Measuring KS0K± interactions using pp collisions at √s=7 TeV

Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

Measuring

K

0

_S

K

±

interactions

using

pp

collisions

at

√

s

=

7 TeV

.

ALICE

Collaboration



a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Article history:

Received27September2018

Receivedinrevisedform28November2018 Accepted13December2018

Availableonline18December2018 Editor:L.Rolandi

We presentthefirstmeasurements offemtoscopiccorrelationsbetweentheK0

S and K±particlesinpp

collisions at √s₌7 TeV measured by the ALICE experiment. The observed femtoscopic correlations are consistentwith final-stateinteractionsproceeding solelyviathe a0(980) resonance.Theextracted

kaon source radius and correlation strength parameters for K0

SK− are found to be equal within the

experimental uncertainties to those forK0

SK+.Results ofthe present study are comparedwith those

fromidentical-kaonfemtoscopicstudiesalsoperformedwithppcollisionsat√s₌7 TeVbyALICEand withaK0_SK±measurementinPb–Pbcollisionsat√sNN=2.76 TeV.CombinedwiththePb–Pbresults,our

ppanalysisisfoundtobecompatiblewiththeinterpretationofthea0(980)havingatetraquarkstructure

insteadofthatofadiquark.

©2018PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense (http://creativecommons.org/licenses/by/4.0/).FundedbySCOAP3.

1. Introduction

Recently, by using Pb–Pb collisions at

√

sNN

=

2

.

76 TeV, the ALICEexperiment [1] has published the first-everstudy ofK0_SK± femtoscopy [2].K0_SK±femtoscopydiffersfromidentical-kaon fem-toscopy,forwhichanumberofstudiesexistintheliterature [3–6], in that the only pair interaction expected is a final-state inter-action (FSI)through the a0

(

980

)

resonance. It was found in that Pb–Pb study that the FSI in K0_SK± proceeds solely through the

a0

(

980

)

resonance,i.e.withnocompetingnon-resonant channels,

andtheextractedkaonsourceparametersagreewithpublished re-sultsfromidentical-kaonstudiesinPb–Pbcollisions.Theseresults werefoundtobecompatiblewiththeinterpretationofthea0 res-onance asatetraquark state ratherthana diquark1 _{state [2,7–9].}

A recenttheoretical calculation has shown that the ALICEPb–Pb results can indeed be described by a model based on the four-quarkmodel [10].

TheargumentgiveninRef. [2] fora tetraquarka0 being

com-patiblewiththePb–PbK0_SK± resultstatedabove isbasedontwo factors: 1) the kaon source geometry, and2) an empirical selec-tionrule(for thesake ofsimplicityofnotation, “a0”willbeused

fortheremainder ofthispapertorepresent“a0

(

980

)

”). Forfactor

1),theproductioncrosssection ofthea0 resonanceinareaction channel such as K0K−

→

a−₀ should depend on whether the a−₀

is composed of du or dssu quarks, the former requiring the an-nihilation of the ss pairand the latterbeing a direct transfer of

 _{E-mail address:alice-publications@cern.ch.}

1 _{Notethattheterm“diquark”willbeusedinthispapertoindicatea}

_q

iqjquark

pair.

the valence quarks from the kaons to the a−₀. Since the femto-scopicsizeofthe0–10%mostcentralPb–Pbcollisionismeasured tobe5–6fm,thelargegeometryinthesecollisionsisfavorablefor the directtransfer ofquarksto thea0, whereasnot favorable for

theannihilationofthestrangequarksduetotheshort-ranged na-tureof thestronginteraction. Forfactor2), thedirect transferof thevalencequarksfromthekaons tothea−₀ isfavoredsincethis is an “OZIsuperallowed” reaction [9].The OZIrule canbe stated as “an inhibition associated with the creation or annihilation of quark lines” [9]. Thus, the annihilation of the strange quarks is suppressedbytheOZIrule.Both ofthesefactorsfavorthe forma-tionofatetraquark a0 andsuppresstheformationofadiquark a0.

