Observation of scaling violations in scaled momentum distributions at HERA

Abstract

Charged particle production has been measured in deep inelastic scattering (DIS) events over a large range of x and Q2 using the ZEUS detector. The evolution of the scaled momentum, xp, with Q2, in the range 10 to 1280 GeV2, has been investigated in the current fragmentation region of the Breit frame. The results show clear evidence, in a single experiment, for scaling violations in scaled momenta as a function of Q2.

Full text

arXiv:hep-ex/9710011v2 28 Oct 1997
Observation of Scaling Violations
in Scaled Momentum Distributions
at HERA
ZEUS Collaboration
Abstract
Charged particle production has been measured in deep inelastic scattering (DIS)
events over a large range of xand Q2using the ZEUS detector. The evolution of the
scaled momentum, xp, with Q2,in the range 10 to 1280 GeV2, has been investigated in
the current fragmentation region of the Breit frame. The results show clear evidence, in
a single experiment, for scaling violations in scaled momenta as a function of Q2.
DESY 97-183

The ZEUS Collaboration
J. Breitweg, M. Derrick, D. Krakauer, S. Magill, D. Mikunas, B. Musgrave, J. Repond, R. Stanek,
R.L. Talaga, R. Yoshida, H. Zhang
Argonne National Laboratory, Argonne, IL, USA p
M.C.K. Mattingly
Andrews University, Berrien Springs, MI, USA
F. Anselmo, P. Antonioli, G. Bari, M. Basile, L. Bellagamba, D. Boscherini, A. Bruni, G. Bruni,
G. Cara Romeo, G. Castellini1, L. Cifarelli2, F. Cindolo, A. Contin, M. Corradi, S. De Pasquale,
I. Gialas3, P. Giusti, G. Iacobucci, G. Laurenti, G. Levi, A. Margotti, T. Massam, R. Nania,
F. Palmonari, A. Pesci, A. Polini, F. Ricci, G. Sartorelli, Y. Zamora Garcia4, A. Zichichi
University and INFN Bologna, Bologna, Italy f
C. Amelung, A. Bornheim, I. Brock, K. Cob¨oken, J. Crittenden, R. Deffner, M. Eckert,
M. Grothe, H. Hartmann, K. Heinloth, L. Heinz, E. Hilger, H.-P. Jakob, U.F. Katz, R. Kerger,
E. Paul, M. Pfeiffer, Ch. Rembser5, J. Stamm, R. Wedemeyer6, H. Wieber
Physikalisches Institut der Universit¨at Bonn, Bonn, Germany c
D.S. Bailey, S. Campbell-Robson, W.N. Cottingham, B. Foster, R. Hall-Wilton, M.E. Hayes,
G.P. Heath, H.F. Heath, J.D. McFall, D. Piccioni, D.G. Roff, R.J. Tapper
H.H. Wills Physics Laboratory, University of Bristol, Bristol, U.K. o
M. Arneodo7, R. Ayad, M. Capua, A. Garfagnini, L. Iannotti, M. Schioppa, G. Susinno
Calabria University, Physics Dept.and INFN, Cosenza, Italy f
J.Y. Kim, J.H. Lee, I.T. Lim, M.Y. Pac8
Chonnam National University, Kwangju, Korea h
A. Caldwell9, N. Cartiglia, Z. Jing, W. Liu, B. Mellado, J.A. Parsons, S. Ritz10, S. Sampson,
F. Sciulli, P.B. Straub, Q. Zhu
Columbia University, Nevis Labs., Irvington on Hudson, N.Y., USA q
P. Borzemski, J. Chwastowski, A. Eskreys, J. Figiel, K. Klimek, M.B. Przybycie´n, L. Zawiejski
Inst. of Nuclear Physics, Cracow, Poland j
L. Adamczyk11, B. Bednarek, M. Bukowy, K. Jele´n, D. Kisielewska, T. Kowalski,
M. Przybycie´n, E. Rulikowska-Zar¸ebska, L. Suszycki, J. Zaj¸ac
Faculty of Physics and Nuclear Techniques, Academy of Mining and Metallurgy, Cracow, Poland j
Z. Duli´nski, A. Kota´nski
Jagellonian Univ., Dept. of Physics, Cracow, Poland k

