EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH
CERN-PPE/92-216
18 Dec 1992
QCD coherence studies using two particle azimuthal
correlations
The OPAL Collab oration
Abstract
From a sample of 146,900 hadronic Z
0
decays recorded by the OPAL detector at LEP,wehave studied
the azimuthal correlations of particles in hadronic events. It is expected that these correlations are
sensitivetointerference eects in QCD. Wehave compared the data to QCD Monte Carlo models
which include and which do not include interference eects. We nd that the distributions of azimuthal
correlations are not reproduced by the parton shower models wehave tested unless interference eects
are included, no matter which hadronisation scheme is used.
(To be submitted to Z. Phys. C )
The OPAL Collab oration
P.D. Acton
25
, G. Alexander
23
, J. Allison
16
,P.P. Allp ort
5
, K.J. Anderson
9
, S. Arcelli
2
, A. Astbury
28
,
D. Axen
29
, G. Azuelos
18
;a
, G.A. Bahan
16
, J.T.M. Baines
16
, A.H. Ball
17
, J. Banks
16
, R.J. Barlow
16
,
S. Barnett
16
, J.R. Batley
5
, G. Beaudoin
18
, A. Beck
23
, J. Becker
10
, T. Behnke
27
, K.W. Bell
20
, G. Bella
23
,
P. Berlich
10
, S. Bethke
11
, O. Biebel
3
, U. Binder
10
, I.J. Blo odworth
1
,P.Bock
11
, B. Bo den
3
,
H.M. Bosch
11
, S. Bougerolle
29
, H. Breuker
8
, R.M. Brown
20
, A. Buijs
8
, H.J. Burckhart
8
, C. Burgard
27
,
P. Capiluppi
2
, R.K. Carnegie
6
, A.A. Carter
13
, J.R. Carter
5
, C.Y. Chang
17
, D.G. Charlton
8
,
P.E.L. Clarke
25
, I. Cohen
23
, J.C. Clayton1, W.J. Collins
5
, J.E. Conboy
15
, M. Cooper
22
, M. Coupland
14
,
M. Cuani
2
, S. Dado
22
, G.M. Dallavalle
2
, S. De Jong
8
, L.A. del Pozo
5
, H. Deng
17
, A. Dieckmann
11
,
M. Dittmar
4
, M.S. Dixit
7
, E. do Couto e Silva
12
, J.E. Dub oscq
8
, E. Duchovni
26
, G. Duckeck
11
,
I.P. Duerdoth
16
, D.J.P. Dumas
6
,P.A. Elcombe
5
,P.G. Estabro oks
6
, E. Etzion
23
, H.G. Evans
9
,
F. Fabbri
2
, M. Fincke-Keeler
28
, H.M. Fischer
3
, D.G. Fong
17
,M.Foucher
17
, A. Gaidot
21
, O. Ganel
26
,
J.W. Gary
4
, J. Gascon
18
, R.F. McGowan
16
, N.I. Geddes
20
, C. Geich-Gimbel
3
, S.W. Gensler
9
,
F.X. Gentit
21
, G. Giacomelli
2
, V. Gibson
5
, W.R. Gibson
13
, J.D. Gillies
20
, J. Goldb erg
22
,
M.J. Go odrick
5
, W. Gorn
4
, C. Grandi
2
, F.C. Grant
5
, J. Hagemann
27
, G.G. Hanson
12
, M. Hansroul
8
,
C.K. Hargrove
7
,P.F. Harrison
13
, J. Hart
8
,P.M. Hattersley
1
, M. Hauschild
8
, C.M. Hawkes
8
, E. Hein
4
,
R.J. Hemingway
6
, R.D. Heuer
8
, J.C. Hill
5
, S.J. Hillier
1
, T. Hilse
10
, D.A. Hinshaw
18
, J.D. Hobbs
8
,
P.R. Hobson
25
,D.Hochman
26
, R.J. Homer
1
, A.K. Honma
28
;a
, C.P.Howarth
15
, R.E. Hughes-Jones
16
,
R. Humbert
10
,P. Igo-Kemenes
11
, H. Ihssen
11
, D.C. Imrie
25
, A.C. Janissen
6
,A.Jawahery
17
,
P.W. Jereys
20
, H. Jeremie
18
, M. Jimack
2
, M. Job es
1
, R.W.L. Jones
13
,P.Jovanovic
1
, C. Jui
4
,
D. Karlen