As a resultof this, if the a0 were a diquark, one would expect competingnon-resonantchannelspresentand/or noFSIatall,i.e. free-streaming, ofthe kaonpairthus diluting thestrength ofthe

a0 resonant FSI. The fact that this isnot seen to be the casein Pb–Pbcollisionsfavorsthetetraquarka0 interpretation.

Thegeometryofthekaonsourceisseentobeanimportant fac-torintheargumentgivenabove,i.e.thelargekaonsourceseenin Pb–Pb collisionssuppressestheannihilationofthestrange quarks in the kaon pair and enhances the direct transfer of quarks to the a0. It is interesting to speculate on the dependence of the

strength of the a0 resonant FSI on the size of the kaon source,

particularlyfora verysmallsourceofsize

∼

1 fm that wouldbe obtainedin pp collisions[4,5]. Fora kaonsource ofsize

∼

1 fm, the kaons in a produced kaon pair would be overlapping with each otheratthesource,thusgivingageometricenhancementof thestrange-quarkannihilationchannelthatcouldcompetewith,or evendominateover,theOZIrulesuppressionofquarkannihilation. Thus we might expect that the tetraquark a0 resonant FSI could be diluted or completely suppressed by competingnon-resonant

https://doi.org/10.1016/j.physletb.2018.12.033

annihilation channels that could open up, whereas a diquark a0

resonantFSI,whichwasnotseentobesuppressedbyeither geom-etryortheOZIruleinPb–Pb,wouldnotbediluted.Afemtoscopic measurementofK0_SK±correlationsinppcollisionsshouldbeable totestthisbydeterminingthestrengthofthea0FSIbymeasuring

thefemtoscopic

λ

parameter. Inmoreconcreteterms,ifwe were tocomparethe

λ

parametersextractedinK0_SK±femtoscopic mea-surementsinppcollisionsandPb–Pbcollisions,foratetraquarka0

wewouldexpect

λ

_K0

SK±(PbPb)

> λ

K0SK±(pp)whereasforadiquarka0

we would expect

λ

_K0

SK±(PbPb)

∼ λ

KS0K±(pp). An independent check

couldalsobemadeby comparing

λ

fromK0_SK± femtoscopyinpp collisionswith

λ

fromidentical-kaonfemtoscopyinppcollisionsin asimilarwayaswasdoneforPb–Pbcollisions [2].Sinceweexpect identical-kaoncorrelationstogosolelythroughquantumstatistics (and FSI for neutral kaons), our expectation for a tetraquark a0

wouldbe

λ

K K(pp)

> λ

K0

SK±(pp)whereasforadiquark a0 wewould

expect

λ

K K(pp)

∼ λ

K0

SK±(pp).

In this Letter, femtoscopic correlations with the particle pair combinationsK0

SK± are studiedforthe first timein pp collisions

at

√

s

=

7 TeVbythe ALICEexperiment.The physics goalsofthe presentK0

SK±femtoscopystudyarethefollowing:1)showtowhat

extenttheFSIthrough thea0 resonancedescribesthecorrelation functions,2) studytheK0 andK0 sources tosee ifthereare dif-ferencesin the sourceparameters, 3) comparethe results ofthe extractedkaonsourceparametersfromthepresentstudywiththe publishedresultsfromPb–Pbcollisions andidenticalkaonresults from pp collisions, and 4) see if the results from this pp study arecompatiblewitha tetraquarka0 assuggestedfromthePb–Pb study.

2. Descriptionofexperimentanddataselection

The ALICEexperiment andits performance in the LHC Run1 (2009–2013) are described in Ref. [1] and Refs. [11,12], respec-tively.About 370

×

106 _{minimum-bias 7 TeV pp collision events}

takenin 2010 were used in this analysis. Events were classified using the measured amplitudes in the V0 detectors, which con-sistoftwo arraysof scintillatorslocated along thebeamline and covering the full azimuth [13,14]. Charged particles were recon-structed and identified with the central barrel detectors located within a solenoid magnet with a field strength of B

= ±

0

.