G. Abbiendi12, L.A.T. Bauerdick, U. Behrens, H. Beier, J.K. Bienlein, G. Cases13 , O. Deppe,
K. Desler, G. Drews, U. Fricke, D.J. Gilkinson, C. Glasman, P. G¨ottlicher, T. Haas, W. Hain,
D. Hasell, K.F. Johnson14, M. Kasemann, W. Koch, U. K¨otz, H. Kowalski, J. Labs,
L. Lindemann, B. L¨ohr, M. L¨owe15, O. Ma´nczak, J. Milewski, T. Monteiro16 , J.S.T. Ng17 ,
D. Notz, K. Ohrenberg18, I.H. Park19, A. Pellegrino, F. Pelucchi, K. Piotrzkowski, M. Roco20,
M. Rohde, J. Rold´an, J.J. Ryan, A.A. Savin, U. Schneekloth, F. Selonke, B. Surrow, E. Tassi,
T. Voß21, D. Westphal, G. Wolf, U. Wollmer22, C. Youngman, A.F. ˙
Zarnecki, W. Zeuner
Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany
B.D. Burow, H.J. Grabosch, A. Meyer, S. Schlenstedt
DESY-IfH Zeuthen, Zeuthen, Germany
G. Barbagli, E. Gallo, P. Pelfer
University and INFN, Florence, Italy f
G. Maccarrone, L. Votano
INFN, Laboratori Nazionali di Frascati, Frascati, Italy f
A. Bamberger, S. Eisenhardt, P. Markun, T. Trefzger23 , S. W¨olfle
Fakult¨at f¨ur Physik der Universit¨at Freiburg i.Br., Freiburg i.Br., Germany c
J.T. Bromley, N.H. Brook, P.J. Bussey, A.T. Doyle, N. Macdonald, D.H. Saxon, L.E. Sinclair,
E. Strickland, R. Waugh
Dept. of Physics and Astronomy, University of Glasgow, Glasgow, U.K. o
I. Bohnet, N. Gendner, U. Holm, A. Meyer-Larsen, H. Salehi, K. Wick
Hamburg University, I. Institute of Exp. Physics, Hamburg, Germany c
L.K. Gladilin24, D. Horstmann, D. K¸cira, R. Klanner, E. Lohrmann, G. Poelz, W. Schott25,
F. Zetsche
Hamburg University, II. Institute of Exp. Physics, Hamburg, Germany c
T.C. Bacon, I. Butterworth, J.E. Cole, G. Howell, B.H.Y. Hung, L. Lamberti26 , K.R. Long,
D.B. Miller, N. Pavel, A. Prinias27, J.K. Sedgbeer, D. Sideris
Imperial College London, High Energy Nuclear Physics Group, London, U.K. o
U. Mallik, S.M. Wang, J.T. Wu
University of Iowa, Physics and Astronomy Dept., Iowa City, USA p
P. Cloth, D. Filges
Forschungszentrum J¨ulich, Institut f¨ur Kernphysik, J¨ulich, Germany
J.I. Fleck5, T. Ishii, M. Kuze, I. Suzuki28, K. Tokushuku, S. Yamada, K. Yamauchi, Y. Yamazaki29
Institute of Particle and Nuclear Studies, KEK, Tsukuba, Japan g
S.J. Hong, S.B. Lee, S.W. Nam30, S.K. Park
Korea University, Seoul, Korea h
F. Barreiro, J.P. Fern´andez, G. Garc´ıa, R. Graciani, J.M. Hern´andez, L. Herv´as5, L. Labarga,
M. Mart´ınez, J. del Peso, J. Puga, J. Terr´on31 , J.F. de Troc´oniz
Univer. Aut´onoma Madrid, Depto de F´ısica Te´orica, Madrid, Spain n

F. Corriveau, D.S. Hanna, J. Hartmann, L.W. Hung, W.N. Murray, A. Ochs, M. Riveline,
D.G. Stairs, M. St-Laurent, R. Ullmann
McGill University, Dept. of Physics, Montr´eal, Qu´ebec, Canada a,b
T. Tsurugai
Meiji Gakuin University, Faculty of General Education, Yokohama, Japan
V. Bashkirov, B.A. Dolgoshein, A. Stifutkin
Moscow Engineering Physics Institute, Moscow, Russia l
G.L. Bashindzhagyan, P.F. Ermolov, Yu.A. Golubkov, L.A. Khein, N.A. Korotkova,
I.A. Korzhavina, V.A. Kuzmin, O.Yu. Lukina, A.S. Proskuryakov, L.M. Shcheglova32,
A.N. Solomin32, S.A. Zotkin
Moscow State University, Institute of Nuclear Physics, Moscow, Russia m
C. Bokel, M. Botje, N. Br¨ummer, F. Chlebana20, J. Engelen, E. Koffeman, P. Kooijman,
A. van Sighem, H. Tiecke, N. Tuning, W. Verkerke, J. Vossebeld, M. Vreeswijk5, L. Wiggers,
E. de Wolf
NIKHEF and University of Amsterdam, Amsterdam, Netherlands i
D. Acosta, B. Bylsma, L.S. Durkin, J. Gilmore, C.M. Ginsburg, C.L. Kim, T.Y. Ling,
P. Nylander, T.A. Romanowski33
Ohio State University, Physics Department, Columbus, Ohio, USA p
H.E. Blaikley, R.J. Cashmore, A.M. Cooper-Sarkar, R.C.E. Devenish, J.K. Edmonds,
J. Große-Knetter34, N. Harnew, C. Nath, V.A. Noyes35 , A. Quadt, O. Ruske, J.R. Tickner27 ,
H. Uijterwaal, R. Walczak, D.S. Waters
Department of Physics, University of Oxford, Oxford, U.K. o
A. Bertolin, R. Brugnera, R. Carlin, F. Dal Corso, U. Dosselli, S. Limentani, M. Morandin,
M. Posocco, L. Stanco, R. Stroili, C. Voci
Dipartimento di Fisica dell’ Universit`a and INFN, Padova, Italy f
J. Bulmahn, B.Y. Oh, J.R. Okrasi´nski, W.S. Toothacker, J.J. Whitmore
Pennsylvania State University, Dept. of Physics, University Park, PA, USA q
Y. Iga
Polytechnic University, Sagamihara, Japan g
G. D’Agostini, G. Marini, A. Nigro, M. Raso
Dipartimento di Fisica, Univ. ’La Sapienza’ and INFN, Rome, Italy f
J.C. Hart, N.A. McCubbin, T.P. Shah
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, U.K. o
D. Epperson, C. Heusch, J.T. Rahn, H.F.-W. Sadrozinski, A. Seiden, R. Wichmann, D.C. Williams
University of California, Santa Cruz, CA, USA p
O. Schwarzer, A.H. Walenta
Fachbereich Physik der Universit¨at-Gesamthochschule Siegen, Germany c

