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Subjet distributions in deep inelastic scattering at HERA

European Physical Journal C (Impact Factor: 5.08). 10/2009; 63(4):527-548. DOI: 10.1140/epjc/s10052-009-1090-3
ABSTRACT
Subjet distributions were measured in neutral current deep inelastic ep scattering with the ZEUS detector at HERA using an integrated luminosity of 81.7pb−1. Jets were identified using the k

T
cluster algorithm in the laboratory frame. Subjets were defined as jet-like substructures identified by a reapplication of
the cluster algorithm at a smaller value of the resolution parameter ycuty_{\rm cut}. Measurements of subjet distributions for jets with exactly two subjets for ycut=0.05y_{\rm cut}=0.05 are presented as functions of observables sensitive to the pattern of parton radiation and to the colour coherence between
the initial and final states. Perturbative QCD predictions give an adequate description of the data.

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Eur. Phys. J. C (2009) 63: 527–548
DOI 10.1140/epjc/s10052-009-1090-3
Regular Article - Experimental Physics
Subjet distributions in deep inelastic scattering at HERA
The ZEUS Collaboration
S. Chekanov
1
, M. Derrick
1
, S. Magill
1
, B. Musgrave
1
, D. Nicholass
1,c
, J. Repond
1
, R. Yoshida
1
, M.C.K. Mattingly
2
,
P. Antonioli
3
, G. Bari
3
, L. Bellagamba
3
, D. Boscherini
3
, A. Bruni
3
, G. Bruni
3
, F. Cindolo
3
, M. Corradi
3
,
G. Iacobucci
3
, A. Margotti
3
, R. Nania
3
, A. Polini
3
, S. Antonelli
4
,M.Basile
4
,M.Bindi
4
, L. Cifarelli
4
, A. Contin
4
,
S. De Pasquale
4,d
, G. Sartorelli
4
, A. Zichichi
4
, D. Bartsch
5
,I.Brock
5
, H. Hartmann
5
, E. Hilger
5
, H.-P. Jakob
5
,
M. Jüngst
5
, A.E. Nuncio-Quiroz
5
,E.Paul
5
, U. Samson
5
, V. Schönberg
5
, R. Shehzadi
5
, M. Wlasenko
5
, N.H. Brook
6
,
G.P. Heath
6
, J.D. Morris
6
,M.Kaur
7
, P. Kaur
7,e
,I.Singh
7,e
, M. Capua
8
, S. Fazio
8
, A. Mastroberardino
8
,
M. Schioppa
8
, G. Susinno
8
,E.Tassi
8
,J.Y.Kim
9
, Z.A. Ibrahim
10
, F. Mohamad Idris
10
, B. Kamaluddin
10
,
W.A.T. Wan Abdullah
10
,Y.Ning
11
,Z.Ren
11
, F. Sciulli
11
, J. Chwastowski
12
, A. Eskreys
12
, J. Figiel
12
, A. Galas
12
,
K. Olkiewicz
12
,B.Pawlik
12
, P. Stopa
12
,L.Zawiejski
12
, L. Adamczyk
13
,T.Bołd
13
, I. Grabowska-Bołd
13
,
D. Kisielewska
13
, J. Łukasik
13,f
, M. Przybycie
´
n
13
, L. Suszycki
13
,A.Kota
´
nski
14,g
,W.Słomi
´
nski
14,h
, O. Behnke
15
,
U. Behrens
15
, C. Blohm
15
, A. Bonato
15
, K. Borras
15
,D.Bot
15
, R. Ciesielski
15
, N. Coppola
15
, S. Fang
15
,
J. Fourletova
15,i
,A.Geiser
15
, P. Göttlicher
15,j
, J. Grebenyuk
15
, I. Gregor
15
,T.Haas
15,a
,W.Hain
15
, A. Hüttmann
15
,
F. Januschek
15
,B.Kahle
15
,I.I.Katkov
15,k
, U. Klein
15,l
,U.Kötz
15
,H.Kowalski
15
,M.Lisovyi
15
, E. Lobodzinska
15
,
B. Löhr
15
, R. Mankel
15,m
, I.-A. Melzer-Pellmann
15
, S. Miglioranzi
15,n
, A. Montanari
15
,T.Namsoo
15
,D.Notz
15,m
,
A. Parenti
15
, L. Rinaldi
15,o
,P.Roloff
15
, I. Rubinsky
15
, U. Schneekloth
15
, A. Spiridonov
15,p
, D. Szuba
15,q
, J. Szuba
15,r
,
T. Theedt
15
, J. Ukleja
15,s
,G.Wolf
15
, K. Wrona
15
, A.G. Yagües Molina
15
, C. Youngman
15
, W. Zeuner
15,m
,
V. Drugakov
16
, W. Lohmann
16
, S. Schlenstedt
16
, G. Barbagli
17
, E. Gallo
17
,P.G.Pelfer
18
, A. Bamberger
19
,
D. Dobur
19
, F. Karstens
19
,N.N.Vlasov
19,t
,P.J.Bussey
20,u
,A.T.Doyle
20
, W. Dunne
20
, M. Forrest
20
,M.Rosin
20
,
D.H. Saxon
20
, I.O. Skillicorn
20
, I. Gialas
21,v
, K. Papageorgiu
21
,U.Holm
22
, R. Klanner
22
, E. Lohrmann
22
,
H. Perrey
22
, P. Schleper
22
, T. Schörner-Sadenius
22
, J. Sztuk
22
, H. Stadie
22
, M. Turcato
22
, C. Foudas
23
,C.Fry
23
,
K.R. Long
23
, A.D. Tapper
23
,T.Matsumoto
24
, K. Nagano
24
, K. Tokushuku
24,w
, S. Yamada
24
, Y. Yamazaki
24,x
,
A.N. Barakbaev
25
,E.G.Boos
25
, N.S. Pokrovskiy
25
, B.O. Zhautykov
25
, V. Aushev
26,y
, O. Bachynska
26
, M. Borodin
26
,
I. Kadenko
26
, A. Kozulia
26
,V.Libov
26
, D. Lontkovskyi
26
, I. Makarenko
26
, I. Sorokin
26
, A. Verbytskyi
26
,
O. Volynets
26
, D. Son
27
, J. de Favereau
28
, K. Piotrzkowski
28
, F. Barreiro
29
,C.Glasman
29
, M. Jimenez
29
,
L. Labarga
29
, J. del Peso
29
,E.Ron
29
, M. Soares
29
, J. Terrón
29
, C. Uribe-Estrada
29
, M. Zambrana
29
, F. Corriveau
30
,
C. Liu
30
, J. Schwartz
30
,R.Walsh
30
, C. Zhou
30
, T. Tsurugai
31
, A. Antonov
32
, B.A. Dolgoshein
32
, D. Gladkov
32
,
V. Sosnovtsev
32
, A. Stifutkin
32
, S. Suchkov
32
, R.K. Dementiev
33
,P.F.Ermolov
33,b
, L.K. Gladilin
33
, Y.A. Golubkov
33
,
L.A. Khein
33
, I.A. Korzhavina
33
, V.A. Kuzmin
33
, B.B. Levchenko
33,z
, O.Y. Lukina
33
, A.S. Proskuryakov
33
,
L.M. Shcheglova
33
, D.S. Zotkin
33
,I.Abt
34
, A. Caldwell
34
, D. Kollar
34
, B. Reisert
34
, W.B. Schmidke
34
,
G. Grigorescu
35
, A. Keramidas
35
,E.Koffeman
35
, P. Kooijman
35
, A. Pellegrino
35
, H. Tiecke
35
, M. Vázquez
35,n
,
L. Wiggers
35
, N. Brümmer
36
,B.Bylsma
36
, L.S. Durkin
36
,A.Lee
36
,T.Y.Ling
36
,P.D.Allfrey
37
,M.A.Bell
37
,
A.M. Cooper-Sarkar
37
, R.C.E. Devenish
37
, J. Ferrando
37
,B.Foster
37
, C. Gwenlan
37,aa
, K. Horton
37,ab
,K.Oliver
37
,
A. Robertson
37
, R. Walczak
37
, A. Bertolin
38
, F. Dal Corso
38
,S.Dusini
38
, A. Longhin
38
, L. Stanco
38
, P. Bellan
39
,
R. Brugnera
39
, R. Carlin
39
, A. Garfagnini
39
, S. Limentani
39
,B.Y.Oh
40
,A.Raval
40
, J.J. Whitmore
40,ac
,Y.Iga
41
,
G. D’Agostini
42
, G. Marini
42
,A.Nigro
42
,J.E.Cole
43,ad
, J.C. Hart
43
, H. Abramowicz
44,ae
, R. Ingbir
44
, S. Kananov
44
,
A. Levy
44
,A.Stern
44
,M.Kuze
45
, J. Maeda
45
, R. Hori
46
, S. Kagawa
46,af
, N. Okazaki
46
, S. Shimizu
46
, T. Tawara
46
,
R. Hamatsu
47
,H.Kaji
47,ag
, S. Kitamura
47,ah
,O.Ota
47,ai
,Y.D.Ri
47
,M.Costa
48
, M.I. Ferrero
48
, V. Monaco
48
,
R. Sacchi
48
, V. Sola
48
, A. Solano
48
, M. Arneodo
49
,M.Ruspa
49
, S. Fourletov
50,i
, J.F. Martin
50
, T.P. Stewart
50
,
S.K. Boutle
51,v
, J.M. Butterworth
51
, T.W. Jones
51
, J.H. Loizides
51
,M.Wing
51,aj
, B. Brzozowska
52
,
J. Ciborowski
52,ak
, G. Grzelak
52
, P. Kulinski
52
,Pu˙zniak
52,al
, J. Malka
52,al
,R.J.Nowak
52
,J.M.Pawlak
52
,
W. Perlanski
52,al
, T. Tymieniecka
52,am
,A.F.