5 T. ChargedparticletrackingwasperformedusingtheTimeProjection Chamber(TPC) [15] and the Inner Tracking System(ITS) [1]. The ITSallowedforhighspatialresolutionindeterminingtheprimary (collision)vertex. Amomentum resolutionof lessthan10MeV/c was typically obtained for the charged tracks of interest in this analysis [16]. The primary vertexwas obtainedfromthe ITS, the positionofthe primary vertexbeingconstrainedalong the beam direction(the “z-position”)tobe within

±

10 cmofthecenterof theALICEdetector.Inadditiontothestandardtrackquality selec-tions [16], theselectionsbasedon thequalityoftrackfittingand thenumber ofdetected tracking points in the TPCwere used to ensurethatonlywell-reconstructedtracksweretakeninthe anal-ysis [11,15,16].

Particleidentification(PID)forreconstructedtrackswascarried outusing boththe TPCandtheTime-of-Flight(TOF) detectorsin thepseudorapidityrange

|

η

|

<

0

.

8 [11,12].ForthePIDsignalfrom both detectors, a value was assigned to each track denoting the number of standard deviations between the measured track in-formationandcalculatedvalues (Nσ )[6,11,12,16]. ForTPCPID,a parametrizedBethe–Blochformulawas usedtocalculatethe spe-cific energy loss



dE

/

dx



in the detector expected for a particle withagivenmassandmomentum.ForPIDwithTOF,theparticle

masswas usedtocalculatetheexpectedtime-of-flightasa func-tionoftracklengthandmomentum.Thisprocedurewasrepeated forfour“particlespecieshypotheses”,i.e.electron,pion,kaonand proton,and,foreachhypothesis,adifferentNσ valuewasobtained perdetector.

2.1. Kaonselection

Themethods usedtoselectandidentifyindividual K0_S andK± particles are the sameasthose used forthe ALICEK0

SK0S [4] and

K±K± [5] analyses from

√

s

=

7 TeVppcollisions. Theseare now describedbelow.

2.1.1. K0 Sselection

The K0

S particles were reconstructed from the decay K0S

→

π

+

π

−,withthedaughter

π

+and

π

−tracksdetectedintheTPC, ITSandTOF detectors.The secondaryvertexfinderusedtolocate theneutralkaondecaysemployed the“on-the-fly”reconstruction method [16],whichrecalculatesthedaughtertrackmomenta dur-ing the original tracking process under the assumption that the tracks came from a decay vertex instead of the primary vertex. Pions with pT

>

0

.

15 GeV/c were accepted (since for lower pT

track finding efficiency drops rapidly) and the distance of clos-est approach to the primary vertex (DCA) of the reconstructed K0_S was requiredto be lessthan 0.3cmin alldirections. The re-quired Nσ valuesforthe pions were NTPC

σ

<

3 (forall momenta)

and NTOF

σ

<

3 for p

>

0

.

8 GeV/c. An invariant mass distribution

for the

π

+

π

− pairs was produced and the K0_S was defined to be resulting from a pair that fell into the invariant mass range 0

.

480

<

_mπ+_π−

<

0

.

515 GeV/c2_{, corresponding to}

_±

₄

_.

₇

_σ

_{, where}

σ

=

3

.

7 MeV/c2_{isthewidthofaGaussianfittotheinvariantmass}

distribution.

2.1.2. K±selection

Chargedkaontracksweredetected usingtheTPCandTOF de-tectors, andwere accepted ifthey were within the range0

.

14

<

pT

<

1

.

2 GeV/c in order to obtain good PID. The determination ofthe momentaofthe trackswas performedusingtracks recon-structedwiththeTPConlyandconstrainedtotheprimaryvertex. In order to reduce the number of secondary tracks (for instance the chargedparticles produced inthe detectormaterial,particles fromweakdecays,etc.),theprimarychargedkaontrackswere se-lectedbasedontheDCA,suchthattheDCAtransversetothebeam directionwaslessthan2.4cmandtheDCAalongthebeam direc-tion was less than 3.2 cm. If the TOF signal were not available, the required Nσ valuesforthe chargedkaons were NTPC

σ

<

2 for pT

<

0

.

5 GeV/c, andthe trackwasrejectedfor pT

>

0

.

5 GeV/c. If

the TOFsignal were also available and pT

>

0

.