H. Abramowicz36, G. Briskin, S. Dagan36 , S. Kananov36, A. Levy36
Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics, Tel-Aviv University,
Tel-Aviv, Israel e
T. Abe, T. Fusayasu, M. Inuzuka, K. Nagano, K. Umemori, T. Yamashita
Department of Physics, University of Tokyo, Tokyo, Japan g
R. Hamatsu, T. Hirose, K. Homma37, S. Kitamura38, T. Matsushita
Tokyo Metropolitan University, Dept. of Physics, Tokyo, Japan g
R. Cirio, M. Costa, M.I. Ferrero, S. Maselli, V. Monaco, C. Peroni, M.C. Petrucci, M. Ruspa,
R. Sacchi, A. Solano, A. Staiano
Universit`a di Torino, Dipartimento di Fisica Sperimentale and INFN, Torino, Italy f
M. Dardo
II Faculty of Sciences, Torino University and INFN - Alessandria, Italy f
D.C. Bailey, C.-P. Fagerstroem, R. Galea, G.F. Hartner, K.K. Joo, G.M. Levman, J.F. Martin,
R.S. Orr, S. Polenz, A. Sabetfakhri, D. Simmons, R.J. Teuscher5
University of Toronto, Dept. of Physics, Toronto, Ont., Canada a
J.M. Butterworth, C.D. Catterall, T.W. Jones, J.B. Lane, R.L. Saunders, M.R. Sutton, M. Wing
University College London, Physics and Astronomy Dept., London, U.K. o
J. Ciborowski, G. Grzelak39, M. Kasprzak, K. Muchorowski40, R.J. Nowak, J.M. Pawlak,
R. Pawlak, T. Tymieniecka, A.K. Wr´oblewski, J.A. Zakrzewski
Warsaw University, Institute of Experimental Physics, Warsaw, Poland j
M. Adamus
Institute for Nuclear Studies, Warsaw, Poland j
C. Coldewey, Y. Eisenberg36, D. Hochman, U. Karshon36
Weizmann Institute, Department of Particle Physics, Rehovot, Israel d
W.F. Badgett, D. Chapin, R. Cross, S. Dasu, C. Foudas, R.J. Loveless, S. Mattingly, D.D. Reeder,
W.H. Smith, A. Vaiciulis, M. Wodarczyk
University of Wisconsin, Dept. of Physics, Madison, WI, USA p
S. Bhadra, W.R. Frisken, M. Khakzad, W.B. Schmidke
York University, Dept. of Physics, North York, Ont., Canada a

1also at IROE Florence, Italy
2now at Univ. of Salerno and INFN Napoli, Italy
3now at Univ. of Crete, Greece
4supported by Worldlab, Lausanne, Switzerland
5now at CERN
6retired
7also at University of Torino and Alexander von Humboldt Fellow at DESY
8now at Dongshin University, Naju, Korea
9also at DESY
10 Alfred P. Sloan Foundation Fellow
11 supported by the Polish State Committee for Scientific Research, grant No. 2P03B14912
12 supported by an EC fellowship number ERBFMBICT 950172
13 now at SAP A.G., Walldorf
14 visitor from Florida State University
15 now at ALCATEL Mobile Communication GmbH, Stuttgart
16 supported by European Community Program PRAXIS XXI
17 now at DESY-Group FDET
18 now at DESY Computer Center
19 visitor from Kyungpook National University, Taegu, Korea, partially supported by DESY
20 now at Fermi National Accelerator Laboratory (FNAL), Batavia, IL, USA
21 now at NORCOM Infosystems, Hamburg
22 now at Oxford University, supported by DAAD fellowship HSP II-AUFE III
23 now at ATLAS Collaboration, Univ. of Munich
24 on leave from MSU, supported by the GIF, contract I-0444-176.07/95
25 now a self-employed consultant
26 supported by an EC fellowship
27 PPARC Post-doctoral Fellow
28 now at Osaka Univ., Osaka, Japan
29 supported by JSPS Postdoctoral Fellowships for Research Abroad
30 now at Wayne State University, Detroit
31 partially supported by Comunidad Autonoma Madrid
32 partially supported by the Foundation for German-Russian Collaboration DFG-RFBR
(grant no. 436 RUS 113/248/3 and no. 436 RUS 113/248/2)
33 now at Department of Energy, Washington
34 supported by the Feodor Lynen Program of the Alexander von Humboldt foundation
35 Glasstone Fellow
36 supported by a MINERVA Fellowship
37 now at ICEPP, Univ. of Tokyo, Tokyo, Japan
38 present address: Tokyo Metropolitan College of Allied Medical Sciences, Tokyo 116, Japan
39 supported by the Polish State Committee for Scientific Research, grant No. 2P03B09308
40 supported by the Polish State Committee for Scientific Research, grant No. 2P03B09208