˙
Zarnecki
52
, M. Adamus
53
, P. Plucinski
53,an
, A. Ukleja
53
, Y. Eisenberg
54
,
D. Hochman
54
, U. Karshon
54
,E.Brownson
55
, D.D. Reeder
55
,A.A.Savin
55
,W.H.Smith
55
,H.Wolfe
55
, S. Bhadra
56
,
C.D. Catterall
56
,Y.Cui
56
, G. Hartner
56
, S. Menary
56
, U. Noor
56
, J. Standage
56
,J.Whyte
56
Page 1
528 Eur. Phys. J. C (2009) 63: 527–548
1
Argonne National Laboratory, Argonne, IL 60439-4815, USA
bb
2
Andrews University, Berrien Springs, MI 49104-0380, USA
3
INFN Bologna, Bologna, Italy
as
4
University and INFN Bologna, Bologna, Italy
as
5
Physikalisches Institut der Universität Bonn, Bonn, Germany
ap
6
H.H. Wills Physics Laboratory, University of Bristol, Bristol, UK
ba
7
Department of Physics, Panjab University, Chandigarh, India
8
Physics Department and INFN, Calabria University, Cosenza, Italy
as
9
Chonnam National University, Kwangju, South Korea
10
Jabatan Fizik, Universiti Malaya, 50603 Kuala Lumpur, Malaysia
bf
11
Nevis Laboratories, Columbia University, Irvington on Hudson, NY 10027, USA
bc
12
The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland
aw
13
Faculty of Physics and Applied Computer Science, AGH-University of Science and Technology, Cracow, Poland
bd
14
Department of Physics, Jagellonian University, Cracow, Poland
15
Deutsches Elektronen-Synchrotron DESY, Hamburg, Germany
16
Deutsches Elektronen-Synchrotron DESY, Zeuthen, Germany
17
INFN Florence, Florence, Italy
as
18
University and INFN Florence, Florence, Italy
as
19
Fakultät für Physik der Universität Freiburg i.Br., Freiburg i.Br., Germany
ap
20
Department of Physics and Astronomy, University of Glasgow, Glasgow, UK
ba
21
Department of Engineering in Management and Finance, Univ. of Aegean, Mytilene, Greece
22
Institute of Exp. Physics, Hamburg University, Hamburg, Germany
ap
23
High Energy Nuclear Physics Group, Imperial College London, London, UK
ba
24
Institute of Particle and Nuclear Studies, KEK, Tsukuba, Japan
at
25
Institute of Physics and Technology of Ministry of Education and Science of Kazakhstan, Almaty, Kazakhstan
26
Institute for Nuclear Research, National Academy of Sciences, Kiev and Kiev National University, Kiev, Ukraine
27
Center for High Energy Physics, Kyungpook National University, Daegu, South Korea
au
28
Institut de Physique Nucléaire, Université Catholique de Louvain, Louvain-la-Neuve, Belgium
be
29
Departamento de Física Teórica, Universidad Autónoma de Madrid, Madrid, Spain
az
30
Department of Physics, McGill University, Montréal, Québec, Canada H3A 2T8
ao
31
Faculty of General Education, Meiji Gakuin University, Yokohama, Japan
at
32
Moscow Engineering Physics Institute, Moscow, Russia
ax
33
Institute of Nuclear Physics, Moscow State University, Moscow, Russia
ay
34
Max-Planck-Institut für Physik, Munich, Germany
35
NIKHEF and University of Amsterdam, Amsterdam, Netherlands
av
36
Physics Department, Ohio State University, Columbus, OH 43210, USA
bb
37
Department of Physics, University of Oxford, Oxford, UK
ba
38
INFN Padova, Padova, Italy
as
39
Dipartimento di Fisica dell’ Università and INFN, Padova, Italy
as
40
Department of Physics, Pennsylvania State University, University Park, PA 16802, USA
bc
41
Polytechnic University, Sagamihara, Japan
at
42
Dipartimento di Fisica, Università ‘La Sapienza’ and INFN, Rome, Italy
as
43
Rutherford Appleton Laboratory, Chilton, Didcot, Oxon, UK
ba
44
Raymond and Beverly Sackler Faculty of Exact Sciences, School of Physics, Tel Aviv University, Tel Aviv, Israel
ar
45
Department of Physics, Tokyo Institute of Technology, Tokyo, Japan
at
46
Department of Physics, University of Tokyo, Tokyo, Japan
at
47
Department of Physics, Tokyo Metropolitan University, Tokyo, Japan
at
48
Università di Torino and INFN, Torino, Italy
as
49
Università del Piemonte Orientale, Novara, and INFN, Torino, Italy
as
50
Department of Physics, University of Toronto, Toronto, Ontario, Canada M5S 1A7
ao
51
Physics and Astronomy Department, University College London, London, UK
ba
52
Institute of Experimental Physics, Warsaw University, Warsaw, Poland
53
Institute for Nuclear Studies, Warsaw, Poland
54
Department of Particle Physics, Weizmann Institute, Rehovot, Israel
aq
55
Department of Physics, University of Wisconsin, Madison, WI 53706, USA
bb
56
Department of Physics, York University, Toronto, Ontario, Canada M3J 1P3
ao
Received: 7 February 2009 / Revised: 13 May 2009 / Published online: 27 August 2009
© Springer-Verlag / Società Italiana di Fisica 2009
a
e-mail: tobias.haas@desy.de
b
Deceased.
c
Also affiliated with University College London, United Kingdom.
d
Now at University of Salerno, Italy.
Page 2
Eur. Phys. J. C (2009) 63: 527–548 529
Abstract Subjet distributions were measured in neutral cur-
rent deep inelastic ep scattering with the ZEUS detector at
HERA using an integrated luminosity of 81.7 pb
1
.Jets
were identified using the k
T
cluster algorithm in the lab-
oratory frame. Subjets were defined as jet-like substruc-
tures identified by a reapplication of the cluster algorithm
at a smaller value of the resolution parameter y
cut
. Measure-
ments of subjet distributions for jets with exactly two sub-
jets for y
cut
=0.05 are presented as functions of observables
sensitive to the pattern of parton radiation and to the colour
e
Also working at Max Planck Institute, Munich, Germany.
f
Now at Institute of Aviation, Warsaw, Poland.
g
Supported by the research grant no. 1 P03B 04529 (2005–2008).
h
This work was supported in part by the Marie Curie Actions Transfer
of Knowledge project COCOS (contract MTKD-CT-2004-517186).
i
Now at University of Bonn, Germany.
j
Now at DESY group FEB, Hamburg, Germany.
k
Also at Moscow State University, Russia.
l
Now at University of Liverpool, UK.
m
On leave of absence at CERN, Geneva, Switzerland.
n
Now at CERN, Geneva, Switzerland.
o
Now at Bologna University, Bologna, Italy.
p
Also at Institut of Theoretical and Experimental Physics, Moscow,
Russia.
q
Also at INP, Cracow, Poland.
r
Also at FPACS, AGH-UST, Cracow, Poland.
s
Partially supported by Warsaw University, Poland.
t
Partly supported by Moscow State University, Russia.
u
Royal Society of Edinburgh, Scottish Executive Support Research
Fellow.
v
Also affiliated with DESY, Germany.
w
Also at University of Tokyo, Japan.
x
Now at Kobe University, Japan.
y
Supported by DESY, Germany.
z
Partly supported by Russian Foundation for Basic Research grant no.