5 GeV/c: NTPC_σ

<

2 andNTOF_σ

<

2 (0

.

5

<

pT

<

1

.

2 GeV/c).

TheK0_SK±experimentalpairpuritywasestimatedfromaMonte Carlo(MC) studybasedon PYTHIA [17] simulationswiththe Pe-rugia2011 tune [18], and using GEANT3 [19] to model particle transportthroughtheALICEdetectors.Thepuritywasdetermined from the fraction of the reconstructed MC simulated pairs that were identified asknown K0

SK± pairs fromPYTHIA.The pair

pu-ritywas estimatedto be

∼

83% forall kinematicregions studied in thisanalysis. The single-particle puritiesfor K0_S andK± parti-clesusedinthisanalysiswereestimatedtobe

∼

92%and

∼

91%, respectively.The uncertaintyincalculatingthepairpurityis esti-matedtobe

±

1%.

3. Analysismethods

3.1. Experimentalcorrelationfunctions

ThisanalysisstudiesthemomentumcorrelationsofK0_SK±pairs usingthetwo-particlecorrelationfunction,definedas

C

(k

∗

)

=

A(k

∗

₎

B(k∗

)

,

(1)

where A

(

k∗

)

isthemeasured distributionofpairsfromthesame event, B

(

k∗

)

is the reference distribution of pairs from mixed events,andk∗ isthemagnitudeofthemomentumofeachofthe particlesinthepairrestframe(PRF),

k∗

=



(s

−

m2 K0

−

m2_K±

)

2

−

4m2_K0m2_K± 4s (2) where s

=

m2_K0

+

m2_K±

+

2EK0E_K±

−

2



p_K0

· 

p_K± (3)

andmK0 (E_K0)andm_K± (E_K±)aretherestmasses(total energies) oftheK0

S andK±,respectively.

Thedenominator B

(

k∗

)

wasformedby mixingK0_S andK± par-ticlesfromeacheventwithK± andK0_S particles,respectively,from tenother events,whereeach eventhasatleastboth aK± anda K0

S [2]. The vertices of the mixedevents were constrained to be

within2cmofeachotherinthez-direction.

Two-trackeffects, suchasthe mergingof tworeal tracksinto onereconstructedtrackandthesplittingofonerealtrackintotwo reconstructedtracks,isanimportantissueforfemtoscopicstudies. Thisanalysisdealtwiththeseeffectsusingthefollowingmethod. For each kaon pair, the distance between the K0_S pion daughter trackandthesame-chargedK±trackwascalculatedatuptonine points throughouttheTPC(every 20cmfrom85cm to245cm) andthenaveraged.Comparingpairsfromthesameeventtothose frommixed events,one observes a splittingpeak foran average separationof

<

11 cm. Tocorrectforthis,thisanalysisdemanded thatthesame-charge particlesfromeachkaonpairmusthavean averageTPCseparationofatleast13cm.Mixed-eventtrackswere normalizedby subtracting theprimary vertexposition fromeach usedtrackpoint.

Correlationfunctions were createdseparately forthe two dif-ferent charge combinations,K0_SK+ and K0_SK−, andforthree over-lapping/non-exclusive pair transverse momentum kT

= |

pT,1

+



pT,2

|/

2 ranges: all kT, kT

<

0

.

85 and kT

>

0

.

85 GeV/c, where kT

=

0

.

85 GeV/c is the location of the peak of the kT distribu-tion.ThemeankTvaluesforthesethreebinswere0.66,0.49and 1.17 GeV/c, respectively. The raw K0

SK+ correlation functions for

thesethreebinscomparedwiththosegeneratedfromPYTHIA sim-ulations withthe Perugia2011 tune and usingGEANT3 to model particletransportthroughtheALICEdetectorsareshowninFig.1. The PYTHIA correlation functions are normalized to the data in thevicinityofk∗

=

0

.

8 GeV/c.TherawK0_SK−correlationfunctions lookverysimilartothese.ItisseenthatalthoughPYTHIA qualita-tivelydescribesthetrendsofthebaselineofthedata,itdoesnot describeitquantitatively suchthat itcouldbe usedtomodelthe baseline directly.Instead,forthepresentanalysisthestrategy for dealingwiththebaselinewastodescribeitwithseveralfunctional formstobefittedtotheexperimentalcorrelationfunctionsandto usePYTHIA to test the appropriatenessof the proposed baseline functionalforms.