6
,K.Kawagoe
24
,T.Kawamoto
24
, R.K. Keeler
28
, R.G. Kellogg
17
, B.W. Kennedy
15
, S. Kluth
5
,
T. Kobayashi
24
, T.P. Kokott
3
, S. Komamiya
24
,L.Kopke
8
, J.F. Kral
8
,R.Kowalewski
6
,J.von Krogh
11
,
J. Kroll
9
,M.Kuwano
24
,P. Kyb erd
13
, G.D. Laerty
16
, F. Lamarche
18
, J.G. Layter
4
,P.Le Du
21
,
P. Leblanc
18
, A.M. Lee
17
, M.H. Lehto
15
, D. Lellouch
26
,P. Lennert
11
, C. Leroy
18
, J. Letts
4
,
S. Levegrun
3
, L. Levinson
26
, S.L. Lloyd
13
, F.K. Lo ebinger
16
, J.M. Lorah
17
, B. Lorazo
18
, M.J. Losty
7
,
X.C. Lou
12
, J. Ludwig
10
, M. Mannelli
8
, S. Marcellini
2
, G. Maringer
3
, C. Markus
3
, A.J. Martin
13
,
J.P. Martin
18
, T. Mashimo
24
,P.Mattig
3
, U. Maur
3
, J. McKenna
28
, T.J. McMahon
1
, J.R. McNutt
25
,
F. Meijers
8
, D. Menszner
11
, F.S. Merritt
9
, H. Mes
7
, A. Michelini
8
, R.P. Middleton
20
, G. Mikenberg
26
,
J. Mildenberger
6
, D.J. Miller
15
, R. Mir
12
, W. Mohr
10
, C. Moisan
18
, A. Montanari
2
, T. Mori
24
,
M. Morii
24
, T. Mouthuy
12
;b
, B. Nellen
3
, H.H. Nguyen
9
, M. Nozaki
24
, S.W. O'Neale
8
;c
, F.G. Oakham
7
,
F. Odorici
2
, H.O. Ogren
12
, C.J. Oram
28
;a
, M.J. Oreglia
9
, S. Orito
24
, J.P.Pansart
21
,
B. Panzer-Steindel
8
,P.Paschievici
26
, G.N. Patrick
20
,N.Paz-Jaoshvili
23
,P. Pster
10
, J.E. Pilcher
9
,
D. Pitman
28
, D.E. Plane
8
,P.Poenberger
28
,B.Poli
2
,A.Pouladdej
6
, E. Prebys
8
, T.W. Pritchard
13
,
H. Przysiezniak
18
, G. Quast
27
, M.W. Redmond
9
, D.L. Rees
1
, G.E. Richards
16
, D. Robinson
8
,
A. Rollnik
3
, J.M. Roney
9
, E. Ros
8
, S. Rossb erg
10
, A.M. Rossi
2
;d
, M. Rosvick
28
,P. Routenburg
6
,
K. Runge
10
, O. Runolfsson
8
, D.R. Rust
12
, M. Sasaki
24
, C. Sbarra
8
, A.D. Schaile
10
,O.Schaile
10
,
W. Schappert
6
,P.Schar-Hansen
8
,P.Schenk
28
,H.von der Schmitt
11
,S.Schreiber
3
,C.Schwick
27
,
J. Schwiening
3
, W.G. Scott
20
, M. Settles
12
, T.G. Shears
5
, B.C. Shen
4
, C.H. Shepherd-Themistocleous
7
,
P. Sherwood
15
,R.Shypit
29
, A. Simon
3
,P. Singh
13
, G.P. Siroli
2
, A. Skuja
17
, A.M. Smith
8
, T.J. Smith
8
,
G.A. Snow
17
, R. Sobie
28
;e
, R.W. Springer
17
, M. Sproston
20
, K. Stephens
16
, J. Steuerer
28
,
R. Strohmer
11
, D. Strom
30
,T.Takeshita
24
;f
,P.Taras
18
,S.Tarem
26
,M.Tecchio
9
,P.Teixeira-Dias
11
,
N. Tesch
3
, N.J. Thackray
1
,G.Transtromer
25
, N.J. Tresilian
16
, T. Tsukamoto
24
, M.F. Turner
5
,
G. Tysarczyk-Niemeyer
11
,D.Van den plas
18
,R.Van Kooten
8
, G.J. VanDalen
4
,G.Vasseur
21
,
C.J. Virtue
7
,A.Wagner
27
, D.L. Wagner
9
,C.Wahl
10
, J.P.Walker
1
, C.P.Ward
5
, D.R. Ward
5
,
P.M. Watkins
1
, A.T. Watson
1
, N.K. Watson
8
,M.Web er
11
,P.Weber
6
,S.Weisz
8
,P.S. Wells
8
,
N. Wermes
11
, M.A. Whalley
1
, G.W. Wilson
4
, J.A. Wilson
1
, V-H. Winterer
10
, T. Wlo dek
26
,
S. Wotton
11
, T.R. Wyatt
16
,R.Yaari
26
,A.Yeaman
13
,G.Yekutieli
26
,M.Yurko
18
, W. Zeuner
8
,
G.T. Zorn
17
.
