in 11 experimental runs with incident m u o n energies of 100, 120, 200 and 280 GeV. The data sample consists of two parts, data taken in 1978/79 with a hydrogen target and in 1985 with a combined deuterium/copper target. The appara- tus and target for the hydrogen data is described in detail elsewhere [-11, 12]. The forward spectrometer for the 1985 data was similar to that described in [11], but mod- ified to allow data to be taken at higher incident beam intensities [13]. The combined deuterium/copper target was designed to study the E M C effect [14] in detail, but for this analysis only events with a reconstructed vertex inside the liquid deuterium targets have been used.

A comparison between the hadronic distributions from

lad-

and laCu-scattering can be found in [15].

The data were passed through a chain of analysis programs, in which pattern recognition and geometrical reconstruction of the incident and scattered m u o n as well as any charged hadron, which passed through the forward spectrometer, was performed. A vertex fit using the incident and scattered muons and hadrons was also performed. The vertex resolution is such that the individ- ual targets can be clearly separated. Details of the hydro- gen data analysis can be found in [16] and for the deute- rium analysis in [17]. Although the reconstruction and analysis programs for the two data sets are different due to the large time gap, the philosophy of data reconstruc- tion and analysis is almost the same.

F o r the track and event selection kinematical cuts (see Table 1) have been applied to both data sets. They were chosen to avoid regions where smearing, due to resolution and radiative effects, was large or where the acceptance was small or varied rapidly. This leaves for the hydrogen data set 154000 events and 219000 events for the deuterium data set, both covering the same kine- matic range (see Table 2). A track is considered to belong

Table 1. K i n e m a t i c cuts for the data Event selection

0 . 2 < y < 0 . 8 Q 2 > 2 GeV2 0 . 2 < y < 0 . 8 Q 2 > 3 GeV 2 0 . 2 < y < 0 . 8 Q 2 > 4 GeV2 0.2 < y <0.8 Q z > 5 G e V : Track selection

zha d > 0.1 Phaa > 2 GeV Zh.a > 0.1 phad> 2 GeV Zha a > 0.1 Phad > 3 GeV ZhaO > 0.1 Ph.a > 5 GeV

0 r, > 17 m r a d 0 r, > 17 m r a d 0 r, > 15 m r a d 0 r, > 14 m r a d

for E . = 100 GeV for E r = 120 GeV for E r = 200 GeV for E r = 280 GeV

for Eu = 100 GeV for E u = 120 GeV for E u = 200 GeV for E . = 280 GeV

Table 2. SPS periods and n u m b e r of deep inelastic events after selection

SPS period Target Energy D a t a M C

P3A85 Dz 100 GeV 92000 150000

P3 B 85 D z 100 GeV 60 000 75 000

P3B 85 Dz 280 GeV 24000 22000

P3C85 De 280 GeV 4 3 1 3 0 0 112000

N u m b e r of events d-target: 219000 359000

P3B279 H 2 120 GeV 24000 35000

P3A 179 He 200 GeV 10000 49000

P3A2 79 Hz 200 GeV 23000 71000

P3 B 179 H 2 200 GeV 20000 83000

P4A79 H2 280 GeV 17000 32000

P4B 79 He 280 GeV 24000 35000

P8B78 Hz 280 GeV 36000 45000

N u m b e r of events p-target: 154000 350000

to an event, if its distance of closest approach to the vertex formed from the incoming and scattered muons is compatible with its error [16, 17]. F o r all data the acceptance of the apparatus was calculated from a com- plete M o n t e Carlo simulation using the Lund string model [-18 20] to simulate the fragmentation processes.

F o r the pZ-distribution, where the agreement between data and M o n t e Carlo was unsatisfactory the M o n t e Carlo tracks have been reweighted in an iterative proce- dure to follow data. Radiative effects due to Q E D pro- cesses have been included in the simulation [21] as well as secondary interactions of the produced particles in the target material. The scattered m u o n and the pro- duced hadrons were tracked through the spectrometer taking into account the effects of multiple coulomb scat- tering. F o r the analysis of the deuterium data secondary interactions of all particles inside the spectrometer mate- rial have also been simulated. The effects of hodoscope and chamber inefficiencies and resolutions have been taken into account when generating the response of the apparatus. In addition to these signals, b a c k g r o u n d hits determined from the data has been added. F o r the analy- sis of the deuterium data a more refined m e t h o d has been used [22]. The simulated data were "digitised" and then passed through the full reconstruction chain to cor- rect for imperfections in the off-line analysis. The mea-