Three functional forms for the baseline were tested with PYTHIA:quadratic,Gaussianandexponential,givenby

Fig. 1. RawK0

SK+ correlationfunctionsforthethree

k

T binscomparedwiththose

from PYTHIA.Theerror barsarestatistical. Thescaleof C(k∗)is arbitrary.The PYTHIA correlationfunctionsarenormalized tothedata inthe vicinityof

k

∗= 0.8 GeV/c.

Cquadratic

(k

∗

)

=

a(1

−

bk∗

+

ck∗2

)

(4)

CGaussian

(k

∗

)

=

a(1

+

b exp(

−

ck∗2

))

(5)

Cexponential

(k

∗

)

=

a(1

+

b exp(

−

ck∗

))

(6)

where a, b and c are fit parameters. Fig.2 showsfits of Eq. (4), Eq. (5) and Eq. (6) to the PYTHIA correlation functions shown in Fig. 1 for the three kT ranges used in this analysis. As seen,

all three functionalforms do reasonablywell inrepresenting the PYTHIA correlation functions. Thus, all three forms were used in fittingthe experimentalcorrelation function andthe different re-sultsobtainedwillbeusedtoestimatethesystematicuncertainty due to the baseline estimation. Of course there are an infinite number offunctionsone could tryto representthe baseline,but atleast thethree thatwere chosen forthiswork are simpleand representativeofthreebasicfunctionalforms.

Correlationfunctionswere correctedformomentumresolution effectsusingPYTHIAcalculations.Theparticlemomentum resolu-tioninALICEfortherelativelylow-momentumtracksusedinthe present analysis was

<

10 MeV/c [1]. Two correlation functions were generatedwithPYTHIA:one intermsofthe generator-level

Fig. 2. Comparisonsoffitsofthree possiblebaseline functionalformswith the PYTHIAcorrelationfunctionsthatwereshowninFig.1.Fitsweremadeinthe

k

∗ range0–0.8 GeV/c.Thescaleof

C

(k∗)isarbitrary.

PYTHIA does not incorporate final-state interactions, simulated femtoscopicweights were determined usinga 9th-order polyno-mial fitin k∗ to theexperimental correlation function forthe kT

range considered. When filling the same-event distributions, i.e.

A

(

k∗

)

in Eq. (1), kaon pairs were individually weighted by this 9th-order fit according to their generator-level k∗. Then, the ra-tioofthe “ideal”correlation function to the“measured”one (for eachk∗ bin) was multipliedtothe datacorrelation functions be-forethe fitprocedure. Thiscorrection mostly affectedthe lowest

k∗bins,increasingtheextractedsourceparametersby

∼

2%.

3.2.Final-stateinteractionmodel

Thefinal-stateinteraction modelused inthepresentpp colli-sionanalysisfollowsthesameprinciplesastheonesusedforthe ALICEPb–Pbcollisionanalysis [2].ThemeasuredK0_SK± correlation functionswere fit withformulas that include a parameterization whichincorporatesstrongFSI. Itwas assumedthat theFSIarises intheK0_SK±channelsduetothenear-thresholdresonance,a0.This parameterizationwas introduced by R. Lednickyand isbased on the model by R. Lednicky and V.L. Lyuboshitz [20,21] (see also Ref. [3] formoredetailsonthisparameterization).

Using an equal emission time approximation in the PRF [20], the elastic K0_SK± transition is written as a stationary solution



_−k∗

(



r∗

)

ofthescatteringprobleminthePRF.Thequantity



r∗ rep-resentstheemissionseparationofthepairinthePRF,andthe

−

k∗

subscriptreferstoareversaloftimefromtheemissionprocess.At largedistancesthishastheasymptoticformofasuperpositionof anincomingplanewaveandanoutgoingsphericalwave,



_−k∗

(



r∗

)

=

e−ik∗·r∗

+

f

(k

∗

)

eik∗r∗

r∗

,

(7)

where f

(

k∗

)

is the s-wave K0_K− _{or K}0_K+ _{scattering amplitude}

whose contribution is the s-wave isovector a0 resonance (see Eq. (11)inRef. [3])and

f

(k

∗

)

=

γ

a0→KK

m2a0

−

s

−

i(

γ

a0→KKk∗

+

γ

a0→π ηkπ η

)

.