asupported by the Natural Sciences and Engineering Research Council of
Canada (NSERC)
bsupported by the FCAR of Qu´ebec, Canada
csupported by the German Federal Ministry for Education and Science,
Research and Technology (BMBF), under contract numbers 057BN19P,
057FR19P, 057HH19P, 057HH29P, 057SI75I
dsupported by the MINERVA Gesellschaft f¨ur Forschung GmbH, the German
Israeli Foundation, and the U.S.-Israel Binational Science Foundation
esupported by the German Israeli Foundation, and by the Israel Science
Foundation
fsupported by the Italian National Institute for Nuclear Physics (INFN)
gsupported by the Japanese Ministry of Education, Science and Culture (the
Monbusho) and its grants for Scientific Research
hsupported by the Korean Ministry of Education and Korea Science and Engi-
neering Foundation
isupported by the Netherlands Foundation for Research on Matter (FOM)
jsupported by the Polish State Committee for Scientific Research, grant
No. 115/E-343/SPUB/P03/002/97, 2P03B10512, 2P03B10612, 2P03B14212,
2P03B10412
ksupported by the Polish State Committee for Scientific Research (grant No.
2P03B08308) and Foundation for Polish-German Collaboration
lpartially supported by the German Federal Ministry for Education and Science,
Research and Technology (BMBF)
msupported by the Fund for Fundamental Research of Russian Ministry for
Science and Education and by the German Federal Ministry for Education
and Science, Research and Technology (BMBF)
nsupported by the Spanish Ministry of Education and Science through funds
provided by CICYT
osupported by the Particle Physics and Astronomy Research Council
psupported by the US Department of Energy
qsupported by the US National Science Foundation
VII

1 Introduction
The observation of scaling violations in structure functions [1] measured in neutral current,
deep inelastic scattering (DIS) helped to establish Quantum Chromodynamics (QCD) as the
theory of strong interactions and has led to measurements of the strong coupling constant,
αs.Similar scaling violations are predicted in the fragmentation functions, which represent the
probability for a parton to fragment into a particular hadron carrying a fraction of the parton’s
energy. Fragmentation functions incorporate the long distance, non-perturbative physics of the
hadronization process in which the observed hadrons are formed from final state partons of the
hard scattering process and, like structure functions, cannot be calculated in perturbative QCD,
but can be evolved from a starting distribution at a defined energy scale. If the fragmentation
functions are combined with the cross sections for the inclusive production of each parton
type in the given physical process, predictions can be made for scaling violations in the scaled
momentum spectra of final state hadrons [2]. These scaling violations allow a measurement of
αsand such studies have been performed at LEP [3, 4] by incorporating lower energy PETRA
data.
The event kinematics of DIS are determined by the negative square of the 4-momentum transfer
at the positron vertex, Q2≡ −q2, and the Bjorken scaling variable, x=Q2/2P·q, where P
is the four-momentum of the proton. In the Quark Parton Model (QPM), the interacting
quark from the proton carries the four-momentum xP . The variable y, the fractional energy
transfer to the proton in its rest frame, is related to xand Q2by y≃Q2/xs, where √sis
the positron-proton centre of mass energy. A natural frame in which to study the dynamics
of the hadronic final state in DIS is the Breit frame [5, 6], which has been used in previous
studies of QCD effects [7, 8, 9] at HERA. In this frame the exchanged virtual boson is purely
space-like with 3-momentum ~q = (0,0,−Q), the incident quark carries momentum Q/2 in the
positive Z-direction, and the outgoing struck quark carries Q/2 in the negative Z-direction.
A final state particle has momentum pBin this frame, and is assigned to the current region
if pB
Zis negative, and to the target frame if pB
Zis positive. The advantage of this frame lies
in the maximal separation of the outgoing parton from radiation associated with the incoming
parton and the proton remnant, thus providing the optimal environment for the study of its
fragmentation.
In this analysis the inclusive charged particle distributions of the scaled momenta, xp,in the
current region of the Breit frame are measured; xpis the momentum of a track measured in
the Breit frame, pB, scaled by Q/2, the maximum possible momentum (ignoring effects due to
the intrinsic kTof the quark within the proton).
The scaled momentum distributions are studied as a function of Qand x, in the range 6×10−4<
x < 5×10−2and 10 < Q2<1280 GeV2.Thus the evolution of fragmentation functions can
be observed within a single experiment over a wide range of Q. A similar analysis has recently
been performed by the H1 collaboration [10].
1