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365 Table 3. Systematic errors on the differential distributions of

charged hadrons

Correction Systematic error

1 dN 1 dN

N u dz Nu dP 2 @2)

p d p d p d

Apparatus losses 4% 4% 4% 4% -

Signal background 5% 3% 5% 3% -

Hadronicreinteraction 5% 5% 5% 6% 3% 4%

Electron background 3% 5% 2%

Track selection 7% 3% 7% 3% 5% 3%

Radiative corrections 2% 2% 2% 2% 2% 2%

Momentum measurement 3% 3% 5% 5% 2% 2%

of #, #', h

Total systematic error 11% 8% 13% 10% 7% 6%

sured and simulated (accepted as well as generated) data of all SPS periods have been merged before performing the acceptance correction, in which the relative weights in the M o n t e Carlo data sets have been adjusted accord- ing to the n u m b e r of scattered muons for each SPS peri- od.

In Table 3 we show all the individual contributions to the total systematic error, which were considered to be relevant, for the normalised differential distributions

1 d N 1 d N

- - and for (p2), separately for the hydrogen N u d z ' N u d p 2

and deuterium analyses. These quantities do not depend on the absolute flux normalisation. The smaller errors for the latter analysis reflect a better understanding and simulation of the apparatus; a detailed discussion can be found in [17, 233. All contributions have been added in quadrature as they are essentially uncorrelated. The final systematic errors are almost independent of the kin- ematics and are also given in Table 3. F o r the mean transverse m o m e n t u m ( p 2 ) the systematic error is signif- icantly smaller as contributions affecting the normalisa- tion cancel. Neglecting normalisation uncertainties, the remaining systematic error amounts to about 60% of the quoted total systematic error. The final systematic errors have been checked by making comparisons be- tween the different data sets in all variables.

Figure 1 shows the x and

Q2

dependence of the differ- ential scaled energy distributions for all charged hadrons from both targets. Both data sets agree well within the statistical and systematic errors. This is expected within the QPM. Due to isospin invariance, the charge multipli- cities of pions from scattering from protons and deuter- ons are expected to be equal. However, because of the presence of kaons and protons in the hadronic final state small differences are expected. Using the Lund fragmen- tation model [20] one can show that the expected differ- ences should be smaller then 0.5% for z < 0.4 and smaller than 2% for z > 0.4. Such small differences are well below the accuracy of the data. The x- and QZ-dependence pres- ent in the data is more clearly evident from the linear fits in In Q2 to the data (see dotted lines in Fig. 1). The behaviour of the data has already been discussed in de- tail in previous E M C publications [24-26] using a subset of this data. Especially in [25] evidence for Q C D scaling violations in the hadronic final state at fixed centre of mass energy W 2 has been presented. In particular it has d(1/U, d N / d z ) been shown that the logarithmic slopes

d . l n Q2 as function of z show the pattern typical for Q C D scaling violations.

The scaled energy distributions were compared with different versions of the Lund fragmentation model [18- 20], which have been available during the data analysis.

F o r this comparison we have merged the p r o t o n and deuteron data to form one high statistics data set (see Table 15 in the Appendix). Figure 2 shows the compari- son of the merged data set with the following versions of the Lund models:

Model 1: Lund 4.3 ( L E P T O 4.3, J E T S E T 4.3) string model with soft gluon radiation;

Model 2: Lund 6.3 ( L E P T O 5.2, J E T S E T 6.3) string model with exact first order Q C D calculation;

M o d e l 3 : Lund 6.3 ( L E P T O 5.2, J E T S E T 6.3) p a r t o n shower model.

The Lund 6.3 matrix element and the parton shower ver- sion (model 2 and 3) with their standard parameters de- scribe the pattern of the data well in the whole kinematic range. The decreasing multiplicity for increasing Q2 at high z is reasonably simulated by the inclusion of Q C D processes. The older Lund version 4.3 (model 1) also de- scribes qualitatively the kinematic dependences of the data.

4 Results

4.1 Scaled energy distributions

The normalised differential scaled energy distributions 1 d N

N u d z have been determined separately for positive and negative hadrons as well as for all charged hadrons in small bins of x and

Q2 or

Wand

Q2.