(8)

In Eq. (8), ma0 is the mass of the a0 resonance, and

γ

a0→KK and

γa

0→π η are the couplings of the a0 resonance to the K

0_K− (or K0K+) and

π η

channels, respectively. Also, s

=

4

(

m2

K0

+

k∗2

)

Table 1

The

a

0massandcouplingparameters,allinGeV/c2,usedinthepresentstudy.

Reference ma0 γa0→KK γa0→πη

Achasov2 [7] 1.003 0.8365 0.4580

andkπη denotesthemomentumintheseconddecaychannel(

π η

) (seeTable1).

The correlation function due to the FSI is then calculated by integrating



_−k∗

(



r∗

)

intheKoonin–Prattequation [22,23],

CFSI

(

k∗

)

=



d3



r∗S(



r∗

)





_−k∗

(



r∗

)





2

,

(9)

where S

(



r∗

)

isaone-dimensionalGaussiansourcefunctionofthe PRFrelativedistance



r∗



withaGaussianwidthR oftheform

S(



r∗

)

∼

e−r∗2/(4R2)

.

(10)

Equation (9) can be integrated analytically for K0_SK± correla-tionswithFSIfortheone-dimensionalcase,withtheresult

CFSI

(k

∗

)

=

1

+ λ

α



1 2





f

(k

_R∗

)





2

+

2

R

√

f

(k

∗

)

π

R F1

(

2k ∗_R)

−

I

f

(k

∗

)

R F2

(

2k ∗_R)

₊

_C



,

(11) where F1

(z)

≡

√

π

e−z2erfi

(z)

2z

;

F2

(z)

≡

1

−

e−z2 z

.

(12)

Intheabove equations

α

isthefractionofK0

SK± pairsthat come

from the K0_K− _{or K}0_K+ _{system, set to 0.5 assuming symmetry}

in K0 andK0 production[3], R istheradius parameter fromthe spherical Gaussian sourcedistribution givenin Eq. (10), and

λ

is the correlation strength. The correlation strength is unity in the idealcaseofpure a0-resonant FSI,perfectPID,aperfectGaussian kaon sourceand theabsence oflong-lived resonances which de-cayintokaons.Theterm

C isa calculatedcorrection factorthat takesintoaccountthedeviationofthesphericalwave assumption usedinEq. (7) intheinnerregionoftheshort-rangepotential(see theAppendix inRef. [3]).Its effectontheextracted R and

λ

pa-rametersistoincrease themby

∼

14%.Notethattheformofthe FSIterminEq. (11) differsfromtheformoftheFSItermforK0_SK0_S correlations(Eq. (9)ofRef. [3])byafactorof1

/

2 duetothe non-identicalparticlesinK0

SK±correlationsandthustheabsenceofthe

requirementtosymmetrizethewavefunctiongiveninEq. (7). AsseeninEq. (8),theK0K−orK0K+ s-wavescattering ampli-tudedependsonthea0massanddecaycouplings.FromtheALICE

Pb–Pb collision K0_SK± study [2], it was found that source param-etersextractedwiththe“Achasov2”parameters ofRef. [7] agreed bestwiththeidenticalkaonmeasurements,thusinthepresentpp collisionstudyonlythe Achasov2parameters areused.These pa-rameters areshown inTable1. Sincethe correction factor

C is

foundtomainlydependon

γ

a0KK¯ [3],itisjudgedthatthe system-aticuncertaintyonthecalculationof

C isnegligible.

The experimental K0

SK± correlation functions, calculated using

Eq. (1),werefitwiththeexpression

C

(k

∗

)

=

CFSI

(k

∗

)C

baseline

(k

∗

),

(13)

whereCbaseline

(

k∗

)

isEq. (4),Eq. (5) orEq. (6).