05-02-39028-NSFC-a.
aa
STFC Advanced Fellow.
ab
Nee Korcsak-Gorzo.
ac
This material was based on work supported by the National Science
Foundation, while working at the Foundation.
ad
Now at University of Kansas, Lawrence, USA.
ae
Also at Max Planck Institute, Munich, Germany, Alexander von
Humboldt Research Award.
af
Now at KEK, Tsukuba, Japan.
ag
Now at Nagoya University, Japan.
ah
Member of Department of Radiological Science, Tokyo Metropolitan
University, Japan.
ai
Now at SunMelx Co. Ltd., Tokyo, Japan.
aj
Also at Hamburg University, Inst. of Exp. Physics, Alexander von
Humboldt Research Award and partially supported by DESY, Ham-
burg, Germany.
coherence between the initial and final states. Perturbative
QCD predictions give an adequate description of the data.
1 Introduction
Jet production in ep collisions provides a wide testing
ground of perturbative QCD (pQCD). Measurements of dif-
ferential cross sections for jet production [118]haveal-
lowed for detailed studies of parton dynamics, tests of the
proton and photon parton distribution functions (PDFs) as
ak
Also at Łód´z University, Poland.
al
Member of Łód´z University, Poland.
am
Also at University of Podlasie, Siedlce, Poland.
an
Now at Lund University, Lund, Sweden.
ao
Supported by the Natural Sciences and Engineering Research Coun-
cil of Canada (NSERC).
ap
Supported by the German Federal Ministry for Education and Re-
search (BMBF), under contract numbers 05 HZ6PDA, 05 HZ6GUA,
05 HZ6VFA and 05 HZ4KHA.
aq
Supported in part by the MINERVA Gesellschaft für Forschung
GmbH, the Israel Science Foundation (grant no. 293/02-11.2) and the
US–Israel Binational Science Foundation.
ar
Supported by the Israel Science Foundation.
as
Supported by the Italian National Institute for Nuclear Physics
(INFN).
at
Supported by the Japanese Ministry of Education, Culture, Sports,
Science and Technology (MEXT) and its grants for Scientific Re-
search.
au
Supported by the Korean Ministry of Education and Korea Science
and Engineering Foundation.
av
Supported by the Netherlands Foundation for Research on Matter
(FOM).
aw
Supported by the Polish State Committee for Scientific Research,
project no. DESY/256/2006-154/DES/2006/03.
ax
Partially supported by the German Federal Ministry for Education
and Research (BMBF).
ay
Supported by RF Presidential grant N 1456.2008.2 for the leading
scientific schools and by the Russian Ministry of Education and Sci-
ence through its grant for Scientific Research on High Energy Physics.
az
Supported by the Spanish Ministry of Education and Science through
funds provided by CICYT.
ba
Supported by the Science and Technology Facilities Council, UK.
bb
Supported by the US Department of Energy.
bc
Supported by the US National Science Foundation. Any opinion,
findings and conclusions or recommendations expressed in this ma-
terial are those of the authors and do not necessarily reflect the views
of the National Science Foundation.
bd
Supported by the Polish Ministry of Science and Higher Education
as a scientific project (2006–2008).
be
Supported by FNRS and its associated funds (IISN and FRIA) and
by an Inter-University Attraction Poles Programme subsidised by the
Belgian Federal Science Policy Office.
bf
Supported by an FRGS grant from the Malaysian government.
Page 3
530 Eur. Phys. J. C (2009) 63: 527–548
well as precise determinations of the strong coupling con-
stant, α
s
.
Gluon emission from primary quarks was investigated
[19, 20] by means of the internal structure of jets; these type
of studies gave insight into the transition between a parton
produced in a hard process and the experimentally observ-
able jet of hadrons. The pattern of parton radiation within a
jet is dictated in QCD by the splitting functions. These func-
tions, P
ab
(z, μ) with a,b = q or g, are interpreted as the
probability that a parton of type b, having radiated a parton
of type a, is left with a fraction z of the longitudinal mo-
mentum of the parent parton and a transverse momentum
squared smaller than μ
2
, where μ is the typical hard scale of
the process. The splitting functions are calculable as power
series in α
s
. Thus, the characteristics of jet substructure pro-
vide direct access to the QCD splitting functions and their
dependence on the scale.
The understanding of jet substructure is also important
in the context of jet identification in boosted systems, like
hadronic top decays [21, 22]orb
¯
b final states at LHC [23].
The first example calls for a direct application of jet sub-
structure, the second requires knowledge about jet substruc-
ture to distinguish between single- and double-quark in-
duced jets. This paper presents a study of jet substructure
in a more controlled hadronic-type environment than that
provided by hadron–hadron colliders.
Jet production in neutral current (NC) deep inelastic scat-
tering (DIS) was previously used to study the mean subjet
multiplicity [19] and the mean integrated jet shape [20] with
values of α
s
(M
Z
) extracted from those measurements. In the
present study, the pattern of QCD radiation is investigated
by means of the subjet topology, providing a more stringent
test of the pQCD calculations.
In this paper, measurements of normalized differential
subjet cross sections for those jets which contain two sub-
jets at a given resolution scale are presented. The measure-
ments were done as functions of the ratio between the sub-
jet transverse energy and that of the jet, E
sbj
T
/E
jet
T
, the dif-
ference between the subjet pseudorapidity
1
(azimuth) and
that of the jet, η
sbj
η
jet
(|φ
sbj
φ
jet
|), and α
sbj
, the an-
gle, as viewed from the jet center, between the subjet with
higher transverse energy and the proton beam line in the
pseudorapidity–azimuth plane (see Fig. 1). The predictions
of pQCD at next-to-leading order (NLO) were compared to
the data.
1
The ZEUS coordinate system is a right-handed Cartesian system, with
the Z axis pointing in the proton beam direction, referred to as the
“forward direction”, and the X axis pointing left towards the center of
HERA. The coordinate origin is at the nominal interaction point. The
pseudorapidity is defined as η =−ln(tan
θ
2
), where the polar angle θ
is taken with respect to the proton beam direction.
Fig. 1 Schematic representation of the α
sbj
variable
2 Jets and subjets
Inclusive deep inelastic lepton–proton scattering can be de-
scribed in terms of the kinematic variables x, y and Q
2
.
The variable Q
2
is defined as Q
2
=−q
2
=−(k k
)
2
,
where k and k
are the four-momenta of the incoming and
scattered lepton, respectively. Bjorken x is defined as x =
Q
2
/(2P ·q), where P is the four-momentum of the incom-
ing proton. The fraction of the lepton energy transferred to
the proton in its rest frame is given by y =P ·q/P ·k.The
variables x, y and Q
2
are related by Q
2
= sxy, where s is
the squared center-of-mass energy.
The analysis of subjets presented in this paper was per-
formed using the laboratory frame. In this frame, the calcu-
lations of the subjet distributions can be performed up to
O
2
s
), i.e. NLO, with jets consisting of up to three par-
tons. The analysis used events with high virtuality of the
exchanged boson, Q
2
; at low values of Q
2
, the sample of
events with at least one jet of high E
jet
T
(E
jet
T
Q
2
)is
dominated by dijet events. In that case, the calculations in-
clude jets consisting of up to only two partons and, therefore,
correspond to lowest-order predictions of jet substructure.
