First Measurement of BoseEinstein Correlations in ProtonProton Collisions at s=0.9 and 2.36 TeV at the LHC
EUROPEAN ORGANIZATION FOR NUCLEAR RESEARCH (CERN)
CERNPHEP20100102010/05/19
CMSQCD10003
First Measurement of Bose–Einstein Correlations inprotonproton Collisions at
√
s
=
0.9 and 2.36TeV at theLHC
The CMS Collaboration
∗
Abstract
Bose–Einstein correlations have been measured using samples of protonproton collisions at 0.9 and 2.36TeV centerofmass energies, recorded by the CMS experiment atthe CERN Large Hadron Collider. The signal is observed in the form of an enhancement of pairs of samesign charged particles with small relative fourmomentum. Thesize of the correlated particle emission region is seen to increase signiﬁcantly with theparticle multiplicity of the event.
∗
See Appendix A for the list of collaboration members
a r X i v : 1 0 0 5 . 3 2 9 4 v 1 [ h e p  e x ] 1 8 M a y 2 0 1 0
1
In particle collisions, the spacetime structure of the hadronization source can be studied usingmeasurements of Bose–Einstein correlations (BEC) between pairs of identical bosons. Since theﬁrst observation of BEC ﬁfty years ago in protonantiproton interactions [1], a number of measurements have been made by several experiments using different initial states; a detailed listof the experimental results can be found in [2, 3]. Boson interferometry at the Large HadronCollider provides a powerful tool to investigate the spacetime structure of the particle emission source on femtometric length scales at different centerofmass energies and with differentinitial states, using the same detector. This letter reports the ﬁrst measurement of BEC parameters in
pp
collisions at 0.9 and 2.36TeV with the CMS detector.Constructive interference affects the joint probability for the emission of a pair of identical bosons with fourmomenta
p
1
and
p
2
. Experimentally, the proximity in phase space betweenﬁnalstate particles is quantiﬁed by the Lorentzinvariant quantity
Q
=
−
(
p
1
−
p
2
)
2
=
M
2
−
4
m
2
π
, where
M
is the invariant mass of the two particles, assumed to be pions withmass
m
π
. The BEC effect is observed as an enhancement at low
Q
of the ratio of the
Q
distributions for pairs of identical particles in the same event, and for pairs of particles in a referencesample that by construction is expected to include no BEC effect:
R
(
Q
) = (
d
N
/d
Q
)
/
(
d
N
ref
/d
Q
)
, (1)which is then ﬁtted with the parameterization
R
(
Q
) =
C
[
1
+
λ
Ω
(
Qr
)]
·
(
1
+
δ
Q
)
. (2)Inastaticmodelofparticlesources,
Ω
(
Qr
)
istheFouriertransformofthespatialdistributionof the emission region of bosons with overlapping wave functions, characterized by an effectivesize
r
. It is often parameterized as an exponential function,
Ω
(
Qr
) =
e
−
Qr
, or with a Gaussianform,
Ω
(
Qr
) =
e
−
(
Qr
)
2
([4] and references therein). The parameter
λ
reﬂects the BEC strengthforincoherentbosonemissionfromindependentsources,
δ
accountsforlongrangemomentumcorrelations, and
C
is a normalization factor.The data used for the present analysis were collected by the CMS experiment in December2009 from protonproton collisions at centerofmass energies of 0.9 and 2.36TeV. A detaileddescription of the CMS detector can be found in [5]. The central feature of the CMS apparatus is a superconducting solenoid of 6 m internal diameter, providing a uniform magneticﬁeld of 3.8 T. The inner tracking system is the most relevant detector for the present analysis. It is composed of a pixel detector with three barrel layers at radii between 4.4 and 10.2cmand a silicon strip tracker with 10 barrel detection layers extending outwards to a radius of 1.1 m. Each system is completed by two endcaps, extending the acceptance up to a pseudorapidity

η

=
2.5. The transversemomentum (
p
T
) resolution, for 1GeV charged particles, is between 0.7% at
η
=
0 and 2% at