2 Experimental Setup
The data presented here were taken in 1994 at the positron-proton collider HERA using the
ZEUS detector. During this period HERA operated with positrons of energy Ee= 27.5 GeV
and protons with energy 820 GeV. The data of this analysis correspond to a luminosity of
2.50 ±0.04 pb−1.A detailed description of the ZEUS detector can be found in [11, 12]; we
present here a brief description of the components most relevant to the present analysis.
Throughout this paper we use the standard ZEUS right-handed coordinate system, in which
X=Y=Z= 0 is the nominal interaction point, the positive Z-axis points in the direction of
the proton beam (referred to as the forward direction) and the X-axis is horizontal, pointing
towards the centre of HERA.
The tracking system consists of a vertex detector (VXD) [13] and a central tracking cham-
ber (CTD) [14] enclosed in a 1.43 T solenoidal magnetic field. Immediately surrounding the
beampipe is the VXD which consists of 120 radial cells, each with 12 sense wires. The CTD,
which encloses the VXD, is a drift chamber consisting of 72 cylindrical layers, arranged in 9
superlayers. Superlayers with wires parallel to the beam axis alternate with those inclined at a
small angle to give a stereo view. The single hit efficiency of the CTD is greater than 95% and
the measured resolution in transverse momentum for tracks with hits in all the superlayers is
σpT/pT= 0.005pTL0.016 (pTin GeV).
Outside the solenoid is the uranium-scintillator calorimeter (CAL) [15], which is divided into
three parts: forward, barrel and rear covering the polar regions 2.6◦to 36.7◦, 36.7◦to 129.1◦and
129.1◦to 176.2◦, respectively. The CAL covers 99.7% of the solid angle, with holes of 20 ×20
cm2in the centres of the forward and rear calorimeters to accommodate the HERA beam pipe.
Each of the calorimeter parts is subdivided into towers which are segmented longitudinally into
electromagnetic (EMC) and hadronic (HAC) sections. These sections are further subdivided
into cells each of which is read out by two photomultipliers. From test beam data, energy
resolutions of σE/E = 0.18/√Efor electrons and σE/E = 0.35/√Efor hadrons (Ein GeV)
have been obtained.
The small angle rear tracking detector (SRTD) [16], which is attached to the front face of the
rear calorimeter, measures the impact point of charged particles at small angles with respect
to the positron beam direction.
The luminosity is measured by means of the Bethe-Heitler process ep →eγp, by detecting the
photon in a calorimeter [17] positioned at Z=−107 m which has an energy resolution of σE/E
= 0.18/qE(GeV) under test beam conditions. The luminosity calorimeter is also used to tag
photons from initial state radiation in DIS events.
3 Kinematic Reconstruction
The ZEUS detector is almost hermetic, allowing the kinematic variables xand Q2to be recon-
structed in a variety of ways using combinations of positron and hadronic system energies and
2

angles. Variables calculated only from the measurements of the energy, E′
e,and angle, θe,of the
scattered positrons are denoted with the subscript e, whilst those calculated from the hadronic
system measurements, with the Jacquet Blondel method [18], are denoted by the subscript JB.
Variables calculated by these approaches are only used in the event selection. In the double
angle method [19], denoted by DA, the kinematic variables are determined using θeand the
angle γH(which is the direction of the struck quark in QPM), defined from the hadronic final
state:
cos γH=(PipX)2+ (PipY)2−(Pi(E−pZ))2
(PipX)2+ (PipY)2+ (Pi(E−pZ))2,
where the sums run over all CAL cells i, excluding those assigned to the scattered positron,
and ~p = (pX, pY, pZ) is the 3-momentum assigned to a cell of energy E. The cell angles are
calculated from the geometric centre of the cell and the vertex position of the event. This angle
is then combined with the measured angle of the scattered positron to calculate xand Q2. The
two angles can also be used to recalculate the energy of the scattered positron:
E′
DA =2Eesin γH
sin γH+ sin θe−sin(γH+θe).
The DA method was used throughout this analysis for the calculation of the boosts and the
kinematic variables because it is less sensitive to systematic uncertainties in the energy mea-
surement than the other methods discussed above.
An additional method of measuring yand Q2(the PT method [20]) was used as a systematic
check of the kinematic reconstruction to determine the binning of the data and the boost vector.
This method uses a more sophisticated combination of the information from the measurements
of both the hadronic system and the positron.
In order to boost to the Breit frame it is necessary to calculate the velocity of the Breit frame
with respect to the laboratory frame, which is given by ~
β= (~q + 2x~
P)/(q0+ 2xP0) where
(q0, ~q) and (P0,~
P) are the 4-momenta of the exchanged photon and the incident proton beam
respectively. The event is then rotated so that the virtual photon is along the negative Z-
axis. The Breit frame boost vector was reconstructed using E′
DA and the polar and azimuthal
angles measured from the impact point of the scattered e+on the calorimeter or SRTD. The
4-momentum vectors of the charged particles were boosted to the Breit frame, assuming the
pion mass to determine the particle’s energy, and were assigned to the current region if pB
Z<0.
4 Event Reconstruction and Selection
The triggering and online event selections were identical to those used for the measurement of
the structure function F2[20].
To reduce the effects of noise due to the uranium radioactivity on the calorimetric measurements
all EMC (HAC) cells with an energy deposit of less than 60 (110) MeV were discarded from
the analysis. For cells with isolated energy deposits this cut was increased to 100 (150) MeV.
3