1
1
School of Physics and Space Research, University of Birmingham, Birmingham, B15 2TT, UK
2
Dipartimento di Fisica dell' Universita di Bologna and INFN, Bologna, 40126, Italy
3
Physikalisches Institut, Universitat Bonn, D-5300 Bonn 1, FRG
4
DepartmentofPhysics, University of California, Riverside, CA 92521 USA
5
Cavendish Lab oratory, Cambridge, CB3 0HE, UK
6
Carleton University, Dept of Physics, Colonel By Drive, Ottawa, Ontario K1S 5B6, Canada
7
Centre for ResearchinParticle Physics, Carleton University, Ottawa, Ontario K1S 5B6, Canada
8
CERN, European Organisation for Particle Physics, 1211 Geneva 23, Switzerland
9
Enrico Fermi Institute and DepartmentofPhysics, University of Chicago, Chicago Illinois 60637,
USA
10
Fakultat fur Physik, Albert Ludwigs Universitat, D-7800 Freiburg, FRG
11
Physikalisches Institut, Universitat Heidelberg, Heidelb erg, FRG
12
Indiana University, Dept of Physics, Swain Hall West 117, Bloomington, Indiana 47405, USA
13
Queen Mary and Westeld College, University of London, London, E1 4NS, UK
14
Birkbeck College, London, WC1E 7HV, UK
15
University College London, London, WC1E 6BT, UK
16
DepartmentofPhysics, Schuster Laboratory, The University, Manchester, M13 9PL, UK
17
DepartmentofPhysics and Astronomy, University of Maryland, College Park, Maryland 20742, USA
18
Laboratoire de Physique Nucleaire, Universite de Montreal, Montreal, Quebec, H3C 3J7, Canada
20
Rutherford Appleton Laboratory, Chilton, Didcot, Oxfordshire, OX11 0QX, UK
21
DAPNIA/SPP, CEN Saclay, F-91191 Gif-sur-Yvette, France
22
DepartmentofPhysics, Technion-Israel Institute of Technology, Haifa 32000, Israel
23
DepartmentofPhysics and Astronomy,Tel Aviv University,Tel Aviv 69978, Israel
24
International Centre for Elementary Particle Physics and Dept of Physics, UniversityofTokyo,
Tokyo 113, and Kob e University, Kob e 657, Japan
25
Brunel University, Uxbridge, Middlesex, UB8 3PH UK
26
Nuclear Physics Department, Weizmann Institute of Science, Rehovot, 76100, Israel
27
Universitat Hamburg/DESY, I I Inst f ur Experimental Physik, 2000 Hamburg 52, Germany
28
University of Victoria, Dept of Physics, P O Box 3055, Victoria BC V8W 3P6, Canada
29
University of British Columbia, Dept of Physics, 6224 Agriculture Road, Vancouver BC V6T 1Z1,
Canada
30
University of Oregon, Dept of Physics, Eugene, Oregon 97403, USA
a
Also at TRIUMF, Vancouver, Canada V6T 2A3
b
Now at Centre de Physique des Particules de Marseille, Faculte des Sciences de Luminy, Marseille
c
On leave from Birmingham University, Birmingham B15 2TT, UK
d
Now at Dipartimento di Fisica, Universita della Calabria and INFN, 87036 Rende, Italy
e
And IPP, McGill University, High Energy Physics Department, 3600 University Str, Montreal, Que-
bec H3A 2T8, Canada
f
Also at Shinshu University, Matsumoto 390, Japan
2
1 Intro duction
A complete calculation of multigluon emission has to takeinto account the interference amongst all the
amplitudes [1]. This is the so-called coherence phenomenon in QCD. In e
+
e
annihilation into hadrons,
interference eects provide an explanation of the shape of the momentum spectra of particles, and
their evolution with energy [2]. They also give a possible explanation of the \string eect" observed
in three-jet hadronic events [3, 4]. The ma jorityofmultihadronic events are two-jet like because the
emitted gluons are mostly either collinear with the quarks and/or havelow energy with respect to the
energy scale of the reaction (soft gluons). Coherence eects are also predicted for this class of events
and will b e investigated through a study of angular correlations between particles as discussed b elow.
The e
+
e
!
q
qgg
cross section when one gluon is soft can b e factorized as [5,6]
(
q
1
q
2
g
3
g
4
)=
(
q
1
q
2
g
3
)
(
q
1
q
2
g
4
)
C=
(
q
1
q
2
)
where C is a correlation term given by
C
=1+
N
2
N
2
1
13
24
+
14
23
12
34
1
(1)
where N is the number of colours,
ij
=1
cos
ij
(
ij
is the angle b etween partons i and j).
