Two-pion Bose-Einstein correlations in pp collisions at sqrt(s)=900 GeV

Abstract

We report on the measurement of two-pion correlation functions from pp
collisions at sqrt(s)=900 GeV performed by the ALICE experiment at the Large
Hadron Collider. Our analysis shows an increase of the HBT radius with
increasing event multiplicity, in line with other measurements done in
particle- and nuclear collisions. Conversely, the strong decrease of the radius
with increasing transverse momentum, as observed at RHIC and at Tevatron, is
not manifest in our data.

Full text

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arXiv:1007.0516v1 [hep-ex] 3 Jul 2010
Two-pion Bose-Einstein correlations in pp collisions at√s = 900 GeV
(The ALICE Collaboration)
K. Aamodt,1N. Abel,2U. Abeysekara,3A. Abrahantes Quintana,4A. Abramyan,5D. Adamov´ a,6M.M. Aggarwal,7
G. Aglieri Rinella,8A.G. Agocs,9S. Aguilar Salazar,10Z. Ahammed,11A. Ahmad,12N. Ahmad,12S.U. Ahn,13, aR. Akimoto,14
A. Akindinov,15D. Aleksandrov,16B. Alessandro,17R. Alfaro Molina,10A. Alici,18E. Almar´ az Avi˜ na,10J. Alme,19T. Alt,2, b
V. Altini,20S. Altinpinar,21C. Andrei,22A. Andronic,21G. Anelli,8V. Angelov,2, bC. Anson,23T. Antiˇ ci´ c,24F. Antinori,8, c
S. Antinori,18K. Antipin,25D. Anto´ nczyk,25P. Antonioli,26A. Anzo,10L. Aphecetche,27H. Appelsh¨ auser,25S. Arcelli,18
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H. Zbroszczyk,106P. Zelnicek,2A. Zenin,59A. Zepeda,70I. Zgura,83M. Zhalov,50X. Zhang,68, aD. Zhou,68S. Zhou,103
J. Zhu,68A. Zichichi,18, tA. Zinchenko,44G. Zinovjev,62Y. Zoccarato,71V. Zych´ aˇ cek,54and M. Zynovyev62
1Department of Physics, University of Oslo, Oslo, Norway
2Kirchhoff-Institut f¨ ur Physik, Ruprecht-Karls-Universit¨ at Heidelberg, Heidelberg, Germany
3Physics Department, Creighton University, Omaha, NE, United States
4Centro de Aplicaciones Tecnol´ ogicas y Desarrollo Nuclear (CEADEN), Havana, Cuba
5Yerevan Physics Institute, Yerevan, Armenia
6Nuclear Physics Institute, Academy of Sciences of the Czech Republic,ˇReˇ z u Prahy, Czech Republic
7Physics Department, Panjab University, Chandigarh, India
8European Organization for Nuclear Research (CERN), Geneva, Switzerland
9KFKI Research Institute for Particle and Nuclear Physics, Hungarian Academy of Sciences, Budapest, Hungary
10Instituto de F´ ısica, Universidad Nacional Aut´ onoma de M´ exico, Mexico City, Mexico
11Variable Energy Cyclotron Centre, Kolkata, India
12Department of Physics Aligarh Muslim University, Aligarh, India
13Gangneung-Wonju National University, Gangneung, South Korea
14University of Tokyo, Tokyo, Japan
15Institute for Theoretical and Experimental Physics, Moscow, Russia
16Russian Research Centre Kurchatov Institute, Moscow, Russia
17Sezione INFN, Turin, Italy
18Dipartimento di Fisica dell’Universit` a and Sezione INFN, Bologna, Italy
19Department of Physics and Technology, University of Bergen, Bergen, Norway
20Dipartimento Interateneo di Fisica ‘M. Merlin’ and Sezione INFN, Bari, Italy
21Research Division and ExtreMe Matter Institute EMMI,
GSI Helmholtzzentrum f¨ ur Schwerionenforschung, Darmstadt, Germany
22National Institute for Physics and Nuclear Engineering, Bucharest, Romania
23Department of Physics, Ohio State University, Columbus, OH, United States
24Rudjer Boˇ skovi´ c Institute, Zagreb, Croatia
25Institut f¨ ur Kernphysik, Johann Wolfgang Goethe-Universit¨ at Frankfurt, Frankfurt, Germany
26Sezione INFN, Bologna, Italy
27SUBATECH, Ecole des Mines de Nantes, Universit´ e de Nantes, CNRS-IN2P3, Nantes, France
28Departamento de F´ ısica de Part´ ıculas and IGFAE, Universidad de Santiago de Compostela, Santiago de Compostela, Spain
29Yale University, New Haven, CT, United States