The bins are defined in Table 7 in the Appendix. The corresponding cross sections together with the mean values of the event vari- ables are also presented in the Appendix (Tables 9-14).

4.2 Transverse m o m e n t u m distributions

In this Sect. we present the pt 2 dependence of the cross section for all charged particles. Because extensive stu- dies [23] have not shown any significant difference be- tween the p r o t o n and deuterium data, both data sets have been merged. The high statistics of the resulting data set allow studies of the cross sections up to high values of p2 in different kinematical regions.

In Fig. 3 we show the inclusive p2 distributions in z and W 2 bins. The corresponding cross sections are

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N

z

Z

10

0.1

10

0.1

10

0.1

= $ , 9 o = A ,u.p

oa~. /.zd

+ +

... it '+

~ 9 o ' .

t

:~ . ~ ,~. .~ ~ ~ . . .

~ , . . ,~ .,, r ~

4,...4...,~. b , 9 . . ~ , . . . , ~ . . . , 0 . 0 3 5 < X < 0 . 0 9

I I

, ~ - o " . . ~ , . . ,~ ... ,

i ' § 2 - ~ ... i

, ~ ,~,... , ~ . . . .

t . . ~ . i

. . .

{

0 . 2 < X < 0 . 4 . . . I

1 10 10 2 1

o . , , . . ! ! ~ . o 0 . 1 0 < Z < 0 . 1 5

~ ' - = 9 = ~ im = e 0 . 1 5 < Z < 0 . 2 5

. . . 9 - 9 -i,~.- ~ r 0 . 2 5 < Z < 0 . 3 5

. . . . 9 :- 9 ii + ~ -~ q, 0 . 3 5 < Z < 0 . 4 5 o

; , - ~ ' o.,~<z<o.~o

3

" ~ ... ~- + + + o.6o<z<~.o

0,02<•

hi

f ... .o.- $ ~ .... ~ , . . @ /

: A ~ h

~'~ * e r 't

~t...:

~-..-... ....~

0 . 0 9 < X < 0 . 2

0 . 4 < X < 1

. . . i

O 2 [GeV 2]

10

,'1

! + ~ .... t . . .

T, ,

. . . . , , , J 102

Fig. 1. Comparison of normalised differential scaled energy distributions for charged hadrons in bins of x, Q2 and z. The dotted lines represent linear fits in In Q2 inspired by QCD.

The errors shown are statistical only

given in Tables 16a, b in the Appendix. At large values of p~ a tail is observed, which clearly increases with W 2, as expected from QCD. The dotted lines are fits to the 1 9 d41~oc 1/(m 2 + p ~ ) ' , inspired by data using the ansatz Nuu ap,

a p r o p a g a t o r form. The mass term m obtained from the fits is in the range 0.6-1.6 GeV (excluding the very low z and W 2 bin), the power e is in the range 1.4~2.6, with a central value close to two. Thus the fall off of the measured cross section at large p2 (p2 ~ m 2) indicates the power law behaviour o c l / p 4, as expected from

Q C D .

Further, the measured mean squared transverse mo- m e n t u m ( p ~ ) for charged hadrons was analysed. Fig- ure 4 shows the W 2 dependence of ( p { ) in z and Q2 bins (Table 17). A linear increase of ( p 2 ) with In W z is seen for all z, Q2 bins, and this is more p r o n o u n c e d

in the high z region. The lines represent linear fits in In W 2 to the data.

To investigate a possible Q2 dependence, such as that observed for the z distributions at fixed W 2 [25], we plot in Fig. 5 the fitted ( p 2 ) in each z bins for a central W 2 value of 200 GeV 2. The data for Q2 > 5 GeV 2 show no Q2 dependence. Only for the lowest Q2 bin (2 GeV 2

< Q 2 < 5 GeV 2) the average pt 2 is slightly smaller, which is presumably due to the contribution of elastic and qua- si-elastic events9 Because x ~ ( W Z / Q 2 + 1)- 1, this implies no significant x dependence, except for very small x. This confirms, with increased precision, the conclusions of earlier E M C experiments [27, 28] that W 2 and z are the relevant variables for the p2 behaviour.

In Fig. 6 the W 2 dependence of ( p ~ ) (see also Ta- ble 18) are compared to those from other experiments.

Here the high precision of our data can be seen. They

(7)

N -O Z "

"O Z

10

0.1

10

0.1

10

0.1

. . . . alL. T

, ~ ... ,~ ....