The k
T
cluster algorithm [24] was used in the longitu-
dinally invariant inclusive mode [25] to define jets in the
hadronic final state. Subjets [2629] were resolved within a
jet by considering all particles associated with the jet and
repeating the application of the k
T
cluster algorithm un-
til, for every pair of particles i and j the quantity d
ij
=
min(E
T,i
,E
T,j
)
2
· ((η
i
η
j
)
2
+
i
φ
j
)
2
), where E
T,i
,
η
i
and φ
i
are the transverse energy, pseudorapidity and az-
imuth of particle i, respectively, was greater than d
cut
=
y
cut
·(E
jet
T
)
2
. All remaining clusters were called subjets.
Page 4
Eur. Phys. J. C (2009) 63: 527–548 531
The subjet multiplicity depends upon the value chosen
for the resolution parameter y
cut
. Subjet distributions were
studied for those jets with exactly two subjets at a value of
the resolution parameter of y
cut
= 0.05. This value of y
cut
was chosen as a compromise between resolution, size of the
hadronization correction factors and statistics. The effect of
the parton-to-hadron corrections on the shape of the subjet
distributions becomes increasingly larger as y
cut
decreases.
On the other hand, the number of jets with exactly two sub-
jets decreases rapidly as y
cut
increases.
Subjet distributions were studied as functions of
E
sbj
T
/E
jet
T
, η
sbj
η
jet
, |φ
sbj
φ
jet
| and α
sbj
. One of the goals
of this study was to investigate the extent to which pQCD
calculations are able to reproduce the observed distribu-
tions. In addition, the dependence of the splitting functions
P
ab
(z, μ) on z can be investigated using the E
sbj
T
/E
jet
T
distri-
bution. The splitting functions at leading order (LO) do not
depend on μ but acquire a weak dependence due to higher-
order corrections. Such a dependence can be investigated
by measuring the subjet distributions in different regions of
E
jet
T
or Q
2
.
The substructure of jets consisting of a quark-gluon pair
(the quark-induced process eq eqg) or a quark-antiquark
pair (the gluon-induced process eg eq ¯q) are predicted
to be different (see Sect. 8.1). Furthermore, the relative
contributions of quark- and gluon-induced processes vary
with Bjorken x and Q
2
. The predicted difference mentioned
above is amenable to experimental investigation by compar-
ing the shape of the subjet distributions in different regions
of x and Q
2
.
Color coherence leads to a suppression of soft-gluon ra-
diation in certain regions of phase space. The effects of
color coherence between the initial and final states have
been studied in hadron–hadron collisions [30]. These effects
are also expected to appear in lepton–hadron collisions. For
the process eq eqg, color coherence implies a tendency
of the subjet with lower (higher) transverse energy, E
sbj
T,low
(E
sbj
T,high
), to have η
sbj
η
jet
> 0(η
sbj
η
jet
< 0). The vari-
able α
sbj
, defined in close analogy to the variables used to
study color coherence in hadron–hadron collisions [30], re-
flects directly whether the subjet with the lower transverse
energy has a tendency to be emitted towards the proton beam
direction.
3 Experimental set-up
A detailed description of the ZEUS detector can be found
elsewhere [31, 32]. A brief outline of the components most
relevant for this analysis is given below.
Charged particles were tracked in the central tracking de-
tector (CTD) [3335], which operated in a magnetic field
of 1.43 T provided by a thin superconducting solenoid. The
CTD consisted of 72 cylindrical drift-chamber layers, or-
ganized in nine superlayers covering the polar-angle re-
gion 15
<164
. The transverse-momentum resolution
for full-length tracks can be parameterized as σ(p
T
)/p
T
=
0.0058p
T
0.0065 0.0014/p
T
, with p
T
in GeV. The
tracking system was used to measure the interaction vertex
with a typical resolution along (transverse to) the beam di-
rection of 0.4(0.1) cm and to cross-check the energy scale
of the calorimeter.
The high-resolution uranium–scintillator calorimeter
(CAL) [3639] covered 99.7% of the total solid angle and
consisted of three parts: the forward (FCAL), the barrel
(BCAL) and the rear (RCAL) calorimeters. Each part was
subdivided transversely into towers and longitudinally into
one electromagnetic section and either one (in RCAL) or
two (in BCAL and FCAL) hadronic sections. The small-
est subdivision of the calorimeter was called a cell. Un-
der test-beam conditions, the CAL single-particle relative
energy resolutions were σ(E)/E =0.18/
E for electrons
and σ(E)/E =0.35/
E for hadrons, with E in GeV.
The luminosity was measured from the rate of the
bremsstrahlung process ep p. The resulting small-
angle energetic photons were measured by the luminosity
monitor [4042], a lead–scintillator calorimeter placed in
the HERA tunnel at Z =−107 m.
4 Data selection
The data were collected during the running period 1998–
2000, when HERA operated with protons of energy E
p
=
920 GeV and electrons or positrons
2
of energy E
e
=
27.5 GeV, and correspond to an integrated luminosity of
81.7 ±1.9pb
1
.
Neutral current DIS events were selected offline using
criteria similar to those reported previously [20]. The main
steps are given below.
A reconstructed event vertex consistent with the nominal
interaction position was required and cuts based on tracking
information were applied to reduce the contamination from
beam-induced and cosmic-ray background. The scattered-
electron candidate was identified using the pattern of energy
deposits in the CAL [43, 44]. The energy, E
e
, and polar an-
gle, θ
e
, of the electron candidate were also determined from
the CAL measurements. The double-angle method [45, 46],
which uses θ
e
and an angle γ that corresponds, in the quark-
parton model, to the direction of the scattered quark, was
used to reconstruct Q
2
. The angle γ was reconstructed us-
ing the CAL measurements of the hadronic final state.
2
In the following, the term “electron” denotes generically both the elec-
tron (e
) and the positron (e
+
).
Page 5
532 Eur. Phys. J. C (2009) 63: 527–548
Electron candidates were required to have an energy
E
e
> 10 GeV, to ensure a high and well understood electron-
finding efficiency and to suppress background from pho-
toproduction. The inelasticity variable, y, as reconstructed
using the electron energy and polar angle, was required to
be below 0.95; this condition removed events in which fake
electron candidates from photoproduction background were
found in the FCAL. The requirement 38 <(E p
Z
)<
65 GeV, where E is the total CAL energy and p
Z
is the Z
component of the energy measured in the CAL cells, was ap-
plied to remove events with large initial-state radiation and
to reduce further the photoproduction background. Remain-
ing cosmic rays and beam-related background were rejected
by requiring the total missing transverse momentum, p
miss
T
,
to be small compared to the total transverse energy, E
tot
T
,
p
miss
T
/
E
tot
T
< 3
GeV. The kinematic range was restricted
to Q
2
> 125 GeV
2
.
The k
T
cluster algorithm was used in the longitudinally
invariant inclusive mode to reconstruct jets in the mea-
sured hadronic final state from the energy deposits in the
CAL cells. The jet algorithm was applied after excluding
those cells associated with the scattered-electron candidate.
Jet transverse-energy corrections were computed using the
method developed in a previous analysis [20]. Events were
required to have at least one jet of E
jet
T
> 14 GeV and
1
jet
< 2.5. The final sample of 128986 events con-
tained 132818 jets, of which 21162 jets had exactly two sub-
jets at y
cut
=0.05.
5 Monte Carlo simulation
Samples of events were generated to determine the re-
sponse of the detector to jets of hadrons and the cor-
rection factors necessary to obtain the hadron-level subjet
cross sections. The hadron level is defined as those hadrons
with lifetime τ 10 ps. The generated events were passed
through the G
EANT 3.13-based [47] ZEUS detector- and
trigger-simulation programs [32]. They were reconstructed
and analysed applying the same program chain as to the
data.
Neutral current DIS events including radiative effects
were simulated using the H
ERACLES 4.6.1 [48, 49] program
with the D
JANGOH 1.1 [50, 51] interface to the hadroniza-
tion programs. H
ERACLES includes corrections for initial-
and final-state radiation, vertex and propagator terms, and
two-boson exchange. The QCD cascade is simulated using
the color-dipole model (CDM) [5255] including the LO
QCD diagrams as implemented in A
RIADNE 4.08 [56, 57]
and, alternatively, with the MEPS model of L
EPTO 6.5 [58].
The CTEQ5D [59] proton PDFs were used for these simu-
lations. Fragmentation into hadrons is performed using the
Lund string model [60] as implemented in J
ETSET [6164].