Page 4

4
30V. Fock Institute for Physics, St. Petersburg State University, St. Petersburg, Russia
31Oak Ridge National Laboratory, Oak Ridge, TN, United States
32Helsinki Institute of Physics (HIP) and University of Jyv¨ askyl¨ a, Jyv¨ askyl¨ a, Finland
33Frankfurt Institute for Advanced Studies, Johann Wolfgang Goethe-Universit¨ at Frankfurt, Frankfurt, Germany
34Sezione INFN, Catania, Italy
35Dipartimento di Fisica Sperimentale dell’Universit` a and Sezione INFN, Turin, Italy
36Commissariat ` a l’Energie Atomique, IRFU, Saclay, France
37Laboratoire de Physique Corpusculaire (LPC), Clermont Universit´ e,
Universit´ e Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France
38Institute of Experimental Physics, Slovak Academy of Sciences, Koˇ sice, Slovakia
39Dipartimento di Fisica e Astronomia dell’Universit` a and Sezione INFN, Catania, Italy
40School of Physics and Astronomy, University of Birmingham, Birmingham, United Kingdom
41The Henryk Niewodniczanski Institute of Nuclear Physics, Polish Academy of Sciences, Cracow, Poland
42Russian Federal Nuclear Center (VNIIEF), Sarov, Russia
43Institut f¨ ur Kernphysik, Westf¨ alische Wilhelms-Universit¨ at M¨ unster, M¨ unster, Germany
44Joint Institute for Nuclear Research (JINR), Dubna, Russia
45Niels Bohr Institute, University of Copenhagen, Copenhagen, Denmark
46Sezione INFN, Cagliari, Italy
47Institut Pluridisciplinaire Hubert Curien (IPHC), Universit´ e de Strasbourg, CNRS-IN2P3, Strasbourg, France
48Wayne State University, Detroit, MI, United States
49Physics Department, University of Athens, Athens, Greece
50Petersburg Nuclear Physics Institute, Gatchina, Russia
51Physics Department, University of Jammu, Jammu, India
52Laboratori Nazionali di Frascati, INFN, Frascati, Italy
53Dipartimento di Fisica dell’Universit` a and Sezione INFN, Padova, Italy
54Faculty of Nuclear Sciences and Physical Engineering,
Czech Technical University in Prague, Prague, Czech Republic
55Nikhef, National Institute for Subatomic Physics, Amsterdam, Netherlands
56Institut de Physique Nucl´ eaire d’Orsay (IPNO), Universit´ e Paris-Sud, CNRS-IN2P3, Orsay, France
57Centro de Investigaciones Energ´ eticas Medioambientales y Tecnol´ ogicas (CIEMAT), Madrid, Spain
58Moscow Engineering Physics Institute, Moscow, Russia
59Institute for High Energy Physics, Protvino, Russia
60Yonsei University, Seoul, South Korea
61Faculty of Science, P.J.ˇSaf´ arik University, Koˇ sice, Slovakia
62Bogolyubov Institute for Theoretical Physics, Kiev, Ukraine
63Saha Institute of Nuclear Physics, Kolkata, India
64Dipartimento di Fisica dell’Universit` a and Sezione INFN, Trieste, Italy
65Institut f¨ ur Kernphysik, Technische Universit¨ at Darmstadt, Darmstadt, Germany
66Physikalisches Institut, Ruprecht-Karls-Universit¨ at Heidelberg, Heidelberg, Germany
67Physics Department, University of Cape Town, iThemba Laboratories, Cape Town, South Africa
68Hua-Zhong Normal University, Wuhan, China
69Secci´ on F´ ısica, Departamento de Ciencias, Pontificia Universidad Cat´ olica del Per´ u, Lima, Peru
70Centro de Investigaci´ on y de Estudios Avanzados (CINVESTAV), Mexico City and M´ erida, Mexico
71Universit´ e de Lyon, Universit´ e Lyon 1, CNRS/IN2P3, IPN-Lyon, Villeurbanne, France
72Universidade Estadual de Campinas (UNICAMP), Campinas, Brazil
73Pusan National University, Pusan, South Korea
74Nikhef and Institute for Subatomic Physics of Utrecht University, Utrecht, Netherlands
75Division of Experimental High Energy Physics, University of Lund, Lund, Sweden
76University of Tsukuba, Tsukuba, Japan
77Hiroshima University, Hiroshima, Japan
78Zentrum f¨ ur Technologietransfer und Telekommunikation (ZTT), Fachhochschule Worms, Worms, Germany
79Dipartimento di Scienze e Tecnologie Avanzate dell’Universit` a del Piemonte Orientale and Gruppo Collegato INFN, Alessandria, Italy
80Benem´ erita Universidad Aut´ onoma de Puebla, Puebla, Mexico
81Instituto de Ciencias Nucleares, Universidad Nacional Aut´ onoma de M´ exico, Mexico City, Mexico
82Sezione INFN, Padova, Italy
83Institute of Space Sciences (ISS), Bucharest, Romania
84Institute of Physics, Bhubaneswar, India
85Universidade de S˜ ao Paulo (USP), S˜ ao Paulo, Brazil
86Dipartimento di Fisica ‘E.R. Caianiello’ dell’Universit` a and Sezione INFN, Salerno, Italy
87Sezione INFN, Bari, Italy
88Dipartimento di Fisica dell’Universit` a and Sezione INFN, Cagliari, Italy
89Soltan Institute for Nuclear Studies, Warsaw, Poland
90Sezione INFN, Rome, Italy
91University of Houston, Houston, TX, United States

Page 5

5
92Laboratoire de Physique Subatomique et de Cosmologie (LPSC), Universit´ e Joseph Fourier,
CNRS-IN2P3, Institut Polytechnique de Grenoble, Grenoble, France
93Faculty of Mathematics, Physics and Informatics, Comenius University, Bratislava, Slovakia
94Sezione INFN, Trieste, Italy
95Budker Institute for Nuclear Physics, Novosibirsk, Russia
96Lawrence Livermore National Laboratory, Livermore, CA, United States
97Universidad Aut´ onoma de Sinaloa, Culiac´ an, Mexico
98Technical University of Split FESB, Split, Croatia
99Institute for Nuclear Research, Academy of Sciences, Moscow, Russia
100University of Tennessee, Knoxville, TN, United States
101Department of Physics, Sejong University, Seoul, South Korea
102Faculty of Engineering, Bergen University College, Bergen, Norway
103China Institute of Atomic Energy, Beijing, China
104Lawrence Berkeley National Laboratory, Berkeley, CA, United States
105Indian Institute of Technology, Mumbai, India
106Warsaw University of Technology, Warsaw, Poland
107California Polytechnic State University, San Luis Obispo, CA, United States
108Fachhochschule K¨ oln, K¨ oln, Germany
109Institute of Physics, Academy of Sciences of the Czech Republic, Prague, Czech Republic
110Dipartimento di Fisica dell’Universit` a ‘La Sapienza’ and Sezione INFN, Rome, Italy
111Physics Department, University of Rajasthan, Jaipur, India
112Laboratori Nazionali di Legnaro, INFN, Legnaro, Italy
113Purdue University, West Lafayette, IN, United States
(Dated: July 6, 2010)
We report on the measurement of two-pion correlation functions from pp collisions at√s = 900 GeV per-
formed by the ALICE experiment at the Large Hadron Collider. Our analysis shows an increase of the HBT
radius with increasing event multiplicity, in line with other measurements done in particle- and nuclear colli-
sions. Conversely, the strong decrease of the radius with increasing transverse momentum, as observed at RHIC
and at Tevatron, is not manifest in our data.
PACS numbers: 25.75.-q, 25.75.Gz, 25.70.Pq
aAlso at Laboratoire de Physique Corpusculaire (LPC), Clermont Univer-
sit´ e, Universit´ e Blaise Pascal, CNRS–IN2P3, Clermont-Ferrand, France
bAlso atFrankfurt Institute forAdvanced Studies, Johann WolfgangGoethe-
Universit¨ at Frankfurt, Frankfurt, Germany
cNow at Sezione INFN, Padova, Italy
dNow at Research Division and ExtreMe Matter Institute EMMI, GSI
Helmholtzzentrum f¨ ur Schwerionenforschung, Darmstadt, Germany
eNow at Institut f¨ ur Kernphysik, Johann Wolfgang Goethe-Universit¨ at
Frankfurt, Frankfurt, Germany
fNow at Physics Department, University of Cape Town, iThemba Labora-
tories, Cape Town, South Africa
gNow at National Institute for Physics and Nuclear Engineering, Bucharest,
Romania
hAlso at University of Houston, Houston, TX, United States
iNow at European Organization for Nuclear Research (CERN), Geneva,
Switzerland
jAlso at Dipartimento di Fisica dell´Universit` a, Udine, Italy
kNow at Helsinki Institute of Physics (HIP) and University of Jyv¨ askyl¨ a,
Jyv¨ askyl¨ a, Finland
lNow at Institut Pluridisciplinaire Hubert Curien (IPHC), Universit´ e de
Strasbourg, CNRS-IN2P3, Strasbourg, France
mNow at Institut f¨ ur Kernphysik, Westf¨ alische Wilhelms-Universit¨ at
M¨ unster, M¨ unster, Germany
nNow at : University of Technology and Austrian Academy of Sciences,
Vienna, Austria
oAlso at Lawrence Livermore National Laboratory, Livermore, CA, United
States
pAlso at European Organization for Nuclear Research (CERN), Geneva,
Switzerland
qDeceased
rNow at Yale University, New Haven, CT, United States
sNow at University of Tsukuba, Tsukuba, Japan
tAlso at Centro Fermi – Centro Studi e Ricerche e Museo Storico della
Fisica “Enrico Fermi”, Rome, Italy
uAlso at Moscow State University, Moscow, Russia
vAlso at Laboratoire de Physique Subatomique et de Cosmologie (LPSC),
Universit´ e Joseph Fourier, CNRS-IN2P3, Institut Polytechnique de Greno-
ble, Grenoble, France
wNow at SUBATECH, Ecole des Mines de Nantes, Universit´ e de Nantes,
CNRS-IN2P3, Nantes, France
xNow at Dipartimento di Fisica Sperimentale dell’Universit` a and Sezione
INFN, Turin, Italy
yNow at Commissariat ` a l’Energie Atomique, IRFU, Saclay, France
zAlso at Department of Physics, University of Oslo, Oslo, Norway
aaAlso at Wrocław University, Wrocław, Poland
bbNow at Physikalisches Institut, Ruprecht-Karls-Universit¨ at Heidelberg,
Heidelberg, Germany
ccNow at Department of Physics and Technology, University of Bergen,
Bergen, Norway
ddNow at Dipartimento di Fisica dell’Universit` a and Sezione INFN, Padova,
Italy
eeNow at Physics Department, University of Athens, Athens, Greece
ffAlso at Institut f¨ ur Kernphysik, Westf¨ alische Wilhelms-Universit¨ at
M¨ unster, M¨ unster, Germany
ggNow at Universit´ e de Lyon, Universit´ e Lyon 1, CNRS/IN2P3, IPN-Lyon,
Villeurbanne, France
hhNow at Faculty of Science, P.J.ˇSaf´ arik University, Koˇ sice, Slovakia
iiNow at : Centre de Calcul IN2P3, Lyon, France
jjAlso at Dipartimento di Fisica dell’Universit` a and Sezione INFN, Padova,
Italy
kkAlso at Sezione INFN, Bologna, Italy