η

=
2.5. The events were selected by requiring activity in both beam scintillator counters [6]. A minimumbias Monte Carlo (MC) sample was generatedusing PYTHIA (with D6T tune) [7] followed by full detector simulation based on the Geant4program [8]. Additional PYTHIA MC samples were generated to simulate BEC effects with both Gaussian and exponential forms of
Ω
(
Qr
)
.Charged particles are required to have
p
T
>
200MeV, which is sufﬁcient for particles emittedfrom the interaction region to cross all three barrel layers of the pixel detector and ensure goodtwotrack separation. Their pseudorapidity is required to satisfy

η
track

<
2.4. To ensure highpurity of the primary track selection, the trajectories are required to be reconstructed in ﬁtswith more than ﬁve degrees of freedom (dof) and
χ
2
/
N
dof
<
5.0. The transverse impact parameter with respect to the collision point is required to satisfy

d
xy

<
0.15 cm. The innermost
2
measured point of the track must be less than 20cm from the beam axis , in order to reduceelectrons and positrons from photon conversions in the detector material and secondary particles from the decay of longlived hadrons (
K
0
S
,
Λ
, etc.). In a total of 270472 (13548) eventsselected at 0.9 (2.36)TeV centerofmass energy, 2903754 (188140) tracks are accepted by theseselection criteria.All pairs of samecharge particles with
Q
between 0.02 and 2GeV are used for the measurement. The lower limit is chosen to avoid cases of tracks that are duplicated or not well separated, whiletheupperlimitextendsfarenoughbeyondthesignalregiontoverifyagoodmatch between signal and reference samples. A study with simulated data shows that the ratio of thetracking efﬁciencies of particle pairs in the signal and in the reference samples is independentof
Q
in the measurement region.Coulomb interactions between charged particles modify their relative momentum distribution.This effect, which differs for pairs with same charge (repulsion) and opposite charge (attraction), is corrected for by using Gamow factors [9]. As a crosscheck, the enhancement in theproduction of oppositecharge particle pairs with small values of
Q
is measured in the data andis found to be reproduced by the Gamow factors to within
±
15%.Different methods are designed to pair uncorrelated charged particles and to deﬁne referencesamples used to extract the distribution in the denominator of Eq. (1).
Oppositecharge pairs
:this data set is a natural choice but contains resonances (
η
,
ρ
, ...) which are not present inthe samecharge combinations.
Oppositehemisphere pairs
: tracks are paired after inverting inspace the threemomentum of one of the two particles:
(
E
,
p
)
→
(
E
,
−
p
)
; this procedure is applied to pairs with same and opposite charges.
Rotated particles
: particle pairs are constructedafter inverting the
x
and
y
components of the threemomentum of one of the two particles:
(
p
x
,
p
y
,
p
z
)
→
(
−
p
x
,
−
p
y
,
p
z
)
.
Pairs from mixed events:
particles from different events arecombined with the following methods: i) events are mixed at random; ii) events with similar charged particle multiplicity in the same
η
regions are selected; iii) events with an invariantmass of all charged particles similar to that of the signal are used to form the pairs.As an example, the ratios
R
(
Q
)
obtained with the oppositehemisphere, samecharge referencesamples are shown in Fig. 1 both for data and simulation without BEC. A signiﬁcant excess atsmall values of
Q
is observed in the data. Additional details are given in [10].
Q (GeV)00.20.40.60.811.21.41.61.82
R ( Q )
11.11.21.31.41.51.61.7.
DataMC
Ref.: Opposite hem. same charge
= 0.9 TeVsCMS
Figure 1: Ratios
R
(
Q
)