9 =,,, EMC, ,u,p & ,u,d LUND m o d e l 1 - - m o d e l 2 m o d e l ,3

- 0 . 0 1 < X < 0 . 0 2 i J i i l l * l [

- - . - . . ~ . 9 - -

-

0.035~

i[ ,,i

'_ ~ , : : " : .

,~'" #~'S.~.'2E..~.'EL.E,L'22LL'.~"-___=

+

I 0 . 2 < X < 0 . 4

. . . L . . . L

1 10 102

~ a - - ' : ~ ' ~ - 9

- , 9 0 , 1 0 < Z ' < 0 . 1 5

9 . ~ ~ 0 . 1 5 < Z < 0 . 2 5 '

&

9 ---,; m, 0 . 2 5 < Z < 0 . 3 5

0 . 3 5 < Z < 0 . 4 5

~ 0.45<Z<0.60

0 . 6 0 < Z < 1 . 0 0 . 0 2 < X < 0 . 0 3 5

, t , , t

~ ~

0 . 0 9 < X < 0 . 2

I

_ _ _ . _ _ . . . e

0 . 4 < X < 1

, , i = . . . . i . . . i

1 1 0 102

[GeV 2]

Fig. 2. C o m p a r i s o n of normalised differential scaled energy distributions for charged h a d r o n s of the merged/~p- a n d / t d - d a t a with different versions of the L u n d fragmentation model [18, 20]. The errors shown are statistical only. The relative systematic error is 10%

agree well with the results of a vNe-scattering experiment a low W 2 range [29] and with the previous measurement of this experiment [27] apart from a slight discrepancy in the lowest z bin.

The (p~) dependence o n z 2 for different W 2 bins is shown in Fig. 7. At small z 2 the expected rapid rise of ( p { ) with z 2 (seagull effect) is observed. This is more p r o n o u n c e d for the high W 2 bins. F o r z >0.4, the in- crease is much smaller for the low W 2 bins; for the high W 2 bins ( p 2 ) reaches a plateau or even shows a falling trend.

Figure 8 compares ( p ~ ) as a function of W 2 with the different L u n d models specified in Sect. 4.1. The de- fault parameters have been used, of which the most im- portant for (pZ) are: k t = 0 . 4 4 G e V , a q = 0 . 4 G e V , A

= 0.4 GeV and the cutoff parameter (for model 3 only) train = 1 GeV.

The p a r t o n shower model (model 3), which fits e + e - data well [32], fails to describe the size of ( p 2 ) as well as the dependence on W 2. This is due to an underestima- tion of the cross section at large p~ [23]. Simple retuning of the model parameters does not change the pt z behav- iour sufficiently in order to describe the data [33]. The matrix element version of the model (model 2) describes the shape of the W z dependence. However, it underesti- mates ( p 2 ) significantly for large z (z > 0.4). This discrep- ancy cannot be cured by increasing the intrinsic k,, be- cause this would cause a disagreement with backward produced hadrons as shown earlier by the E M C [28].

Only the older version Lund 4.3 (model 1), which ac- counts for soft gluon radiation processes, reasonably de- scribes the data, except for a small underestimation on (pZ) in the highest z range.

The same behaviour of the models is demonstrated

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101

10 o I i ~ 0.1 < z < 0.2 ,!' 0.2 < z < 0.4 _ 0.4 < z < 1.0

10-' ~ EMC,/zp & #d ~

r ; -:4

10 ~ 9 W 2 < 9 0 G e V = : "-~,

o 9 0 G e V 2 < W z < 1 5 0 G e V =

10 -~ ~ " 9 150Ge~P<W z<200GeV= ~ ~ ~ 9

n 200 OeV 2 < W 2 < 2 7 5 GeV~ =~

10~ ~ ~ " ,',9 275GeVZ<W=<350GeV=350GeV = < w a '~"~.. t . . . . q o t.

~ 0 1 0 - ' I i t

( . 3 1 0 0 'I, ! % + ? ,k

" - ' ' ! ' " " i , " " " , '

. . ~ ~ 9 .

. ; 0% t .

F q m

n O 10~ .... " ~ - " = I |

~. . ::. -- . _ .

Z 10-' :" Q r ~. o e .

\ .

\ r

Z = 10 ~ " "

: ' .... * " " ... l :%. .... * .,

10-' F"~ "~'. ,, ~ . ....