Page 6

6
I.INTRODUCTION
Proton-proton collisions at
recorded by ALICE (A Large Ion Collider Experiment) at the
Large Hadron Collider (LHC) at CERN [1]. Hadron colli-
sions at these energies provide an opportunity to probe Quan-
tum Chromodynamics (QCD) under extreme conditions. The
distinguishing feature of QCD is the mechanism of color con-
finement, the physics of which is not fully understood, due
in part to its theoretical intractability [2]. The confinement
mechanism has a physical scale on the order of the proton ra-
dius and is especially important at low momentum.
Bose-Einstein enhancement of identical-pion pairs at low
relative momentum was first observed in p ¯ p collisions by
Goldhaber, Goldhaber, Lee and Pais 50 years ago [3]. Since
then, two-pion correlations have been successfully applied to
assess the spatial scale of the emitting source in e+e−[4],
hadron-hadron and lepton-hadron [5], and heavy ion [6] col-
lisions. Especially in the latter case, this technique, known as
HanburyBrown-Twiss (HBT)interferometry[7,8]andbeing
a special case of femtoscopy [9, 10], has been developed into
a precision tool to probe the dynamically-generatedgeometry
of the emitting system. In particular, a first order phase tran-
sition between the color-deconfined and -confined states was
precluded by the observation of short timescales [6]. At the
same time, femtoscopic measurement of bulk collective flow,
manifesting itself via dynamical dependences of femtoscopic
scales (“homogeneity lengths” [11, 12]), provided hints that a
strongly self-interacting system was created in the collision.
This was further corroborated by the positive correlation be-
tween the HBT radius and the multiplicity of the event [6].
In particle physics, overviews of femtoscopic measure-
ments in hadron- and lepton-induced collisions [4, 5, 13]
reveal systematics surprisingly similar to those mentioned
above for heavy-ion collisions. Moreover, in the first direct
comparison of femtoscopy in heavy-ion collisions at RHIC,
and proton collisions in the same apparatus, a virtually identi-
cal multiplicity- and momentum-dependence was reported in
the two systems [14].
A systematic program of femtoscopic measurements in
pp and heavy-ion collisions at the LHC will shed consider-
able light on the nature, the similarities, and the differences of
theirdynamics. Withthepresentwork,webeginthisprogram.
√s = 900 GeV have been
II. EXPERIMENT AND DATA ANALYSIS
The data discussed in this article were collected in Decem-
ber 2009, duringthe first stable-beam periodof the LHC com-
missioning. The two beams were at the LHC injection energy
of 450 GeV and each had 2-4 bunches, one of them collid-
ing at the ALICE intersection point. The bunch intensity was
typically 5×109protons, giving a luminosity of the order of
1026cm−2s−1and a rate forinelastic proton-protoncollisions
of a few Hz.
Approximately 3×105minimum bias pp collision events
were identified by signals measured in the forward scintilla-
tors (VZERO) and the two layers of the Silicon Pixel Detec-
tor (SPD) [15]. The VZERO counters are placed on either
side of the interaction region at z = 3.3 m and z = -0.9 m.
They cover the region 2.8 < η < 5.1 and −3.7 < η < −1.7
and record both amplitude and time of signals produced by
charged particles. The minimum-bias trigger required a hit in
one of the VZERO counters or in one of the two SPD layers
which coverthe central pseudorapidityregions |η| <2 (inner)
and |η| < 1.4 (outer). The events were collected in coinci-
dence with the signals from two beam pick-up counters, one
on each side of the interaction region, indicating the presence
ofpassingbunches. The triggerselectionefficiencyforinelas-
tic collisions was estimated to be 95-97% [16].
The VZERO counters were used also to discriminate
against beam-gas and beam-halo events by requiring a strict
matching between their timing signals (see Ref. [1] for de-
tails). This background was also rejected by exploiting the
correlation between the number of clusters of pixels and the
number of tracklets pointing to a reconstructed vertex. After
these selections the fraction of background events remaining
in the sample of events with at least one chargedparticle track
was estimated to be below 0.1%. The trigger and run condi-
tions are discussed in detail in Ref. [16].
The 250 k events used in the analysis were required to have
a primary vertex (collision position) within 10 cm of the cen-
ter of the 5 m long Time Projection Chamber (TPC) [17].
This provides almost uniform acceptance for particles within
the pseudorapidity range |η| < 0.8 for all events in the sam-
ple. Within this sample, we have selected events based on the
measured charged-particle multiplicity M. The three multi-
plicity classes were M ≤ 6, 7 ≤ M ≤ 11, and M ≥ 12; about
70% of all events were falling into the first multiplicity class.
The tracks used in determiningthe multiplicity were the same
as those used for correlation analysis (see below) except that
particle identification cuts were not applied. The measured
multiplicity was converted to the charged-particle pseudora-
pidity density dNch/dη by normalizing it to the pseudorapid-
ity acceptance and by correcting it for the reconstruction ef-
ficiency and contamination. The correction factor was deter-
mined from a Monte Carlo simulation with the PHOJET event
generator [18, 19] and with the full description of the AL-
ICE apparatusand is 0.71, 0.78, and 0.81,respectively,for the
three multiplicity bins. The estimated systematic error is be-
low 4%. The average charged-particle pseudorapidity density
of the analyzed eventsample is ?dNch/dη?=3.6. An alternative
method based on SPD tracklets [16] gave the same result.
The ALICE Time ProjectionChamber(TPC) [17] was used
to record chargedparticle tracks as they leave ionization trails
in the Ne-CO2-N2gas. The ionization electrons drift up to
2.5 m to be measured on 159 pad rows; the position resolu-
tion is better than 2 mm. Combined with a solenoidal mag-
netic field of B=0.5 T this leads to a momentum resolution
∼ 1% for pions with pT< 1 GeV/c. The ALICE Inner Track-
ing System (ITS) has also been used for tracking. It consists
of six silicon layers, two innermost pixel detectors, two lay-
ers of drift detectors, and two outer layers of strip detectors,
whichprovideupto sixspace pointsforeachtrack. Thetracks
used in this analysis were reconstructed using the information