The jet search was performed on the Monte Carlo (MC)
events using the energy measured in the CAL cells in the
same way as for the data. The same jet algorithm was
also applied to the final-state particles (hadron level) and
to the partons available after the parton shower (parton
level) to compute hadronization correction factors (see Sec-
tion 6).
6 QCD calculations
The O
2
s
) NLO QCD calculations used to compare with
the data are based on the program D
ISENT [65]. The cal-
culations used a generalized version of the subtraction
method [66] and were performed in the massless
MS renor-
malization and factorization schemes. The number of flavors
was set to ve; the renormalization (μ
R
) and factorization
(μ
F
) scales were set to μ
R
= μ
F
= Q; α
s
was calculated
at two loops using Λ
(5)
MS
= 220 MeV which corresponds to
α
s
(M
Z
) =0.118. The ZEUS-S [67] parameterizations of the
proton PDFs were used. The results obtained with D
ISENT
were cross-checked by using the program NLOJET++ [68].
Since the measurements refer to jets of hadrons, whereas
the QCD calculations refer to jets of partons, the predictions
were corrected to the hadron level using the MC samples
described in Sect. 5. The multiplicative correction factor,
C
had
, defined as the ratio of the cross section for subjets of
hadrons to that of partons, was estimated with the L
EPTO-
MEPS model, since it reproduced the shape of the QCD cal-
culations better
3
. The normalized cross-section calculations
changed typically by less than ±20% upon application of
the parton-to-hadron corrections, except at the edges of the
distributions, where they changed by up to ±50%. Other ef-
fects not accounted for in the calculations, namely QED ra-
diative corrections and Z
0
exchange, were found to be very
small for the normalized cross-section calculations and ne-
glected.
The dominant source of theoretical uncertainty is in the
modeling of the parton shower, which was estimated by us-
ing different models (see Sect. 5) to calculate the parton-
to-hadron correction factors. As examples of the size of
the uncertainty, average values of the effect on the nor-
malized cross section as functions of E
sbj
T
/E
jet
T
, η
sbj
η
jet
,
|φ
sbj
φ
jet
| and α
sbj
are 5.6%, 13.2%, 7.6% and 5.3%, re-
spectively. Other uncertainties, such as those arising from
higher-order terms, choice of μ
F
, those on the proton PDFs
and that on α
s
(M
Z
), were investigated and found to be
small in comparison. These uncertainties were added in
3
The HERWIG model [6971] has not been used since its predictions
exhibited a different dependence than the calculations [19].
Page 6
Eur. Phys. J. C (2009) 63: 527–548 533
quadrature and are shown as hatched bands in the fig-
ures.
7 Corrections and systematic uncertainties
The sample of events generated with CDM, after applying
the same offline selection as for the data, gives a reasonably
good description of the measured distributions of the kine-
matic, jet and subjet variables; the description provided by
the MEPS sample is somewhat poorer. The comparison of
the measured subjet distributions and the MC simulations is
shown in Fig. 2.
The normalized differential cross sections were obtained
from the data using the bin-by-bin correction method,
1
σ
i
dA
=
1
σ
N
data,i
L·A
i
·
N
had
MC,i
N
det
MC,i
,
where N
data,i
is the number of subjets in data in bin i of
the subjet variable A, N
had
MC,i
(N
det
MC,i
) is the number of sub-
jets in MC at hadron (detector) level, L is the integrated
luminosity and A
i
is the bin width. The MC samples of
CDM and MEPS were used to compute the acceptance cor-
rection factors to the subjet distributions. These correction
factors took into account the efficiency of the trigger, the
selection criteria and the purity and efficiency of the jet
and subjet reconstruction. The average of the correction fac-
tors evaluated with CDM and MEPS were used to obtain
the central values of the normalized differential cross sec-
tions.
The following sources of systematic uncertainty were
considered for the measured subjet cross sections (as exam-
ples of the size of the uncertainties, average values of the
effect of each uncertainty on the normalized cross section as
functions of E
sbj
T
/E
jet
T
, η
sbj
η
jet
, |φ
sbj
φ
jet
| and α
sbj
are
given in parentheses):
The deviations in the results obtained by using either
CDM or MEPS to correct the data from their average
were taken to represent systematic uncertainties due to
the modeling of the parton shower (0.5%, 2.9%, 2.6%,
1.3%).
Variations in the simulation of the CAL response to low-
energy particles (0.3%, 1.6%, 1.2%, 0.6%).
Other uncertainties, such as those arising from the un-
certainty in the absolute energy scale of the jets [1, 2, 73],
the uncertainty in the simulation of the trigger and the un-
certainty in the absolute energy scale of the electron candi-
date [74], were investigated and found to be negligible. The
systematic uncertainties were added in quadrature to the sta-
Fig. 2 Detector-level
normalized subjet data
distributions (dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
(a) E
sbj
T
/E
jet
T
,(b) η
sbj
η
jet
,
(c) |φ
sbj
φ
jet
| and (d) α
sbj
.
The statistical uncertainties are
smaller than the marker size.
For comparison, the
distributions of the CDM (solid
histograms) and MEPS
(dot-dashed histograms) Monte
Carlo models are included
Page 7
534 Eur. Phys. J. C (2009) 63: 527–548
tistical uncertainties and are shown as error bars in the fig-
ures.
8 Results
Normalized differential subjet cross sections were measured
for Q
2
> 125 GeV
2
for jets with E
jet
T
> 14 GeV and 1 <
η
jet
< 2.5 which have exactly two subjets for y
cut
=0.05.
The distribution of the fraction of transverse energy,
(1 )(dσ/d(E
sbj
T
/E
jet
T
)), is presented in Fig. 3a. It con-
tains two entries per jet and is symmetric with respect to
E
sbj
T
/E
jet
T
=0.5 by construction. This distribution has a peak
for 0.4 <E
sbj
T
/E
jet
T
< 0.6, which shows that the two subjets
tend to have similar transverse energies.
The η
sbj
η
jet
data distribution is shown in Fig. 3b and
also has two entries per jet. The measured cross section has
a two-peak structure; the dip around η
sbj
η
jet
=0 is due to
the fact that the two subjets are not resolved when they are
too close together.
Figure 3c presents the measured normalized cross section
as a function of |φ
sbj
φ
jet
|. There are two entries per jet
in this distribution. The distribution has a peak for 0.2 <
|φ
sbj
φ
jet
|< 0.3; the suppression around |φ
sbj
φ
jet
|=0
also arises from the fact that the two subjets are not resolved
when they are too close together.
The data distribution as a function of α
sbj
(one entry per
jet) increases as α
sbj
increases (see Fig. 3d). This shows that
the subjet with higher transverse energy tends to be in the
rear direction. This is consistent with the asymmetric peaks
observed in the η
sbj
η
jet
distribution (see Fig. 3b). Fig-
ure 4 shows the η
sbj
η
jet
distribution for those jets which
have two subjets with asymmetric E
sbj
T
(E
sbj
T,low
/E
jet
T
< 0.4,
or, equivalently, E
sbj
T,high
/E
jet
T
> 0.6), separately for the sub-
jet with higher and lower E
sbj
T
. It is to be noted that since the
jet axis is reconstructed as the transverse-energy-weighted
average of the subjet axes, the subjet with higher E
sbj
T
is
constrained to be closer to the jet axis than that of the lower
E
sbj
T
subjet. The measured distributions show that the higher
(lower) E
sbj
T
subjet tends to be in the rear (forward) direc-
tion. All these observations support the expectation of the
presence of color-coherence effects between the initial and
final states and, in particular, the tendency of the subjet with
lower E
sbj
T
to be emitted predominantly towards the proton
beam direction.
Fig. 3 Measured normalized
differential subjet cross sections
(dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
(a) E
sbj
T
/E
jet
T
,(b) η
sbj
η
jet
,
(c) |φ
sbj
φ
jet
| and (d) α
sbj
.