The track finding algorithm starts with hits in the outer axial superlayers of the CTD. As the
trajectory is followed inwards towards the beam axis, hits from inner superlayers are added to
the track. The momentum vector is determined in a 5-parameter helix fit. The reconstructed
tracks used in this analysis are associated with the primary event vertex and have pT>150 MeV
and |η|<1.75,where ηis the pseudorapidity given by −ln(tan(θ/2)) with θbeing the polar
angle of the measured track with respect to the proton direction. This is a region of high CTD
acceptance where the detector response and systematics are best understood.
Further selection criteria were applied both to ensure accurate reconstruction of the kinematic
variables and to increase the purity of the sample by eliminating background from photopro-
duction processes. These cuts were:
•E′
e≥10 GeV, to achieve a high purity sample of DIS events;
•Q2
DA ≥10 GeV2;
•ye≤0.95, to reduce the photoproduction background;
•yJB ≥0.04, to give sufficient accuracy for DA reconstruction;
•35 ≤δ=Pi(E−pZ)≤60 GeV summed over all calorimeter cells, to remove photopro-
duction events and events with large radiative corrections.
• |X|>16 cm or |Y|>16 cm,where Xand Yare the impact position of the positron on
the CAL as determined using the SRTD to avoid the region directly adjacent to the rear
beam pipe.
• −40 < Zvertex <50 cm,to reduce background events from non ep collisions.
In total, 68066 events satisfy the above cuts and are reconstructed in the (x, Q2) bins (as
calculated by the DA method) that are listed in Table 1. The sizes of the bins in xand Q2
were chosen to have good statistics in each bin and to limit the migrations between bins [7].
5 QCD Models and Event Simulation
Monte Carlo event simulation is used to correct for acceptance and resolution effects. The detec-
tor simulation is based on the GEANT 3.13 [21] program and incorporates our best knowledge
of the apparatus.
To calculate the acceptance, neutral current DIS events were generated, via the DJANGO
program [22], using HERACLES [23] which incorporates first order electroweak corrections.
The QCD cascade was modelled with the colour-dipole model including the boson-gluon fusion
process, using the ARIADNE 4.08 [24] program. In this model coherence effects are implicitly
included in the formalism of the parton cascade. This program uses the Lund string fragmen-
tation model [25] for the hadronisation phase, as implemented in JETSET 7.3 [26]. Two Monte
Carlo samples were generated, 1.6 pb−1with Q2>3 GeV2and 2.6 pb−1with Q2>6 GeV2,
4

using the MRSA [27] parameterisation of the parton distribution functions. Another approach
to modelling the parton cascade is included in the LEPTO(6.5 1) [28] program, which incor-
porates the LO matrix element matched to parton showers (MEPS). This program also uses
the Lund string fragmentation model and was used for the generator level calculations used in
comparisons to our data.
For the studies of the systematics, two additional samples of events were generated (1.2 pb−1
with Q2>4 GeV2and 3.2 pb−1with Q2>100 GeV2) using the HERWIG 5.8c Monte Carlo [29],
where no electroweak radiative corrections were applied. In HERWIG, coherence effects in the
QCD cascades are included by angular ordering of successive parton emissions and a clustering
model is used for the hadronisation [30, 31]. For this sample the parameterisation of the parton
distribution functions was the MRSA′set [32]. The MRSA and MRSA′parameterisations have
both been shown to describe reasonably well the HERA measurements of the proton structure
function F2in the (x, Q2) range of this analysis [33, 34].
6 Correction Procedure
Monte Carlo event generator studies were used to determine the mean charged particle accep-
tance in the current region as a function of (x, Q2). The chosen analysis intervals in (x, Q2)
correspond to regions of high acceptance, 74 to 96%,in the current region of the Breit frame.
xDA range Q2
DA (GeV2) range No. of events
6.0−12.0×10−410 −20 13898
1.2−2.4×10−310 −20 11899
20 −40 8484
40 −80 5093
2.4−10.0×10−320 −40 9399
40 −80 9493
80 −160 5031
160 −320 1369
1.0−5.0×10−2160 −320 2131
320 −640 916
640 −1280 353
Table 1: The (x,Q2) analysis bins showing the the numbers of accepted events in the (x,Q2) bins as
reconstructed by the DA method.
Uncertainty in the reconstruction of the boost vector, ~
β, was found to be the most signif-
icant factor on the resolution of xpand it leads to the choice of variable bin width in xp.
Migration of tracks from the current region to the target region was typically ≃6 to 8% of
the tracks generated in the current region. Migrations into the current region from the target
fragmentation region are typically less than 5% of the tracks assigned to the current region for
5