Page 7

7
fromboththeTPC (signalsfromat least90padrowsrequired)
and the ITS. Separate studies have been done with TPC-only
and ITS-only tracks, and were found to give results consistent
with the combined ITS+TPC analysis. The tracks were re-
quired to project back to the primary interaction vertex within
0.2 cm (2.4 cm) in the transverse plane and 0.25 cm (3.2 cm)
in longitudinal direction, if ITS+TPC (TPC only) information
is used, thereby rejecting most secondary pions from weak
decays. The pion tracks used in the correlation analysis had
transverse momenta between 0.15 GeV/c and 1.0 GeV/c.
ALICE provides excellent particle identification capability.
In this analysis the particle identificationwas achievedby cor-
relating the magnetic rigidity of a track with its specific ion-
ization (dE/dx) in the TPC gas. The dE/dx of the TPC was
calibrated using cosmic rays and its resolution was shown to
be better than 5.5%, the design value. The contamination of
the pion sample is negligible within the momentum range of
0.25 GeV/c < p < 0.65 GeV/c. Below and above this range
it is on the order of 5% and is caused by electrons and kaons,
respectively.
III. TWO-PION CORRELATION FUNCTIONS
The two-particle correlation function is defined as the ratio
C(q) = A(q)/B(q), where A(q) is the measured distribution
of pair momentumdifferenceq =p2−p1, and B(q) is a simi-
lar distribution formed by using pairs of particles from differ-
ent events (event mixing) [20]. The limited statistics available
(520 k identical-pion pairs with qinv< 0.5 GeV/c) allowed us
to perform a detailed analysis only for the one-dimensional
two-pion correlation function C(qinv). The qinvis, for iden-
tical mass particles, equal to the modulus of the momentum
difference |q| in the pair rest frame.
The correlation functions were studied in bins of event
multiplicity and of transverse momentum,
half of the vector sum of the two transverse momenta,
kT= |pT,1+pT,2|/2. During event mixing, all pion tracks from
one event were paired with all pion tracks from another event.
Every event was mixed with five other events with similar
multiplicities; ten multiplicity bins were introduced for this
purpose. The multiplicity binning improved the flatness of
the correlation function at qinv> 1.5 GeV/c. Binning events
according to their vertex position, on the other hand, had no
effect on the correlation function and therefore was not used.
Alternatively to event mixing, the denominator can be ob-
tained by rotating one of the two tracks by 180oin azimuth.
The correlation functions obtained using this technique are
generally flatter at high qinvthan those from event mixing.
The difference between the results obtained utilizing the two
techniques was used in estimating the systematic errors.
For the correlation structures measured here, with charac-
teristic widths ∼ 0.2 GeV/c, track splitting and track merging
in the event reconstructionare small effects overall. Their im-
pact on the results was carefully studied with the Monte Carlo
simulation and turned out to be negligible.
Another apparatus effect considered is the momentum res-
olution. Momentum smearing for single particles has similar
defined as
effect on the correlationstructures in two-particle correlations
i.e. it smears the correlation peak, making it appear lower and
wider. We havestudiedthis effectwith theMonte-Carlosimu-
lationof the ALICE detectorand havefoundthat forthe width
of the correlation peak expected here the effect is on the order
of 1%.
Fig. 1 presents two-pion correlation functions measured by
ALICE in pp collisions at√s = 900 GeV, as a function of
event multiplicity and transverse momentum kT. The denom-
inator of the correlation function was obtained via event mix-
ing and normalized such that the numbers of true and mixed
pairs with 0.4 GeV/c < qinv< 0.6 GeV/c were equal. The
qinvrange used for normalization was chosen to be outside of
the Bose-Einstein peak but as close as possible to it. The nor-
malized distributions of positive and negative pion pairs were
added together before building the ratio of true and mixed
pairs. The Bose-Einstein enhancementis manifest at low qinv.
A slight decrease of the correlationpeak width is seen as mul-
tiplicity grows. The kTdependence is less obvious because
0.8
1.6
1.4
1
1.2
1.0
1.4
1.2
1.6
1.4
1.8
1.6
experiment
simulation
<dN
<k
λ
R
0.8
1.6
1
1.2
1.4
1.6
1.8
<dN
<k
λ
R
0.8
1.6
1
1.2
1.4
1.6
1.8
<dN
<k
λ
R
<0.25
0.8
1.6
1.4
1
1.2
1.0
1.4
1.2
1.8
0.8
1.6
<dN
<k
λ
R
0.8
1.6
1
1.2
1.4
1.8
<dN
<k
λ
R
0.8
1.6
1
1.2
1.4
1.8
<dN
<k
λ
R
<0.40
0.8
1.6
1.4
1
1.2
1.0
1.4
1.2
1.8
0.8
1.6
<dN
<k
λ
R
0.8
1.6
1
1.2
1.4
1.8
<dN
<k
λ
R
0.8
1.6
1
1.2
1.4
1.8
<dN
<k
λ
R
<0.55
0.8
1.6
1.4
1
1.2
1.0
1.4
1.2
1.8
0.8
1.6
<dN
<k
λ
R
0.8
1.6
1
1.2
1.4
1.8
<dN
<k
λ
R
0.8
1.6
1
1.2
1.4
1.8
<dN
<k
λ
R
<0.7
0 0.2 0.4 0.6 0.8 1
00.20.4
q
0.8
0.8
1
1.2
1.0
1.4
1.2
1.8
0.8
1.6
<dN
<k
λ
R
0 0.2 0.4 0.6 0.8 1
00.20.4
(GeV/c)
inv
0.8
1
1.2
1.4
1.8
<dN
<k
λ
R
0 0.2 0.4 0.6 0.8 1
00.20.4
(GeV/c)
0.8
1
1.2
1.4
1.8
<dN
<k
λ
R
T
0.60.6 0.6
(GeV/c)
inv
0.80.80.8 1
1.8
inv
qq
)
inv
C(q
)
inv
C(q
)
inv
C(q
)
inv
C(q
)
inv
C(q
6
≤
M
11
≤
M
≤
7 12
≥
M
T
0.10<k
T
0.25<k
T
0.40<k
T
0.55<k
<1.0
0.70<k
FIG. 1.
sions at√s = 900 GeV (full dots) and those obtained from a simu-
lation using PHOJET (open circles). Positive and negative pion pairs
were combined. The three columns represent collisions with differ-
ent charged-particle multiplicities M; the transverse momentum of
pion pairs kT(GeV/c) increases from top to bottom. The lines going
through the points represent the Gaussian fits discussed in the text.
Correlation functions for identical pions from pp colli-