The inner error bars represent
the statistical uncertainties of
the data, the outer error bars
show the statistical and
systematic uncertainties added
in quadrature. In many cases,
the error bars are smaller than
themarkersizeandaretherefore
not visible. For comparison, the
NLO QCD predictions (solid
histograms) are included. The
hatched bands represent the
theoretical uncertainty
Page 8
Eur. Phys. J. C (2009) 63: 527–548 535
8.1 Comparison with NLO QCD calculations
Next-to-leading-order QCD calculations are compared to
the data in Figs. 3 and 4. The QCD predictions give an
adequate description of the data. However, the data points
are situated at the upper (lower) edge of the theoretical un-
certainty in some regions of the subjet variables such as
E
sbj
T
/E
jet
T
0.5, |φ
sbj
φ
jet
|∼0, α
sbj
0 and the peaks in
the η
sbj
η
jet
distribution (E
sbj
T
/E
jet
T
0.25, |φ
sbj
φ
jet
|>
0.3 and |η
sbj
η
jet
| > 0.5). Since the calculations are nor-
malized to unity, the uncertainties are correlated among the
points; this correlation gives rise to the pulsating pattern ex-
hibited by the theoretical uncertainties.
The calculation of the cross section as a function of
E
sbj
T
/E
jet
T
exhibits a peak at 0.4 <E
sbj
T
/E
jet
T
< 0.6, as seen
in the data. The calculations for the η
sbj
η
jet
and α
sbj
distri-
butions predict that the subjet with higher transverse energy
tends to be in the rear direction, in agreement with the data.
This shows that the mechanism driving the subjet topology
in the data is the eq eqg and eg eq ¯q subprocesses as
implemented in the pQCD calculations.
To gain further insight into the pattern of parton radiation,
the predictions for quark- and gluon-induced processes (see
Sect. 2) are compared separately with the data in Fig. 5.The
NLO calculations predict that the two-subjet rate is domi-
nated by quark-induced processes: the relative contribution
Fig. 4 Measured normalized differential subjet cross sections for jets
with E
jet
T
> 14 GeV and 1
jet
< 2.5 which have two subjets for
y
cut
= 0.05 in the kinematic region given by Q
2
> 125 GeV
2
and
E
sbj
T,low
/E
jet
T
< 0.4 as functions of η
sbj
η
jet
separately for the higher
(dots)andlower(open circles) E
sbj
T
subjets. Other details are as in the
caption to Fig. 3
of quark- (gluon-) induced processes is 81% (19%). The
shape of the predictions for these two types of processes are
different; in quark-induced processes, the two subjets have
more similar transverse energies (see Fig. 5a) and are closer
to each other (see Fig. 5b and 5c) than in gluon-induced
processes. The comparison with the measurements shows
that the data are better described by the calculations for jets
arising from a qg pair than those coming from a q ¯q pair.
8.2 E
jet
T
, Q
2
and x dependence of the subjet distributions
Figures 6, 7, 8, 9 show the normalized differential subjet
cross sections in different regions of E
jet
T
. Even though the
mean subjet multiplicity decreases with increasing E
jet
T
[19],
the measured normalized differential subjet cross sections
have very similar shapes in all E
jet
T
regions for all the ob-
servables considered. This means that the subjet topology
does not change significantly with E
jet
T
. This is better illus-
trated in Fig. 10, where the data for all E
jet
T
regions are plot-
ted together. In particular, it is observed that the maximum
of each measured normalized cross section in every region
of E
jet
T
occurs in the same bin of the distribution. To quantify
the E
jet
T
dependence more precisely, Fig. 11 shows the max-
imum value of the measured normalized cross section for
each observable as a function of E
jet
T
together with the NLO
predictions. The spread of the measured maximum values of
the normalized cross sections is ±(4–6)%. For each observ-
able, the scaling behavior of the normalized differential sub-
jet cross sections is clearly observed and in agreement with
the expectation that the splitting functions depend weakly on
the energy scale. The NLO QCD calculations are in agree-
ment with the data and support this observation.
Figures 12, 13, 14, 15 show the normalized differential
subjet cross sections in different regions of Q
2
. In this case,
it is observed that while the shape of the E
sbj
T
/E
jet
T
dis-
tribution does not change significantly with Q
2
, some de-
pendence can be seen in the other observables. For exam-
ple, the dip in the η
sbj
η
jet
distribution is shallower for
125 <Q
2
< 250 GeV
2
than at higher Q
2
and the shape
of the α
sbj
distribution for 125 <Q
2
< 250 GeV
2
is some-
what different than for the other regions (see Fig. 16). These
features of the data are reasonably reproduced by the NLO
QCD calculations and understood as a combination of two
effects: the fraction of gluon-induced events is predicted to
be 32% for 125 <Q
2
< 250 GeV
2
and below 14% for
higher Q
2
; the shape of the normalized cross sections as
functions of η
sbj
η
jet
and α
sbj
changes from the region
125 <Q
2
< 250 GeV
2
to 250 <Q
2
< 500 GeV
2
(see
Fig. 17) for quark- and gluon-induced events. It is observed
that the maximum of each measured normalized cross sec-
tion in every region of Q
2
occurs in the same bin of the dis-
tribution, except for |φ
sbj
φ
jet
| in the highest-Q
2
region.
Page 9
536 Eur. Phys. J. C (2009) 63: 527–548
Fig. 5 Measured normalized
differential subjet cross sections
(dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
(a) E
sbj
T
/E
jet
T
,(b) η
sbj
η
jet
,
(c) |φ
sbj
φ
jet
| and (d) α
sbj
.For
comparison, the NLO
predictions for quark- (solid
histograms) and gluon-induced
(dot-dashed histograms)
processes are included. Other
details are as in the caption to
Fig. 3
Fig. 6 Measured normalized
differential subjet cross sections
(dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
E
sbj
T
/E
jet
T
in different regions of
E
jet
T
. Other details are as in the
caption to Fig. 3
Page 10
Eur. Phys. J. C (2009) 63: 527–548 537
Fig. 7 Measured normalized
differential subjet cross sections
(dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
η
sbj
η
jet
in different regions of
E
jet
T
. Other details are as in the
caption to Fig. 3
Fig. 8 Measured normalized
differential subjet cross sections
(dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
|φ
sbj
φ
jet
| in different regions
of E
jet
T
. Other details are as in
the caption to Fig. 3
Page 11
538 Eur. Phys. J. C (2009) 63: 527–548
Fig. 9 Measured normalized
differential subjet cross sections
(dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
α
sbj
in different regions of E
jet
T
.
Other details are as in the
caption to Fig. 3
Fig. 10 Measured normalized
differential subjet cross sections
for jets with E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
(a) E
sbj
T
/E
jet
T
,(b) η
sbj
η
jet
,
(c) |φ
sbj
φ
jet
| and (d) α
sbj
in
different regions of E
jet
T
. Details
concerning the error bars are as
in the caption to Fig. 3
Page 12
Eur. Phys. J. C (2009) 63: 527–548 539
Fig. 11 Maximum of the
measured normalized
differential (a) E
sbj
T
/E
jet
T
,
(b) η
sbj
η
jet
,(c) |φ
sbj
φ
jet
|
and (d) α
sbj
subjet cross
sections (dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as a function
of E
jet
T
. For comparison, the
NLO predictions for quark-
(dotted histograms)and
gluon-induced (dot-dashed
histograms) processes are also
shown separately. Other details
are as in the caption to Fig. 3
Fig. 12 Measured normalized
differential subjet cross sections
(dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
E
sbj
T
/E
jet
T
in different regions of
Q
2
. For comparison, the LO
QCD predictions (dashed
histograms) are included. Other
details are as in the caption to
Fig. 3
Page 13
540 Eur. Phys. J. C (2009) 63: 527–548
Fig. 13 Measured normalized
differential subjet cross sections
(dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
η
sbj
η
jet
in different regions of
Q
2
. Other details are as in the
caption to Fig. 12
Fig. 14 Measured normalized
differential subjet cross sections
(dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
|φ
sbj
φ
jet
| in different regions
of Q
2
. Other details are as in the
caption to Fig. 12
Page 14
Eur. Phys. J. C (2009) 63: 527–548 541
Fig. 15 Measured normalized
differential subjet cross sections
(dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
α
sbj
in different regions of Q
2
.