obtained with the oppositehemisphere, samecharge reference samplesfor data (dots) and MC with no BEC effect (crosses).In order to reduce the bias due to the construction of the reference samples, a double ratio
R
isdeﬁned:
R
(
Q
) =
RR
MC
=
d
N
/d
Q
d
N
ref
/d
Q
d
N
MC
/d
Q
d
N
MC,ref
/d
Q
, (3)
3
Table 1: Results of ﬁts to the double ratios
R
for several reference samples, using the parameterization of Eq. (2) with the exponential form, for 0.9TeV data (top) and 2.36TeV data (bottom).Errors are statistical only, and quoted as if independent.
Results of ﬁts to 0.9TeV dataReference sample
p
value (%)
C
λ
r
(fm)
δ
(10
−
3
GeV
−
1
)Opposite charge 21.9 0.988
±
0.003 0.56
±
0.03 1.46
±
0.06
−
4
±
2Opposite hem. same ch. 7.3 0.978
±
0.003 0.63
±
0.03 1.50
±
0.06 11
±
2Opposite hem. opp. ch. 11.9 0.975
±
0.003 0.59
±
0.03 1.42
±
0.06 13
±
2Rotated 0.02 0.929
±
0.003 0.68
±
0.02 1.29
±
0.04 58
±
3Mixed evts. (random) 1.9 1.014
±
0.002 0.62
±
0.04 1.85
±
0.09
−
20
±
2Mixed evts. (same mult.) 12.2 0.981
±
0.002 0.66
±
0.03 1.72
±
0.06 11
±
2Mixed evts. (same mass) 17.0 0.976
±
0.002 0.60
±
0.03 1.59
±
0.06 14
±
2Combined 2.9 0.984
±
0.002 0.63
±
0.02 1.59
±
0.05 8
±
2Results of ﬁts to 2.36TeV dataReference sample
p
value (%)
C
λ
r
(fm)
δ
(10
−
3
GeV
−
1
)Opposite charge 57 1.004
±
0.008 0.53
±
0.08 1.65
±
0.23
−
16
±
6Opposite hem. same ch. 42 0.977
±
0.006 0.68
±
0.11 1.95
±
0.24 15
±
5Opposite hem. opp. ch. 46 0.969
±
0.005 0.70
±
0.11 2.02
±
0.23 24
±
5Rotated 42 0.933
±
0.007 0.61
±
0.07 1.49
±
0.15 58
±
6Mixed evts. (random) 23 1.041
±
0.005 0.74
±
0.15 2.78
±
0.36
−
40
±
4Mixed evts. (same mult.) 35 0.974
±
0.005 0.63
±
0.10 2.01
±
0.23 20
±
5Mixed evts. (same mass) 73 0.964
±
0.005 0.73
±
0.11 2.18
±
0.23 28
±
5Combined 89 0.981
±
0.005 0.66
±
0.07 1.99
±
0.18 13
±
4
where the subscripts “MC” and “MC,ref” refer to the corresponding distributions from the MCsimulated data generated without BEC effects.The results of ﬁts of
R
(
Q
)
based on the parameterization of Eq. (2) with
Ω
(
Qr
) =
e
−
Qr
aregiven in Table 1, both for 0.9 and 2.36TeV data. In the case of the oppositecharge sample, it isfound that the region with 0.6
<
Q
<
0.9GeV, containing a sizeable contribution of pairs from
ρ
→
π
+
π
−
decays, is not well described by the MC [10]. This region is therefore excluded fromthe ﬁts with this reference sample and also with the combined sample deﬁned below.As a crosscheck, the d
E
/d
x
[11] measurements of particles in the tracker are used to select asample enriched in
ππ
pairs, and another sample with one of the particles not consistent withthe pion hypothesis. Figure 2 presents the double ratios for these two samples at
√
s
=
0.9TeV,showing that an enhancement at small
Q
values is observed only in the case of identiﬁed
ππ
pairs.As none of the deﬁnitions of the reference samples is preferable
a priori
, an additional, “com bined” double ratio
R
comb
is formed, where the data and MC distributions are obtained bysumming the
Q
distributions of the seven corresponding reference samples.The distributions of
R
comb
for 0.9 and 2.36TeV data are shown in Fig. 3, and the values of the ﬁtparameters are given in Table 1. A large correlation is found between the parameters
λ
and
r
, aswell as between
δ
and
C
(correlation coefﬁcients of 0.82 and
−
0.97 at 0.9TeV, respectively). Thedata are described by Eq. (2) with an exponential form for
Ω
(
Qr
)
, as shown by the solid linesin Fig. 3 and conﬁrmed by the ﬁt probability (
p
value) in Table 1. The ﬁt with a Gaussian form,
Ω
(
Qr
) =
e
−
(
Qr
)
2
, which yields
λ
=
0.32
±
0.01,
r
=
0.98
±
0.03 fm, does not correctly describethe
R
(
Q
)
distribution, as shown by the dashed lines in Fig. 3 and by a
p
value of 10
−
21
. Gaussian shape ﬁts also proved to offer a poor description of the data in previous measurements[12–14].