Q2>320 GeV2.For 10 < Q2<320 GeV2these migrations are generally of the order of 10 to
15% . At Q2<40 GeV2and low values of ythis assignment can be as high as ≃25%,since in
the low yregion the hadronic activity is low and the measurement of γHbecomes distorted by
noise in the calorimeter leading to a worse xresolution and hence an uncertainty in ~
β.
The correction procedure is based on the detailed Monte Carlo simulation of the ZEUS detector
with the event generators described in the previous section. Since the ARIADNE model gives
the best overall description of our observed energy flow [35] it is used for the standard corrections
to the distributions.
The data are corrected for trigger and event selection cuts; event migration between (x, Q2)
intervals; QED radiative effects; track reconstruction efficiency; track selection cuts in pTand
η; track migration between the current and target regions; and for the products of Λ and K0
S
decays which are assigned to the primary vertex.
Correction factors were obtained from the Monte Carlo simulation by comparing the generated
distributions, without Λ and K0
Sdecay products, with the reconstructed distributions after the
detector and trigger simulations followed by the same reconstruction, selection and analysis as
the real data. The correction factors, F(xp
), were calculated for each xpbin with the formula:
F(xp
) = 1
Ngen dn
dxp!gen ,1
Nobs dn
dxp!obs
where Ngen (Nobs) is the number of generated (observed) Monte Carlo events in each (x, Q2)
interval and nis the number of charged particles (tracks) in the current region in the corre-
sponding (x, Q2) interval. The correction factors are typically between 1.0 and 1.3, except in
the lowest xpbin (0.02 < xp<0.05) of the two lowest Q2bins where they are about 1.5.
7 Results
The inclusive charged particle distributions, 1/σtotdσ/dxpwhere σtot is the DIS cross section
in the chosen (x, Q2) bin, are shown in figure 1. In the low (x, Q2) regions these distributions
peak at xp≈0.2 with a broad tail out to 1.As Q2increases the data fall off more sharply
from the minimum xp.In the same figure the ARIADNE Monte Carlo generator predictions
are also shown, which are in good agreement with the data. The increasingly steep fall-off
towards higher values of xpas Q2increases corresponds to the production of more particles
with a smaller fractional momentum, and is indicative of scaling violation in the fragmentation
function. These scaling violations can be seen more clearly if the data are plotted in bins of
fixed xpas a function of Q2.Figure 2 shows the charged particle distributions with statistical
errors combined in quadrature with the systematic errors which will be discussed below. For
Q2>80 GeV2the distributions rise with Q2at low xpand fall-off at high xpand high Q2. By
measuring the amount of scaling violation one can ultimately measure the amount of parton
radiation and thus determine αs.Below Q2= 80 GeV2the fall-off is due to depopulation of the
current region discussed later.
6

7.1 Systematic Studies
The systematic uncertainties in the measurement can be divided into three classes: errors due
to event reconstruction and selection; to track reconstruction and selection; and to the Monte
Carlo generator used.
•Event Reconstruction and Selection
The event selection procedure was checked by altering the ye, yJ B and δcuts: the resulting
shifts of the corrected distributions were small, with all points moving systematically in
the same direction at the ±1 to 3% level. By removing the noise suppression, described in
section 4, a systematic shift at the ±1 to 3% level is produced. Using the boost calculated
from the PT method produced a larger shift: for Q2<160 GeV2the systematic shift is
+10 to 15% at large xp,whilst +2 to 5% at small xp; for Q2≥160 GeV2the systematic
shift is constant with xpat the +2 to 5% level.
•Track Reconstruction and Selection
The major systematic on the track reconstruction was obtained considering all recon-
structed tracks as opposed to only those assigned to the primary vertex. This produced
a typical shift of 2 to 6% with no systematic dependence on the value of xp,except in
the bin 0.02 < xp<0.05 at low Q2and xwhere the systematic shift was up to +15%.
Tightening the tracking cuts on |η|and pTparticularly affected those (x, Q2) bins where
the track acceptance is strongly dependent on the negative ηcut. The general trend is for
the cross section to be shifted to higher values. The bins most affected have an average
shift of up to 5%, whilst in general the shift is <
∼1%.
•Monte Carlo Generator
Using a different Monte Carlo generator (HERWIG rather than ARIADNE) led to dis-
tributions which were systematically lower by about 10% in the range of 0 ≤xp≤0.3.
In the range xp>0.5, the HERWIG corrected distributions were systematically higher
(lower) by 5 to 10 % for Q2<40 GeV2(Q2>100 GeV2). In the range 0.3≤xp≤0.4
the two generators gave results that were in good agreement.
All positive (negative) systematic shifts in each of the xpbins were combined in quadrature to
give an estimate of the overall positive (negative) systematic uncertainty on the measurement.
These systematic shifts do not affect the observation of scaling violations.
7.2 Discussion
Fragmentation in DIS of a quark carrying momentum Q/2 in the Breit frame may be compared
to fragmentation in e+e−annihilation of the produced qand ¯q, each carrying momentum
√se+e−/2.In figure 2 the ZEUS data are compared at Q2=se+e−to e+e−data [36], divided by
two to account for the production of both a qand ¯q. The e+e−data have also been corrected
by ≃8% for the decay products of Λ and K0
S,using the JETSET 7.3 Monte Carlo tuned to
DELPHI data. In the Q2range shown there is good agreement between the current region of
7