Other details are as in the
caption to Fig. 12
Fig. 16 Measured normalized
differential subjet cross sections
for jets with E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
(a) E
sbj
T
/E
jet
T
,(b) η
sbj
η
jet
,
(c) |φ
sbj
φ
jet
| and (d) α
sbj
in
different regions of Q
2
. Details
concerning the error bars are as
in the caption to Fig. 3
Page 15
542 Eur. Phys. J. C (2009) 63: 527–548
Fig. 17 Predicted normalized
differential subjet cross sections
(solid histograms) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
(a, c) η
sbj
η
jet
and (b, d) α
sbj
in different regions of Q
2
.The
NLO predictions for quark-
(dotted histograms)and
gluon-induced (dot-dashed
histograms) processes are also
shown separately
Figure 18 shows the maximum
4
value of the measured nor-
malized cross section for each observable as a function of
Q
2
together with the NLO predictions. The spread of the
measured maximum values of the normalized cross sections
as functions of E
sbj
T
/E
jet
T
and |φ
sbj
φ
jet
| is ±(3–4)%. On
the other hand, the measured and predicted maximum values
for the normalized cross sections as functions of η
sbj
η
jet
and α
sbj
exhibit a step-like behavior between the lowest-Q
2
region and the rest.
Figures 19, 20, 21, 22 show the normalized differential
subjet cross sections in different regions of x. It should be
noted that due to HERA kinematics, the regions in x and Q
2
are correlated to some extent. Figure 23 shows the data for
all x regions plotted together. It is observed that the max-
imum of each measured normalized cross section in every
region of x occurs in the same bin of the distribution, except
for |φ
sbj
φ
jet
| in the highest x region. Figure 24 shows
the maximum
4
value of the measured normalized cross sec-
tion for each observable as a function of x. The shape of
the E
sbj
T
/E
jet
T
measured distribution does not change signif-
icantly with x, whereas some dependence is expected (see
4
For the |φ
sbj
φ
jet
| distribution, the same bin has been used for con-
sistency.
Fig. 24a). The dependence of the η
sbj
η
jet
and α
sbj
dis-
tributions with x exhibits features similar to those observed
in the study of the Q
2
dependence; in particular, the max-
imum values (see Figs. 24b and 24d) exhibit a monotonic
increase as x increases, which is reasonably reproduced by
the calculations. As discussed previously, these features are
understood as a combination of two effects: a decrease of
the predicted fraction of gluon-induced events from 44% for
0.004 <x<0.009 to 6% for x>0.093 and the change in
shape of the normalized cross sections for quark- and gluon-
induced processes as x increases (see Fig. 25).
To investigate the origin of the change in shape of the nor-
malized differential cross sections between the lowest and
higher Q
2
and x regions, LO and NLO calculations were
compared. The most dramatic change is observed when re-
stricting the kinematic region to 125 <Q
2
< 250 GeV
2
or
0.004 <x<0.009 (see Figs. 12 to 15 and Figs. 19 to 22);
the LO calculation of the η
sbj
η
jet
distribution does not ex-
hibit a two-peak structure as seen in the NLO prediction and
in the data (see Figs. 13 and 20). In addition, the LO calcu-
lation of the α
sbj
distribution peaks at α
sbj
π/2 in contrast
with the NLO prediction and the data (see Figs. 15 and 22).
This proves that the NLO QCD radiative corrections are re-
sponsible for these variations in shape and necessary for de-
scribing the data.
Page 16
Eur. Phys. J. C (2009) 63: 527–548 543
Fig. 18 Maximum of the
measured normalized
differential (a) E
sbj
T
/E
jet
T
,
(b) η
sbj
η
jet
,(c) |φ
sbj
φ
jet
|
and (d) α
sbj
subjet cross
sections (dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as a function
of Q
2
. For comparison, the
NLO predictions for quark-
(dotted histograms)and
gluon-induced (dot-dashed
histograms) processes are also
shown separately. Other details
are as in the caption to Fig. 3
Fig. 19 Measured normalized
differential subjet cross sections
(dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
E
sbj
T
/E
jet
T
in different regions
of x. Other details are as in the
caption to Fig. 12
Page 17
544 Eur. Phys. J. C (2009) 63: 527–548
Fig. 20 Measured normalized
differential subjet cross sections
(dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
η
sbj
η
jet
in different regions
of x. Other details are as in the
caption to Fig. 12
Fig. 21 Measured normalized
differential subjet cross sections
(dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
|φ
sbj
φ
jet
| in different regions
of x. Other details are as in the
caption to Fig. 12
In summary, while the shapes of the normalized differ-
ential cross sections show only a weak dependence on E
jet
T
,
their dependence on Q
2
and x have some prominent fea-
tures at low Q
2
or x. The weak dependence on E
jet
T
is con-
sistent with the expected scaling behavior of the splitting
functions; however, the restriction to low Q
2
or x values
demonstrates that the NLO QCD radiative corrections are
important there. The NLO QCD calculations, which include
Page 18
Eur. Phys. J. C (2009) 63: 527–548 545
Fig. 22 Measured normalized
differential subjet cross sections
(dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
α
sbj
in different regions of x.
Other details are as in the
caption to Fig. 12
Fig. 23 Measured normalized
differential subjet cross sections
for jets with E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
(a) E
sbj
T
/E
jet
T
,(b) η
sbj
η
jet
,
(c) |φ
sbj
φ
jet
| and (d) α
sbj
in
different regions of x. Details
concerning the error bars are as
in the caption to Fig. 3
Page 19
546 Eur. Phys. J. C (2009) 63: 527–548
Fig. 24 Maximum of the
measured normalized
differential (a) E
sbj
T
/E
jet
T
,
(b) η
sbj
η
jet
,(c) |φ
sbj
φ
jet
|
and (d) α
sbj
subjet cross
sections (dots) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as a function
of x. For comparison, the NLO
predictions for quark- (dotted
histograms) and gluon-induced
(dot-dashed histograms)
processes are also shown
separately. Other details are as
in the caption to Fig. 3
Fig. 25 Predicted normalized
differential subjet cross sections
(solid histograms) for jets with
E
jet
T
> 14 GeV and
1
jet
< 2.5 which have two
subjets for y
cut
=0.05 in the
kinematic region given by
Q
2
> 125 GeV
2
as functions of
(a, c) η
sbj
η
jet
and (b, d) α
sbj
in different regions of x.The
NLO predictions for quark-
(dotted histograms)and
gluon-induced (dot-dashed
histograms) processes are also
shown separately
Page 20
Eur. Phys. J. C (2009) 63: 527–548 547
the two competing processes eq eqg and eg eq ¯q
and radiative corrections, adequately reproduce the mea-
surements.
9 Summary
Normalized differential subjet cross sections in inclusive-jet
NC DIS were measured in ep collisions using 81.7pb
1
of data collected with the ZEUS detector at HERA. The
cross sections refer to jets identified in the laboratory
frame with the k
T
cluster algorithm in the longitudi-
nally invariant inclusive mode and selected with E
jet
T
>
14 GeV and 1
jet
< 2.5. The measurements were
made for those jets which have exactly two subjets
for y
cut
= 0.05 in the kinematic region defined by
Q
2
> 125 GeV
2
.
The cross sections were measured as functions of
E
sbj
T
/E
jet
T
, η
sbj
η
jet
, |φ
sbj
φ
jet
| and α
sbj
. The data show
that the two subjets tend to have similar transverse energies
and that the subjet with higher transverse energy tends to be
in the rear direction. This is consistent with the effects of
color coherence between the initial and final states, which
predict that soft parton radiation is emitted predominantly
towards the proton beam direction.
An adequate description of the data is given by NLO
QCD calculations. This means that the pattern of parton ra-
diation as predicted by QCD reproduces the subjet topology
in the data. Furthermore, the subjet distributions in the data
are better described by the calculations for jets arising from
a quark-gluon pair.
The normalized cross sections show a weak dependence
on E
jet
T
, in agreement with the expected scaling behavior of
the splitting functions. By restricting the measurements to
low Q
2
or x values, significant differences in shape are ob-
served, which can be primarily attributed to NLO QCD ra-
diative corrections.
Acknowledgements We thank the DESY Directorate for their
strong support and encouragement. We appreciate the contributions to
the construction and maintenance of the ZEUS detector of many peo-
ple who are not listed as authors. The HERA machine group and the
DESY computing staff are especially acknowledged for their success
in providing excellent operation of the collider and the data-analysis
environment.