Page 8

8
the correlation baseline – the underlying two particle correla-
tion without any Bose-Einstein enhancement – is systemati-
cally changing its shape between the low and high transverse
momenta.
The correlationfunctionswere fitted by a functionaccount-
ing for the Bose-Einstein enhancement and for the mutual
Coulomb interaction between the two particles:
C(qinv) =?(1−λ)+λK(qinv)?1+exp(−R2
with λ describing the correlation strength and Rinvbeing the
Gaussian HBT radius [21]. The factor K is the Coulombfunc-
tion integratedovera spherical sourceof the size 1 fm. It is at-
tenuated by the same factor λ as the Bose-Einstein peak. The
factor D(qinv) accounts for long-range correlations, like those
arising from jets and/or from energy and momentum conser-
vation, and plays an important role in the analysis as will be
discussed later.
Neglecting the Coulomb interaction K(qinv) ≡ 1 the fit
function reduces to
invq2
inv)??D(qinv),
(1)
C(qinv) =?1+λ exp(−R2
The difference between the Rinv values obtained with and
without the Coulomb correction is less than 0.05 fm.
While the Gaussian fit captures the bulk scales of the cor-
relation, at low qinvthe data points lie above the fit line. This
featurewas observedpreviouslyin pioncorrelationsfrompar-
ticle collisions. An exponential fit
invq2
inv)?D(qinv) .
(2)
C(qinv) = [1+λ exp(−Rinvqinv)] D(qinv)
matches the data better. However, contrary to the Gaussian
Rinv, the Rinvparameter from Eq. (3) does not have a straight-
forward interpretation as the “radius of the source”. We have
used both functional forms and leave a detailed investigation
of the correlation peak shape to future studies. In order to
make the connection to established systematics at lower en-
ergy particle and heavy-ion collisions, a careful treatment of
the long-range correlations, visible as a slope in the baseline
of the correlation developing with increasing transverse mo-
mentum and represented by the factor D(qinv) in Eqs. (1-3), is
crucial.
In order to better understand the shape of the correlation
baseline we have calculated correlation functions for pp col-
lisions events generatedby the model PHOJET and propagated
through the ALICE detectors, performing an identical analy-
sis for the simulated events as for the measured ones. The re-
sults are shown as open circles in Fig. 1. The model does not
contain the Bose-Einstein effect, hence the lack of the peak at
lowqinvis expected. AtlowkTandlowmultiplicity,themodel
predicts a flat correlation function. However, as kTincreases,
long-range correlations start becoming visible as a distortion
of the correlation function baseline similar to that seen in the
experimental data.
Theaccuracyofoursimulationin describingthe correlation
baseline was verified with unlike-sign pion pairs. The multi-
plicity and kTdependence of the π+π−functions is shown in
Fig. 2. Correlationstructures for non-identicalpions includea
(3)
0.8
1.6
1.4
1
1.2
1.0
1.4
1.2
1.6
1.4
1.8
1.6
experiment
simulation
0.8
1.6
1
1.2
1.4
1.6
1.8
0.8
1.6
1
1.2
1.4
1.6
1.8
0.8
1.6
1.4
1
1.2
1.0
1.4
1.2
1.8
0.8
1.6
0.8
1.6
1
1.2
1.4
1.8
0.8
1.6
1
1.2
1.4
1.8
0.8
1.6
1.4
1
1.2
1.0
1.4
1.2
1.8
0.8
1.6
0.8
1.6
1
1.2
1.4
1.8
0.8
1.6
1
1.2
1.4
1.8
0.8
1.6
1.4
1
1.2
1.0
1.4
1.2
1.8
0.8
1.6
0.8
1.6
1
1.2
1.4
1.8
0.8
1.6
1
1.2
1.4
1.8
0 0.2 0.4 0.6 0.8 1
00.20.4
q
0.8
0.8
1
1.2
1.0
1.4
1.2
1.8
0.8
1.6
0 0.2 0.4 0.6 0.8 1
00.20.4
(GeV/c)
inv
0.8
1
1.2
1.4
1.8
0 0.2 0.4 0.6 0.8 1
00.2 0.4
(GeV/c)
0.8
1
1.2
1.4
1.8
0.60.60.6
(GeV/c)
inv
0.80.80.8 1
1.8
inv
qq
)
inv
C(q
)
inv
C(q
)
inv
C(q
)
inv
C(q
)
inv
C(q
6
≤
M
11
≤
M
≤
7 12
≥
M
<0.25
T
0.10<k
<0.40
T
0.25<k
<0.55
T
0.40<k
<0.7
T
0.55<k
<1.0
T
0.70<k
FIG. 2. One-dimensional correlation functions for π+π−pairs from
pp collisions at√s = 900 GeV. The columns and rows are defined
as in Fig. 1.
mutual Coulomb interaction peak, here limited to the first bin
at lowest qinv, and peaks coming from meson decays which
shouldbecorrectlymodeledin theeventgenerator. Therefore,
one can directly compare simulations with data. In Fig. 2, the
simulatedcorrelationfunctionsagreereasonablywell with the
experimental data. This suggests that the same model (PHO-
JET) can be used as a reasonable estimate also for identical
particles to describe the correlation baseline under the Bose-
Einstein peak. The presence of resonance peaks (like the K0
one at qinv= 412 MeV/c) and the fact that the simulated corre-
lationsforidenticalandnon-identicalpionpairshavedifferent
slopes, on the other hand, indicate that unlike-sign pion pairs
cannot be directly used for the denominator of the identical
pion correlations.
The procedure employed to extract the HBT radii with
Eq. (1) using the PHOJET baseline is as follows. First, the
simulation points shown in Fig. 1 are fitted with the 2nd-order
polynomial
S
D(qinv) = a+bqinv+cq2
inv.
(4)
Subsequently, the experimental correlation function is fitted
by Eq. (1), taking the D(qinv) from the PHOJET fit and adjust-
ing λ and Rinv. The two fits are represented in Fig. 1 by the