9 r - - " ~ " "

1 0 -~ " *" " " ...

,, t f 9

1 0 -~ . ". ....

I O - " ~' " - .t . . . .

t " .... ~' ~'

10 -=

/

I 0 - '

1 0 -~ , ~ , I ~ , , ~ ~ , I ~ ~ , , , , I ~ ~ ,

0 10 0 10 10

p2 [GeV 2]

Fig. 3. Normalised differential p~ distributions for charged hadrons of the merged #p- and #d-data in different W 2 and z bins. The

. 1 dNh ,/ 2 2,=

dotted lines represent fits using the ansatz ,, .5~-2 oc 1/tm +Pt ) inspired by a propagator form. The errors shown are statistical only r~, ap,

2 < 02 < 5 GeM 2 5 < Q2 < 10 GeM z 10 < 02 < 20 GeV z 20 < Qz < 40 OeV 2 40 GeV z < QZ

g-, 0

>

( . 9 0 . 8

A ~- 0.4 EL V

0

9 EMC, # p &/~d

0.8 -

0.4

i , = l , , , [

I I I f ' ' J

0 . 8 -

0 . 4 -

0 , , , , , , , I , , ,

10 2

,,,I

J

L , , I

f

A

,L

y

Y , , , , I

,,i J , i

Y

, , I , , ,

I l t , l , , I , , I i i , , , , I i J , , , , , * , 1 J J L i I i , , , , [ , ,

1 0 2 1 0 2 1 0 2 1 0 2

W 2 [GeV 21

Fig. 4. W 2 dependence of (p~) for charged hadrons in bins of Q2 and z. The solid lines represent linear fits in In W 2 . The errors shown are statistical only

(9)

g -

>

o) 0 A

s

V 1.2

1

0.8

0.6

0.4

0.2

0

EMC, # p & # d 9 0 . 1 < z < 0 . 2 9 0 . 2 < z < 0 . 4 9 0 . 4 < z < 1 . 0

W 2 = 2 0 0 G e V 2

i i i i i i i i i i i E J i i i

10 102

Q2 [ G e V 2]

Fig. 5. ( p ~ ) o f c h a r g e d h a d r o n s for fixed W 2 as a f u n c t i o n o f Q2 in different z bins. T h e errors s h o w n are statistical o n l y

>

(D A V

1.2

1

0.8

0.6

0.4

0.2

0 0

EMC, lzp & p,d 9 0 . 1 < z < 0 . 2 [] 0.2 < z < 0.4 9 0 . 4 < z < 1 . 0

9 ++ .+

,%, ",+

.+

OOoe 0o r 0o

o EMC, ,u,p ( 1 9 8 0 ) D A B C D L O S , v N e

!+.+

. . . . i , , i i I i i i k I i i i i I i i i r

100 200 300 400 500

W 2 [ G e V 2]

Fig. 6. Comparison of (p~) of charged hadrons as a function of W 2 with BEBC data of the collaboration ABCDLOS [29] and a previous EMC analysis [27]. The three z ranges for the data shown are the same for the three analyses. The errors shown are statistical only

L"

>

A V

1.2

1

0.8

0.6

0.4

0.2

0

9 I

' I

)

EMC, ~p & ~d

I < W = > = 6 0 G e V ~ 9 <W2> = 1 1 4 G e V 2 9 <W2> = 1 7 5 G e V 2 9 <W=> = 3 0 4 GeV 2

i i i i I i i , , I i i i i I i E r , I i i j i

0.2 0.4 0.6 0.8

Z 2

Fig. 7. z z dependence of (p2) (seagull effect) for charged hadrons in different W z bins. The errors are statistical only

369

1.2

EMC, ,u,p & ,u,d L U N D

i 9 0.1 < z < 0.2 model 1

9 0.2 < z < 0.4 ... model 2 9 0.4 < z < 1.0 . . . model 3

0.8 ,

A 0.6

. . . ;.i ...