References
1. S. Chekanov et al. (ZEUS Collaboration), Phys. Lett. B 531,9
(2002)
2. S. Chekanov et al. (ZEUS Collaboration), Eur. Phys. J. C 23, 615
(2002)
3. J. Breitweg et al. (ZEUS Collaboration), Phys. Lett. B 443, 394
(1998)
4. J. Breitweg et al. (ZEUS Collaboration), Phys. Lett. B 507,70
(2001)
5. S. Chekanov et al. (ZEUS Collaboration), Phys. Lett. B 547, 164
(2002)
6. S. Chekanov et al. (ZEUS Collaboration), Eur. Phys. J. C 23,13
(2002)
7. S. Chekanov et al. (ZEUS Collaboration), Phys. Lett. B 560,7
(2003)
8. S. Chekanov et al. (ZEUS Collaboration), Eur. Phys. J. C 31, 149
(2003)
9. S. Chekanov et al. (ZEUS Collaboration), Nucl. Phys. B 765,1
(2007)
10. S. Chekanov et al. (ZEUS Collaboration), Phys. Lett. B 649,12
(2007)
11. C. Adloff et al. (H1 Collaboration), Phys. Lett. B 515, 17 (2001)
12. C. Adloff et al. (H1 Collaboration), Eur. Phys. J. C 19, 289 (2001)
13. C. Adloff et al. (H1 Collaboration), Eur. Phys. J. C 19, 429 (2001)
14. C. Adloff et al. (H1 Collaboration), Eur. Phys. J. C 25, 13 (2002)
15. C. Adloff et al. (H1 Collaboration), Phys. Lett. B 542, 193 (2002)
16. C. Adloff et al. (H1 Collaboration), Eur. Phys. J. C 29, 497 (2003)
17. A. Aktas et al. (H1 Collaboration), Phys. Lett. B 639, 21 (2006)
18. A. Aktas et al. (H1 Collaboration), Phys. Lett. B 653, 134 (2007)
19. S. Chekanov et al. (ZEUS Collaboration), Phys. Lett. B 558,41
(2003)
20. S. Chekanov et al. (ZEUS Collaboration), Nucl. Phys. B 700,3
(2004)
21. J. Thaler, L.-T. Wang, J. High Energy Phys. 0807, 092 (2008)
22. D.E. Kaplan et al., Preprint, arXiv:0806.0848 (2008)
23. J.M. Butterworth et al., Phys. Rev. Lett. 100, 242001 (2008)
24. S. Catani et al., Nucl. Phys. B 406, 187 (1993)
25. S.D. Ellis, D.E. Soper, Phys. Rev. D 48, 3160 (1993)
26. S. Catani et al., Nucl. Phys. B 383, 419 (1992)
27. M.H. Seymour, Nucl. Phys. B 421, 545 (1994)
28. M.H. Seymour, Phys. Lett. B 378, 279 (1996)
29. J.R. Forshaw, M.H. Seymour, J. High Energy Phys. 9909, 009
(1999)
30. F. Abe et al. (CDF Collaboration), Phys. Rev. D
50, 5562 (1994)
31. M. Derrick et al. (ZEUS Collaboration), Phys. Lett. B 293, 465
(1992)
32. U. Holm (ed.) (ZEUS Collaboration), The ZEUS Detector.Sta-
tus Report (unpublished), DESY (1993). Available on http://
www-zeus.desy.de/bluebook/bluebook.html
33. N. Harnew et al., Nucl. Instrum. Methods A 279, 290 (1989)
34. B. Foster et al., Nucl. Phys. Proc. Suppl. B 32, 181 (1993)
35. B. Foster et al., Nucl. Instrum. Methods A 338, 254 (1994)
36. M. Derrick et al., Nucl. Instrum. Methods A 309, 77 (1991)
37. A. Andresen et al., Nucl. Instrum. Methods A 309, 101 (1991)
38. A. Caldwell et al., Nucl. Instrum. Methods A 321, 356 (1992)
39. A. Bernstein et al., Nucl. Instrum. Methods A 336, 23 (1993)
40. J. Andruszków et al., Preprint DESY-92-066, DESY (1992)
41. M. Derrick et al. (ZEUS Collaboration), Z. Phys. C 63, 391 (1994)
42. J. Andruszków et al., Acta Phys. Pol. B 32, 2025 (2001)
43. H. Abramowicz, A. Caldwell, R. Sinkus, Nucl. Instrum. Methods
A 365, 508 (1995)
44. R. Sinkus, T. Voss, Nucl. Instrum. Methods A 391, 360 (1997)
45. S. Bentvelsen, J. Engelen, P. Kooijman, in Proc. of the Workshop
on Physics at HERA, ed. by W. Buchmüller, G. Ingelman, vol. 1.
Hamburg, Germany, DESY (1992), p. 23
46. K.C. Höger, in Proc. of the Workshop on Physics at HERA, ed. by
W. Buchmüller, G. Ingelman, vol. 1. Hamburg, Germany, DESY
(1992), p. 43
47. R. Brun et al.,
GEANT3, Technical Report CERN-DD/EE/84-1,
CERN (1987)
48. A. Kwiatkowski, H. Spiesberger, H.-J. Möhring, Comput. Phys.
Commun. 69, 155 (1992)
Page 21
548 Eur. Phys. J. C (2009) 63: 527–548
49. H. Spiesberger, An Event Generator for ep Interactions at HERA
Including Radiative Processes (Version 4.6) (1996). Available on
http://www.desy.de/~hspiesb/heracles.html
50. K. Charchuła, G.A. Schuler, H. Spiesberger, Comput. Phys. Com-
mun. 81, 381 (1994)
51. H. Spiesberger,
HERACLES and DJANGOH: Event Generation
for ep Interactions at HERA Including Radiative Processes
(1998). Available on http://www.thep.physik.uni-mainz.de/~
hspiesb/djangoh/djangoh.html
52. Y. Azimov et al., Phys. Lett. B 165, 147 (1985)
53. G. Gustafson, Phys. Lett. B 175, 453 (1986)
54. G. Gustafson, U. Pettersson, Nucl. Phys. B 306, 746 (1988)
55. B. Andersson et al., Z. Phys. C 43, 625 (1989)
56. L. Lönnblad, Comput. Phys. Commun. 71, 15 (1992)
57. L. Lönnblad, Z. Phys. C 65, 285 (1995)
58. G. Ingelman, A. Edin, J. Rathsman, Comput. Phys. Commun. 101,
108 (1997)
59. H.L. Lai et al., Eur. Phys. J. C 12, 375 (2000)
60. B. Andersson et al., Phys. Rep. 97, 31 (1983)
61. T. Sjöstrand, Comput. Phys. Commun. 82, 74 (1994)
62. T. Sjöstrand et al., Comput. Phys. Commun. 135, 238 (2001)
63. T. Sjöstrand, Comput. Phys. Commun. 39, 347 (1986)
64. T. Sjöstrand, M. Bengtsson, Comput. Phys. Commun. 43, 367
(1987)
65. S. Catani, M.H. Seymour, Nucl. Phys. B 485, 291 (1997). Erratum
in Nucl. Phys. B 510, 503 (1998)
66. R.K. Ellis, D.A. Ross, A.E. Terrano, Nucl. Phys. B 178, 421
(1981)
67. S. Chekanov et al. (ZEUS Collaboration), Phys. Rev. D 67,
012007 (2003)
68. Z. Nagy, Z. Trocsanyi, Phys. Rev. Lett. 87, 082001 (2001)
69. G. Marchesini et al., Comput. Phys. Commun. 67, 465 (1992)
70. G. Corcella et al., J. High Energy Phys. 0101, 010 (2001)
71. G. Corcella et al., Preprint hep-ph/0107071 (2001)
72. S. Bethke, J. Phys. G 26, R27 (2000). Updated in S. Bethke, Prog.
Part. Nucl. Phys. 58, 351 (2007)
73. M. Wing (on behalf of the ZEUS Collaboration), in Proc. of the
10th International Conference on Calorimetry in High Energy
Physics, ed. by R. Zhu, Pasadena, USA (2002), p. 767. Also in
preprint hep-ex/0206036
74. S. Chekanov et al. (ZEUS Collaboration), Eur. Phys. J. C 21, 443
(2001)
Page 22
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