The fitting strategy used was to carry out a 5-parameter fit ofEq. (13) tothe K0_SK± experimental correlation functionsto ex-tractR,

λ

,a, b andc foreachofthesix(kT range)–(chargestate)

Fig. 3. CorrelationfunctionsdividedbyoneofthebaselinefunctionswithfitsfromEq. (13) forK0

SK+andK0SK−and

k

∗fitrange(0.0–0.6GeV/c)forthethree

k

Tbinsand

thequadraticbaselinefunctionassumption.Statistical(lines)andthequadraticsumofthestatisticalandsystematic(boxes)uncertaintiesareshown.For

k

∗>0.05 GeV/c, thesystematicuncertaintiesbecomenegligibleandtheboxesarenolongershown.

Fig. 4. Sample raw correlation functions for K0

SK+showing the fitted quadratic baseline function, Eq. (4). Statistical uncertainties are shown. The scale of C(k∗)is arbitrary.

combinations.Foreach ofthesesixcombinations,thethree base-linefunctional forms,and two k∗ fit ranges,(0.0–0.6 GeV/c) and (0.0–0.8 GeV/c),werefit,givingsixR andsix

λ

parametervalues foreachcombination.Thesesixvalueswerethenaveragedandthe variance calculated to obtain the final values for the parameters andanestimateofthecombinedsystematicuncertaintiesfromthe baselineassumptionsandfitrange,respectively.

4. Resultsanddiscussion

4.1. Fitstotheexperimentalcorrelationfunctions

Fig. 3 shows sample correlation functions divided by the quadraticbaselinefunctionwithfitsofEq. (13) forK0_SK± andthe

k∗fitrange(0.0–0.6 GeV/c)forthethreekT bins.Thefitsusingthe

otherbaselineassumptionsandtothewiderrange(0.0–0.8 GeV/c) aresimilar inquality. Comparingwiththequadraticbaseline, us-ing theGaussian baseline tends togive

∼

10–20% smallersource parameters whereas usingthe exponential baseline tends to give

∼

10–20% larger source parameters. The average

χ

2

_/

_{ndf and}

p-value over all ofthe fitsare 1.554 and0.172, respectively. Statis-tical (lines)and the quadraticsum ofthe statistical and system-atic(boxes) uncertaintiesare shown.The systematicuncertainties were determined by varying cuts on the data (see the discus-sion of the “cut systematicuncertainty” in the section below on “Systematic Uncertainties”formore details). Fig. 4showssample raw correlationfunctionsfor K0

SK+ forthe threekT bins andthe

quadratic baselinefunction, Eq. (4), that was fitcorresponding to the 5-parameter fits of Eq. (13) to the K0

SK+ data presented in

Fig.3.Statisticaluncertaintiesonthefitparameterswereobtained byconstructingthe1

σ

λ

vs. R contourandtakingtheerrorstobe attheextremeextentsofthecontour.Atypicalvalueofthe corre-lationcoefficientis0.642.Thismethodgivesthemostconservative estimatesofthestatisticaluncertainties.

The Achasov2 a0 FSI parameterization coupled with the

vari-ousbaselineassumptionsgivesagoodrepresentationofthesignal regionofthedata,i.e.reproducingtheenhancementinthek∗ re-gion0.0–0.1 GeV/c andthesmalldipintheregion0.1–0.3 GeV/c. A good representation of the signal region was also seen to be the case for the Pb–Pb analysis with the Achasov2

parameteri-Table 2

Fitresultsforaverage

R and

λshowingstatisticalandsystematicuncertaintiesfromK0

SK±femtoscopywithppcollisionsat √

s=7 TeV.The“[+/−]”inthefirstcolumn referstoK0

SK+orK 0

SK−.Seethetextforthedefinitionsofthevariousuncertainties.