V 0.4 " ... - " " ... ----

0.2

0 , i i i ~ i ~ ~ i I ~ ~ L ~ I ~ i L r [ ~ ~ ~ i

100 200 300 400 500

W 2 [ O e V =]

Fig. 8. C o m p a r i s o n of t h e W 2 a n d z d e p e n d e n c e of ( p 2 ) of c h a r g e d h a d r o n s w i t h different v e r s i o n s of t h e L u n d f r a g m e n t a t i o n m o d e l [18, 20]. T h e errors s h o w n are statistical o n l y

1.2

9 EMC, ~ p & ~ d L U N D

W 2 > 150 OeV 2 model 1

! ... model 2

. . . model 5

0.2

0 i i i i I i i i i I i ~ ~ i I L ~ b i I ~ i i i

0 0.2 0.4 0.6 0.8

Z 2

Fig. 9. Comparison of the z z dependence of (p~) of charged had- rons with different versions of the Lund fragmentation m o d e l [18, 20]. The errors s h o w n are statistical only

% 0.8 0 A 0.6

V 0.4

in Fig. 9, where <p2> of h a d r o n s p r o d u c e d at W 2

> 150 G e V 2 is p l o t t e d versus z 2. M o d e l 1 shows again the best description, b u t the trend o f the d a t a to reach a p l a t e a u or eventually decrease at high z 2 is n o t r e p r o - duced.

S u m m a r i z i n g o u r c o m p a r i s o n s to M o n t e C a r l o m o d - els it c a n be said, t h a t o n l y the older L u n d 4.3 m o d e l (model 1), which includes c o n t r i b u t i o n s due to soft g l u o n radiation, is able to describe b o t h the z a n d p2 b e h a v i o u r of the data.

4.3 Charge multiplicity ratios

I n this Sect. we c o m p a r e ratios of charge multiplicities for #-scattering f r o m p r o t o n s , d e u t e r o n s a n d neutrons.

T h e derivation of the c h a r g e d h a d r o n p r o d u c t i o n rates f r o m n e u t r o n s was p e r f o r m e d using (2). Figure 10 shows the ratio of the integrated c h a r g e multiplicities for m u o n scattering f r o m p r o t o n s , d e u t e r o n s a n d n e u t r o n s versus

(10)

N

N - O t;

+ N

i N

N

+ N

N

1.8

1.6

1.4

1.2

0.8

0.6

3.6 3.2

2 . 8

2 . 4

2

1.6

1.2

0 . 8

O) Z > 0 . 1

EMC 9 ,u,p A /zd 9 ,u,n

+

e

10 - 2 10 -1 1

XBj

O) p.p, z > 0.3 9 EMC 0 CHIO

3.5

2.5

1.5

0.5

2 . 8

2 . 4

1.6

1.2 0.8 0.4

b) Z>0.3 EMC A /.~d 9 /~n

, 4,

9 + ! ... ... + I ...

0 - 2 10 - I I

XBj

L ~

D) /an, en, z > 0 . 3

9 EMC

o CHI0 [ ] Mortln et ol- Z~ Bebek et ol.

... ,...!, !ot t. !.

10 - 2 10 -~ 1 10 - 2 10

XBj XBj

-1 1

Fig. lOa, b. Ratio of the integrated charge multiplicities as a function of x for two different z ranges. The errors shown are statistical only

Fig. l l a , b. Ratio of integrated charge multiplicities as a function of x; a C o m p a r i s o n of the ratio from the # p - d a t a to [35]; b Comparison of the ratio from the # n - d a t a to [35, 36]; The errors shown are statistical only

x in two different regions of z, from 0.1 to 1 and from 0.3 to 1. The data have been integrated over the whole Q2 range, as, for the ratios, no significant dependence on Q2 was seen in our data. Generally, the observed x dependence is stronger for the higher z range, as with increasing z the probability ratios are closer to unity for p, d and n. Here fragmentation effects and resonance decays dominate. The x dependence of the charge multi- plicity ratios in small bins of z can be found in Table 19 in the Appendix.

The observed x dependence of the charge multiplicity ratios can be interpreted as follows. At small x, the ratios

for m u o n scattering from all these targets approach each other close to unity due to the dominant contribution of the sea quarks to the cross section. F o r increasing x we see, when scattering from the proton, the expected strong increase of the excess of positive particles due to the dominance of the positive u quarks at high x.

This effect is still seen for the isoscalar deuteron, as the virtual p h o t o n couples preferentially to the positive u quark. F o r the neutron we observe, for both z ranges, that the charge multiplicity ratio is significantly above unity for a wide range of the x region covered by our data.