When both
g
3
and
g
4
are soft, the
q
and the
q
are nearly collinear and dene a natural axis
with respect to which one can dene the pseudorapidity of the two gluons,
3
and
4
, respectively,
34
(=
3
4
) and the relative azimuth
'
34
. The pseudorapidityis
=
ln
tan
(
=
2), where
is the
angle b etween the particle and the axis. In this case, C reduces to
C
=1+
N
2
N
2
1
cos
'
34
cosh
34
cos
'
34
:
(2)
When
'
34
!
, the correlation term becomes smaller than 1, so that the emission of gluons opposite
in azimuth to
g
3
is suppressed. The eect is maximal when
34
0, for whichC(
)/C(
/2) = 7/16.
This suppression has the same dynamical origin as the string eect. Assuming Local Parton Hadron
Duality[7], such a suppression is exp ected at the hadron level.
From the expression for the
q
qgg
cross section given ab ove and from the fact that the correlation
term depends on the pseudorapidities and azimuth of the emitted gluons (equation 2), it follows that
the interference eects can b e studied by looking at azimuthal correlations between particles (partons
or hadrons) using the expression:
dC
d'
(
1
;
2
;'
)=
d
d
1
d
2
d'
d
d
1
:
d
d
2
(3)
where
i
is the pseudorapidity of particles with respect to some axis and
'
is their relative azimuth.
From now on, the subscripts 1 and 2 refer to the two particles of any pair.
In this pap er, azimuthal correlations are studied in multihadronic events produced in Z
0
decays at
LEP, using two metho ds:
The rst method uses the Energy-Multiplicity-Multipl icity Correlations (EMMC) proposed by
Dokshitzer, Khoze, Marchesini and Webber [6], whichavoid the selection of two-jet events and
the denition of an event axis. Each particle of an event denes in turn an axis with resp ect
to which one calculates the pseudorapidities and the relative azimuth of any pair of the other
3
particles. Both particles of the pair are required to belong to the same pseudorapidityinterval.
In order to reect the direction of the initial quarks, each correlation dened by (3) is weighted
by the energy of the particle dening the reference axis. At leading order the EMMC are given
by the correlation function (2). Higher order corrections have been recently calculated and are
found to b e imp ortant[8]. The correlation at
'
=
is predicted to b e
0
:
93, but in [8], it
is argued that higher order terms not taken into accountwould lower this number by
10%,
leading to a prediction close to 0.8.
In the second method, two jet events are selected (soft gluon case) and the azimuthal correlations
are computed using the sphericity axis of the event as the reference axis. These we refer to as
TwoParticle Azimuthal Correlations (TPAC). The pseudorapidity
2
of the second particle in
(3) is taken at a xed distance from
1
. That is to say, one considers the quantity:
dC
d'
(
1
;
12
;'
)=
d
d
1
d
12
d'
d
d
1
:
d
d
2
(4)
where
12
=
2
1
, for any pair of particles.
Section 2 of this pap er describes the data selection, section 3 explains how the azimuthal correla-
tions are obtained and the errors are discussed in section 4. Experimental correlations are computed
with hadrons and are compared to QCD Monte Carlo mo del calculations with and without interference
eects. The models used in this analysis are presented in section 5 and the comparison with the data
is given in section 6. The interpretation of the results is given in section 7, while section 8 contains
the conclusions.
2 The OPAL Detector and Data Sample
This analysis is based on approximately 146,900 multihadronic Z
0
decays collected with the OPAL
detector at the e
+
e
collider LEP corresp onding to an integrated luminosity of 6.5 pb
1
. The OPAL
detector is described in detail in reference [9]. The selection of the multihadronic events follows the
method described in reference [10].
The detector elements most relevant for this analysis are a large volume central tracking detector
and an electromagnetic calorimeter composed of lead glass blo cks. The tracking chamber allows an
almost 100% track nding eciency in the polar angle region
j
cos
j
<
0
:
92, where the angle
is
dened relative to the b eam axis. Electromagnetic energy deposits are measured for over 98% of the
solid angle with the calorimeter. Each lead glass block subtends approximately 40 mrad x 40 mrad.
Charged tracks were accepted if they originated from within 5 cm of the interaction p ointinthe
plane p erpendicular to the beam axis and within 25 cm in the longitudinal direction. Eachcharged
trackwas required to have a transverse momentum with respect to the beam direction of more than
150 MeV/c and at least 40 measured space p oints. Electromagnetic clusters were accepted if they had
over 200 MeV of energy and were spread over at least two lead glass blocks. Only clusters whichwere
not asso ciated with charged tracks were kept [3], and these will b e referred to as neutral particles.
Hadronic events were required to contain at least vecharged tracks which satised the ab ove criteria.
The polar angle of the thrust axis was required to satisfy
j
cos
thrust
j
<
0
:
9 and the sphericity axis
j
cos
sph
j
<
0
:
875. The total energy of charged particles was required to lie between 20 and 100 GeV.
About 114,000 multihadronic events were accepted, with an average centre of mass energy of 91.3
GeV.
4