the Breit frame in DIS and the e+e−experiments. When our data are compared with the lower
energy SPEAR [37] data (√s= 5.2,6.5 GeV,not shown) discrepancies begin to show up. They
can be explained in terms of the kinematic depopulation of the current region described in the
next paragraph.
The turnover observed in the ZEUS data at low xpand low Q2,figure 2, can be attributed
to processes not present in e+e−(eg scattering off a sea quark and/or boson gluon fusion)
depopulating the current region [8]. This is best illustrated when discussing the production
of a pair of partons in DIS with a large invariant mass, ˆs[6]. When Q2≫ˆs, the radiation
is emitted in the direction of the struck quark in the QPM. However, at low Q2and low x, ˆs
is likely to be bigger than Q2and the radiation will be emitted in the direction opposite to
the QPM direction and will therefore not be in the current region as defined in section 1. In
particular, the boson-gluon fusion diagram, which dominates at low-x, provides a significant
cross section for large mass radiation [38], thus producing this depopulation.
In figure 3 the data are compared to two leading-log Monte Carlo predictions which are im-
plemented within the Lund fragmentation framework. Our data are well described by the
ARIADNE generator, colour dipole model (CDM), over the full range of Q2.This is not true
for the LEPTO, matrix element+parton showers (MEPS), model. In particular LEPTO over-
estimate the data at low xpand there is a greater Q2dependence than that suggested by the
data. A feature of both Monte Carlo models is a trend that, at fixed Q2, the charged particle
distribution increases with x. Such a trend is also observed in the data, see fig 2. No tuning of
the Monte Carlo parameters has been performed to improve the agreement with the data.
Our results can be compared to the next-to-leading order (NLO) QCD calculations, as imple-
mented in CYCLOPS [39], of the charged particle inclusive distributions in the restricted region
Q2>80 GeV2and xp>0.1,where the theoretical uncertainties are small and unaffected by the
hadron mass effects which are not included in the fragmentation function [40]. This comparison
is shown in figure 4. The NLO calculation combines a full next-to-leading order matrix element
with the MRSA′parton densities (with ΛQCD = 230 MeV) and NLO fragmentation functions
derived by Binnewies et al. from fits to e+e−data [41]. The data and the NLO calculations
are in good agreement, supporting the idea of universality of quark fragmentation.
8 Conclusions
Charged particle distributions have been studied in the current region of the Breit frame in
DIS over a wide range of Q2values. These results show clear evidence in a single experiment
for scaling violations in scaled momenta as a function of Q2. The data are also well described
with NLO calculations.
The comparison between e+e−data at Q2=se+e−and the current region of the Breit frame
in DIS for Q2>80 GeV2shows also a good agreement. The observed charged particle spectra
are consistent with the universality of quark fragmentation in e+e−and DIS.
8

Acknowledgements
We appreciate the contributions to the construction and maintenance of the ZEUS detector by
many people who are not listed as authors. We thank the DESY computing staff for providing
the data analysis environment. The HERA machine group is especially acknowledged for the
outstanding operation of the collider. The strong support and encouragement of the DESY
Directorate has been invaluable.
We would like to thank D. Graudenz for valuable discussions and for providing us with the
NLO program, CYCLOPS.
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11

Figure 1: The inclusive charged particle distributions, 1/σtot dσ/dxp, in the current fragmentation
region of the Breit frame compared with the generated distributions from the Monte Carlo (ARIADNE
4.08). The statistical errors are generally within the size of the points.
12

Figure 2: The inclusive charged particle distribution, 1/σtot dσ/dxp, in the current fragmentation
region of the Breit frame. The filled data points are from ZEUS. The full errors are statistical and
systematic combined in quadrature. The thick lines denote the statistical error. The open points
represent data from e+e−experiments divided by two to account for qand ¯qproduction (also corrected
for contributions from K0
Sand Λ.)
13

Figure 3: The inclusive charged particle distribution, 1/σtot dσ/dxp, in the current fragmentation
region of the Breit frame. The data points are from ZEUS. The full errors are statistical and systematic
combined in quadrature. The thick lines denote the statistical error. The curves represent leading-log
Monte Carlo models: the full line is ARIADNE (CDM) and the dashed line is LEPTO (MEPS). For
clarity of presentation, only the higher xbin is shown in each Q2interval.
14

Figure 4: The inclusive charged particle distribution, 1/σtot dσ/dxp, in the current fragmentation
region of the Breit frame compared to the NLO calculation, CYCLOPS [39]. For clarity of presentation,
only the higher xbin is shown in each Q2interval.
15