(11)

371 A neutral electromagnetic current probing a neutral

target shows an excess of positive charged hadrons in the forward scattering hemisphere over a wide kinematic range. This proves a charge composition of the neutron, where the magnitude of the charge of the positive constit- uents must be greater than that of the negative, also implying more than two charged constituents. This was also observed at a significant level in a previous publica- tion [34]. In addition, contrary to the proton and deuter- on data, the charge multiplicity ratio for the neutron shows a slight decrease with x. This confirm indepen- dently the behaviour of the quark distribution functions inferred from the structure functions measurements; at high x the dv(x) distribution in the neutron predominates over the u~(x). A cross over to negative values of the ratio is expected for x between 0.5 and 0.6.

The systematic error on the measured charge multi- plicity ratio for the neutron is estimated to be 3% for low x rising to 12% for the highest x data point. It is dominated by the uncertainty of the different accep- tances for positive and negative hadrons in the EMC forward spectrometer [17].

In the low x region a comparison can be made with a previous experiment [35] in a similar energy range.

The data agree well in the overlap region for both, #p- and # n-scattering (see Fig. 11 a, b).

4.4 Determination of d~(x)/u~(x)

Taking the difference of the normalised scaled energy distribution (1) for positive and negative hadrons the contribution of the sea quarks cancels exactly. Using charge conjugation symmetry [-O~,(z, Q2)=D~i(Q2)] and the definition of valence quark distributions [q~(x,

Q2)

=q(x, QZ)-qs(X ,

Q2)],

the following equation can be derived

l [dN h+ dN h \ x

Nu \ dz dzz

)=g.(euu.(Dy--DV)

2 h +

+ ea dv (Da - D]-)), (4) where ~' e~ qi has been replaced by the correspond-

i - - u , d . . . .

ins structure function F2.

Considering only the production of pions in the had- ronic final state, then using isospin invariance [(D~ +

~z ~ + p _ _ n . p _ _ n .

= Dd ), (D~ = Da ), (u~ - d~-. u~), (d~ - uv-. dr)], (4) can be rewritten for muon scattering from protons and neu- trons separately as follows:

1 ( . a N ; + d N ; - ]

Nf \ dz dz ] dz

- F~X .(%2 u~--ea2d~).(D'~+--D'~-)dz, "

1 /dN,~+ dN,~-'~ d z N~\ dz dz ]

__x

F~" (e2 d ~ - e 2 u,)- (D~ + -- D~ ) d z. (5)

To improve the accuracy of the experimental evaluation, the above equations can be integrated over a range in z. Taking the ratio of these integrated equations, the difference of the fragmentation functions cancels and one can directly solve for dv(x)/u~(x) which, for fixed

Q2,

is a function of x only

d~(x)_4.N~(x)+l

uv(x) 4+N"(x) ' (6)

where N~(x) is to be measured by the experiment

1 . /dN/, dN,~ \

T. J [ ~ (x)-- ~ (x)] d z

. / d N ~ F~(x)" (7)

In this experiment the possibility to identify hadrons is limited. Therefore (6) has to be corrected for the presence of charged kaons and (anti-)protons in the hadronic final state, but as pions are the dominant particles, the correc- tion is expected to be small. If one includes the fragmen- tation into charged kaons and (anti-)protons, the ratio takes the following form

dr(x) 4.~h(x) + 1 - A

u~ (x) - 4 + Nh (x) (1 -- A)' (8)

where Nh(x) denotes the same ratio as N~(x) above, ex- cept that all hadrons are used now instead of only pions in case of N~(x). A contains only the fragmentation func- tions, which in the QPM are independent of the scatter- ing process thus independent of x:

Z 2

j" (D] --D~ +) dz

A = 1 5, (9)

Z 2

I (D~ +-D~-)dz

51

A is limited to be between 0 and 1 and has been estimated with the recent fragmentation models by the Lund group [-19, 20] to be 0.4-t-0.1. For the experimental evaluation of (8), all quantities in Nh(x) containing hadron produc- tion rates from neutrons have to be expressed by produc- tion rates from deuterons using (2). Further, after inte- gration over the whole range accessible in z, it becomes

~h(X):=N~0.a \ dz (x)-- (x dz 1 ; [ d N p h+ hdd@ )) Nun o. 1 \ dz ( x ) - (x dz

L H ( x ) \ _

'/l+

F : q x i ) - '"

(lO)

Figure 12 shows the difference of the integrated charge multiplicities in the z range 0.1-1 for muon scattering from protons and deuterons in different bins of x. The main systematic uncertainties in the determination of dv(x)/uv(x), which are discussed in more detail in [17], are the following:

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