Page 9

9
linesgoingthroughthesimulationandexperimentdatapoints,
respectively.
In order to estimate the systematic error from the baseline
determination we repeated the fitting procedure using a sim-
ulation performed with the PYTHIA [22] generator (version
6.4.21, Perugia-0 (320) tune [23]) instead of PHOJET. The
HBT radiiobtainedinthetwowaysdifferbyupto10%. Inthe
following we use the average between them and we estimate
the systematic error related to the baseline shape assumption
to be half of the difference.
It is interesting to see what happens with the radii if the
slope of the baseline is neglected. Assuming a flat baseline
D(qinv) ≡ a and treating a as the third fit parameter in Eq. (1)
leads to Rinvvalues that are similar to those obtained with the
PHOJET or PYTHIA baseline at low kTvalues but smaller by
up to 30% at high transverse momenta. This is because the
broad enhancement caused by long-range correlations will be
attributed to Bose-Einstein correlations, giving rise to smaller
radii (wider correlation function). The resulting apparent kT
dependence will be discussed in Section V.
The Rinvobtained from the fit (the two highest multiplic-
ity bins combined) is shown in Fig. 3. In order to reduce
the statistical errors and to compare to other experiments, in
the following sections of this article we analyze separately the
multiplicity and the transverse momentum dependences.
> (GeV/c)
T
<k
00.1 0.20.3 0.40.50.60.7 0.8
(fm)
inv
R
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
6
7
≤
≥
multiplicity M
multiplicity M
FIG. 3. Extracted HBT radius as a function of kTfor low (black cir-
cles) and high (red squares) multiplicity events. The error bars are
statistical. The shaded bands represent the systematic errors related
to the baseline shape assumption and to the fit range, added quadrat-
ically.
IV.MULTIPLICITY DEPENDENCE OF THE HBT RADIUS
The multiplicity dependence of the obtained HBT radius
is shown in Fig. 4 and Table I. The analysis here was re-
>
η
/d
ch
<dN
05101520
(fm)
inv
R
0
0.5
1
1.5
2
2.5
3
=900 GeVs ALICE pp at
=44 GeV
=62 GeV
=1.8 TeV
=200 GeVs
s
s
ABCDHW pp at
ABCDHW pp at
pE735 p
STAR pp at
s at
FIG. 4.
at√s = 900 GeV determined using pion pairs with kT = 0.1-
0.55 GeV/c, ?kT?= 0.32 GeV/c, and shown as a function of the
charged-particle multiplicity at midrapidity (full dots). The shaded
band represents the systematic errors (see text). For comparison,
open symbols, red stars, and green filled boxes represent the data
taken at the ISR [24], RHIC [14], and Tevatron [25], respectively.
One-dimensional Gaussian HBT radius in pp collisions
TABLE I. One-dimensional HBT radius in pp collisions at√s =
900 GeV determined using pion pairs with kT= 0.1-0.55 GeV/c,
?kT?= 0.32 GeV/c, as a function of the charged-particle pseudorapid-
ity density at midrapidity. The radii were obtained using the Gaus-
sian fit function defined by Eq. (1).
?dNch/dη?
3.2
7.7
11.2
λ
Rinv(fm)
0.386 ± 0.022
0.331 ± 0.023
0.310 ± 0.026
0.874 ± 0.047 (stat.)+0.047
1.082 ± 0.068 (stat.)+0.069
1.184 ± 0.092 (stat.)+0.067
−0.181(syst.)
−0.206(syst.)
−0.168(syst.)
stricted to the first three transverse momentum bins kT= 0.1-
0.55 GeV/c. The mean transverse momentum for pairs with
qinv< 0.2 GeV/c is ?kT?= 0.32 GeV/c. The HBT radii were
obtained by using PHOJET and PYTHIA to estimate the shape
of the baseline, as explained in the previous section. The sys-
tematic errors related to the baseline assumption reflect the
differencebetweenthetwo. Thesystematicerrorrelatedtothe

Page 10

10
choice of the normalization and/or fit range was estimated to
be 5%. An additional downward systematic error of 13-20%
accounts for the difference between the event mixing and the
rotation denominator techniques. The shaded area represents
the three systematic errors added in quadrature.
The charged-particle pseudorapidity density ?dNch/dη? of
the lowest multiplicity bin was calculated excluding events
with multiplicities M < 2 because these events do not con-
tribute to the numerator of the correlation function. Including
all events and including only events with at least one like-sign
pair would shift the point by 0.8 to the left and to the right,
respectively.
An increase of the HBT radius with multiplicity is ob-
served, consistent with the hadron-hadron collision system-
atics above√s ∼ 50 GeV [13]. While the average transverse
momentum is similar in all four data sets, other aspects of the
analysis, e.g. the average orientation of the momentum differ-
ence vector, can differ so the trends, not the absolute values,
should be compared. In heavy-ion collisions, this multiplicity
dependencehas been associated with the particle composition
and overallvolume of the final state system [6, 26, 27] or with
final-state hadronic rescattering [28]. The relation observed
in heavy-ion collision data [6], R ∼ a+b(dNch/dη)1/3, where
a and b are constants, appears to be consistent with our data
within our systematic errors. For high energy pp collisions,
it has been suggested that a similar behavior could originate
from final-state hadronic rescattering for short hadronization
times [29]. In an alternative scenario, the increase of the HBT
radiuswith multiplicityresults fromthefact thatthe highmul-
tiplicity pp events mostly come from hard parton scattering,
and the hadronization length, i.e. the distance travelled by
a parton before hadronization, is roughly proportional to the
parton energy [30].
The fitted correlation strength λ is lower than unity, the
value expected for the ideal Bose-Einstein case. One rea-
son for this is the non-Gaussian shape of the peak, caused at
least partially by pions from decays of short- (∆, ρ) and long-
lived resonances (ω, η, η′). On the detector side, λ can be
reduced by the particle misidentification; this effect is how-
ever small in our data sample. In ALICE, λ decreases from
0.37±0.03 to 0.32±0.03 between the lowest and the highest
multiplicity, in close agreement with the E735 measurements
at Tevatron [25]. A similar trend was observed by UA1 in
p ¯ p collisions at√s = 630 GeV/c [31]; the fact that their λ
values were lower may have to do with the lack of the par-
ticle identification and the resulting dilution of the correla-
tion peak. In a final-state hadronic rescattering model [29], a
correlation strength droppingwith multiplicity in high-energy
pp collisionswas attributedto the increasedcontributionfrom
long-lived resonances in higher multiplicity events.
An increase of the HBT radius with increasing particle
multiplicity was recently reported by the CMS Collabora-
tion for the same collision system and energy [32].
authors fit the correlation peak by an exponential (Eq. (3)).
An analogous approach in our case (Table II) yields radii
that are rather similar to the Gaussian ones (Table I) once
scaled down by√π [32]. In order to compare between the
two experiments we perform a fit to an inclusive correla-
The
tion (all multiplicities and kT’s). The exponential fit to the
correlation functions obtained using event mixing and using
rotation yields Rinv=1.61±0.07 (stat.)±0.05 (syst.) fm and
Rinv=1.31±0.05 (stat.)±0.22 (syst.) fm, respectively. This is
in close agreement with the corresponding values quoted by
CMS, 1.72±0.06fm and 1.29±0.04 fm.
TABLE II. One-dimensional HBT radius in pp collisions at√s =
900 GeV determined using pion pairs with kT= 0.1-0.55 GeV/c,
?kT?= 0.32 GeV/c, as a function of the charged-particle pseudorapid-
ity density at midrapidity. The radii were obtained using the expo-
nential fit function defined by Eq. (3).
?dNch/dη?
3.2
7.7
11.2
λ
Rinv/√π (fm)
0.704 ± 0.048
0.577 ± 0.054
0.548 ± 0.051
0.809 ± 0.061 (stat.)+0.049
0.967 ± 0.095 (stat.)+0.071
1.069 ± 0.104 (stat.)+0.063
−0.208(syst.)
−0.206(syst.)
−0.203(syst.)
V. TRANSVERSE MOMENTUM DEPENDENCE OF THE
HBT RADIUS
One of the key features of the bulk system created in nu-
clear collisions is its large collective flow. The fingerprint
of this flow is a specific space-momentum correlation signa-
ture, revealed in the transverse momentum dependence of the
Gaussian HBT radius [6]. While quantitative comparison be-
tween particle and heavy ion studies is complicated by exper-
iments using different acceptances and techniques, a recent
comparison of the HBT radii from pp and Au+Au collisions
at RHIC indicates an almost identical pTdependencebetween
these collision systems [14]. Again, this raises the interesting
question whether hadron collisions at the highest energies al-
ready develop a bulk, collective behavior.
The kTdependence of our measured HBT radius is shown
in Fig. 5. The choice of the fitting method, which only weakly
affects the multiplicity dependence of the HBT radius dis-
cussed in the previous section, is of crucial importance for the
transverse momentum dependence. Taking the baseline shape
from the Monte Carlo leads to an HBT radius that is nearly
independent of kT(filled black circles and red boxes for PHO-
JET and PYTHIA, respectively). Assuming a flat baseline, on
the other hand, results in a radius falling with kT(green stars).
As discussed in the previous section, the experimental unlike-
sign pion correlation functions are close to the predictions of
PHOJET and PYTHIA and we consider using the average be-
tween the two cases as baseline to be a reliable estimate for
the HBT radii.
The radii obtained in this fashion are summarized in Ta-
bles III and IV and shown in Fig. 6 where we compare them
to RHIC and Tevatron data [13]. Like for the multiplicity
dependence, the systematic error band represents a quadratic
sum of the error related to the baseline assumption (0-10%),
the fit range (10%), and the denominator construction method
(mixing/rotating,7-17%). The lowest-kTpoint is significantly
below the RHIC and Tevatron results. It should be noted that

Page 11

11
> (GeV/c)
T
<k
0 0.2 0.40.60.81
(fm)
inv
R
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
phojet baseline
pythia baseline
flat baseline
FIG. 5. One-dimensional Gaussian HBT radius in pp collisions at
√s = 900 GeV as a function of transverse momentum kT. Three fit-
ting methods, differing by the choice of the baseline parametrization,
are compared.
the ALICE analysis was performed on a minimum bias event
sample and the averagedcharged-particlepseudorapidityden-
sity is ?dNch/dη?=3.6 while the Tevatron events are biased to
high multiplicity, ?dNch/dη?=14.4, similar to our highest mul-
tiplicity bin. As visible in Fig. 3, the lowest-kTpoint at the
high multiplicity is at Rinv≈1.2 fm, approaching the Tevatron
points. The STAR results, on the other hand, were obtained
from events with ?dNch/dη?= 4.3 i.e. similar to the ALICE
case and thus a similar reasoning cannot explain the differ-
ence.
Two tests were performed to make sure that the low HBT
radius value at low transverse momenta is not caused by ap-
paratus effects. First, the analysis was repeated using only the
ITS and thus reducing the low-momentum cut-off by about
TABLE III. One-dimensional HBT radius in pp collisions at√s =
900 GeV as a function of the pair kT. The radii were obtained using
the Gaussian fit function defined by Eq. (1).
?kT? (GeV/c)
0.20
0.32
0.47
0.62
0.81
λ
Rinv(fm)
0.35 ± 0.03
0.33 ± 0.03
0.30 ± 0.04
0.35 ± 0.06
0.31 ± 0.06
1.00 ± 0.06 (stat.)+0.10
1.06 ± 0.06 (stat.)+0.11
0.99 ± 0.09 (stat.)+0.10
0.99 ± 0.11 (stat.)+0.10
0.91 ± 0.12 (stat.)+0.10
−0.20(syst.)
−0.19(syst.)
−0.14(syst.)
−0.13(syst.)
−0.12(syst.)
TABLE IV. One-dimensional HBT radius in pp collisions at√s =
900 GeV as a function of the pair kT. The radii were obtained using
the exponential fit function defined by Eq. (3).
?kT?(GeV/c)
0.20
0.32
0.47
0.62
0.81
λ
Rinv/√π (fm)
0.63 ± 0.05
0.58 ± 0.04
0.55 ± 0.07
0.70 ± 0.11
0.60 ± 0.12
0.94 ± 0.07 (stat.)+0.09
0.93 ± 0.07 (stat.)+0.09
0.92 ± 0.10 (stat.)+0.09
0.98 ± 0.14 (stat.)+0.10
0.90 ± 0.16 (stat.)+0.12
−0.20(syst.)
−0.20(syst.)
−0.14(syst.)
−0.14(syst.)
−0.15(syst.)
> (GeV/c)
T
<k
0 0.2 0.4 0.60.81
(fm)
inv
R
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
=900 GeVsALICE pp at
= 200 GeV
= 1.8 TeV
s
s
STAR pp at
E735 p at p
FIG. 6. One-dimensional Gaussian HBT radius in pp collisions at
√s = 900 GeV as a function of transverse momentum kT(full dots).
The mean charged-particle multiplicity density was ?dNch/dη?=3.6.
PHOJET simulation was used to determine the baseline of the cor-
relations. Using PYTHIA and a flat baseline leads to systematic de-
viations up and down, respectively; the related systematic errors as
indicated by the shaded area. Stars and filled boxes represent the
radii measured at RHIC [14] and Tevatron [25], respectively.
50 MeV. This analysis yielded the same HBT radius which
demonstrates that the energy loss is not an issue. Second,
as seen in Fig. 3 the low-kTpoint is mostly driven down by
the contribution of the low multiplicity events. Since the ver-
tex resolution in these events is worse this might in principle
deteriorate the momentum resolution and smear out the cor-
relation function peak. In order to test this the analysis was
performed without using the event vertex constraint for mo-
mentum determination. The results, again, were unchanged.
This, and the distinct K0
Speak in the unlike-sign pion corre-

Page 12

12
lation functions in the low-multiplicity low-kTbin of Fig. 2,
indicate that the momentum resolution is not spoiled in low
multiplicity events.
Even more important than the position of the first point,
albeit related to it, is the question of the slope of the points
in Fig. 6. Our measured HBT radius is practically indepen-
dent of kT within the studied transverse momentum range.
The slope crucially depends on the baseline shape assump-
tion, as was shown in Fig. 5. The results from the experiments
to which we are comparing in Fig. 6 were extracted using a
flat background (although the STAR experiment also studied
the effects of using other types of backgrounds for their data
to account for the non-femtoscopic effects [14]). Assuming
that PHOJET and PYTHIA are correct such a procedure may
lead to a misinterpretation of the low-q enhancement of the
correlation function, that is coming from long-range corre-
lations (most probably mini-jet like), as a Bose-Einstein en-
hancement. As the impact of this may depend on the details
of each experiment (certainly on the collision energy) we do
not attempt to resolve this question quantitatively. However,
we stress again the usefulness of non-identical pion correla-
tion in constraining the correlation baseline.
VI.SUMMARY
In summary, ALICE has measured two-pion correlation
functions in pp collisions at√s = 900 GeV at the LHC. Con-
sistent with previous measurements of high-energy hadron-
hadron and nuclear collisions, the extracted HBT radius Rinv
increases with event multiplicity. Less consistent is the rela-
tion between Rinvand the pion transverse momentum where
the ALICE measured HBT radius in minimum bias events is
practicallyconstantwithinourerrorsandwithinthetransverse
momentum range studied.
ACKNOWLEDGMENTS
The ALICE collaboration would like to thank all its en-
gineers and technicians for their invaluable contributions to
the construction of the experiment and the CERN accelerator
teams for the outstanding performance of the LHC complex.
The ALICE collaboration acknowledges the following
funding agencies for their support in building and running the
ALICE detector:
• Calouste Gulbenkian Foundation from Lisbon and
Swiss Fonds Kidagan, Armenia;
• Conselho Nacional de Desenvolvimento Cient´ ıfico e
Tecnol´ ogico (CNPq), Financiadora de Estudos e Pro-
jetos (FINEP), Fundac ¸˜ ao de Amparo ` a Pesquisa do Es-
tado de S˜ ao Paulo (FAPESP);
• National Natural Science Foundationof China (NSFC),
the Chinese Ministry of Education (CMOE) and the
Ministry of Science and Technology of China (MSTC);
• Ministry of Education and Youth of the Czech Repub-
lic;
• Danish Natural Science Research Council, the Carls-
berg Foundation and the Danish National Research
Foundation;
• The European Research Council under the European
Community’s Seventh Framework Programme;
• Helsinki Institute of Physics and the Academy of Fin-
land;
• French CNRS-IN2P3, the ‘Region Pays de Loire’, ‘Re-
gion Alsace’, ‘Region Auvergne’ and CEA, France;
• German BMBF and the Helmholtz Association;
• HungarianOTKA and National Office for Research and
Technology (NKTH);
• Department of Atomic Energy and Department of Sci-
ence and Technology of the Government of India;
• Istituto Nazionale di Fisica Nucleare (INFN) of Italy;
• MEXT Grant-in-Aid for Specially Promoted Research,
Japan;
• Joint Institute for Nuclear Research, Dubna;
• Korea Foundation for International Cooperation of Sci-
ence and Technology (KICOS);
• CONACYT, DGAPA, M´ exico, ALFA-EC and the HE-
LEN Program (High-Energy physics Latin-American–
European Network);
• Stichting voor Fundamenteel Onderzoek der Materie
(FOM) and the Nederlandse Organisatie voor Weten-
schappelijk Onderzoek (NWO), Netherlands;
• Research Council of Norway (NFR);
• Polish Ministry of Science and Higher Education;
• National Authority for Scientific Research - NASR
(Autoritatea Nat ¸ional˘ a pentru Cercetare S ¸tiint ¸ific˘ a -
ANCS);
• Federal Agency of Science of the Ministry of Educa-
tion and Science of Russian Federation, International
Science and Technology Center, Russian Acedemy of
Sciences, Russian Federal Agency of Atomic Energy,
Russian Federal Agency for Science and Innovations
and CERN-INTAS;
• Ministry of Education of Slovakia;
• CIEMAT, EELA, Ministerio de Educaci´ on y Ciencia of
Spain, Xunta de Galicia (Conseller´ ıa de Educaci´ on),
CEADEN, Cubaenerg´ ıa, Cuba, and IAEA (Interna-
tional Atomic Energy Agency);

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13
• Swedish Reseach Council (VR) and Knut & Alice Wal-
lenberg Foundation (KAW);
• Ukraine Ministry of Education and Science;
• United Kingdom Science and Technology Facilities
Council (STFC);
• The United States Department of Energy, the United
States National Science Foundation, the State of Texas,
and the State of Ohio.
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