R orλ[+/−] kTcut (GeV/c) Fit value Statistical uncert. Fit systematic uncert. Cut systematic uncert. Total systematic uncert. Total quadratic uncert. R[+](fm) kT<0.85 0.905 0.063 0.243 0.033 0.245 0.253 kT>0.85 0.788 0.077 0.168 0.031 0.171 0.188 All kT 0.922 0.048 0.188 0.038 0.192 0.198 λ[+] kT<0.85 0.189 0.046 0.070 0.012 0.071 0.085 kT>0.85 0.222 0.080 0.066 0.015 0.068 0.105 All kT 0.242 0.046 0.066 0.020 0.069 0.083 R[−](fm) kT<0.85 1.039 0.060 0.244 0.039 0.247 0.254 kT>0.85 0.786 0.082 0.145 0.032 0.148 0.169 All kT 0.995 0.046 0.185 0.041 0.190 0.195 λ[−] kT<0.85 0.253 0.044 0.096 0.016 0.097 0.107 kT>0.85 0.208 0.084 0.038 0.016 0.042 0.094 All kT 0.277 0.038 0.074 0.023 0.078 0.087

zation, which has a qualitatively different k∗ dependence of the correlationfunctionthatisdominatedbyadipatlowk∗ (compare presentFig.3withFig. 2fromRef. [2]).Theenhancementseenfor thesmall-R systematlowk∗ isexpectedfromEq. (11) asa con-sequenceofthefirstterminthebracketsthat goesas1

/

R2_.This

demonstratestheabilityofEq. (11) todescribetheFSIinboththe smallandlargesizeregimesasgoingthroughthea0resonance.

4.2.ExtractedR and

λ

parameters

Theresultsforthe extractedaverage R and

λ

parameters and thestatisticalandsystematicuncertaintiesontheseforthepresent analysisofK0_SK± femtoscopyfrom7TeV pp collisions areshown inTable2.Thestatisticaluncertaintiesgivenaretheaveragesover the6fits foreachcase. As canbe seen, R and

λ

forK0

SK+ agree

withinthestatisticaluncertaintieswiththoseforK0_SK−inallcases.

4.3.Systematicuncertainties

Table 2 shows the total systematic uncertainties on the ex-tracted R and

λ

parameters. As is seen, formost casesthe total systematic uncertainty is larger than the statistical uncertainty. The total systematic uncertainty is broken down in Table 2 into two main contributions, the “fit systematicuncertainty” and the “cut systematic uncertainty”, andis the quadratic sum of these. The fitsystematic uncertaintyis the combinedsystematic uncer-tainty due to the various baseline assumptions and varying the

k∗ fitrange,asdescribedearlier.Thecutsystematicuncertaintyis thesystematicuncertaintyrelatedtothevariouscutsmadeinthe dataanalysis.Todeterminethis,singleparticlecutswerevariedby

∼

10%,andthevaluechosenfortheminimumseparationdistance ofsame-sign tracks was varied by

∼

20%. Taking the upper-limit valuesof thevariations tobe conservative,this ledto additional errorsof4% for R and8% for

λ

.Asseeninthetable, thefit sys-tematicuncertaintydominatesoverthecutsystematicuncertainty inall cases,demonstratingthelarge uncertainties indetermining thenon-femtoscopicbaselineinppcollisions.The“totalquadratic uncertainty” is the quadratic sum of the “statistical uncertainty” columnandthe“totalsystematicuncertainty”column.

4.4. ComparisonswithK0_SK±resultsfromPb–Pbcollisionsat

√

sNN

=

2

.

76 TeVandidentical-kaonresultsfromppcollisionsat

√

s

=

7 TeV

Inthissection comparisonsofthepresentresultsfor R and

λ

withK0_SK±measurementsfromALICE2.76 TeVPb–Pbcollisionsfor 0–10%centrality [2],andwithidentical-kaonmeasurements from ALICE7 TeV pp collisions [4,5] are presented.Since it is seen in Table 2that the extractedparameters forK0_SK+ agree within the statisticaluncertainties withthoseforK0_SK−inallcases,theseare averaged overweighted bythestatisticaluncertainties inthe fol-lowingfigures.

Fig. 5 shows the comparison with the ALICE Pb–Pb collision K0_SK± measurements.The

λ

parameters havebeendividedby the pairpurityforeachcase,i.e.83%forthepresentppcollisionsand 88% for the Pb–Pb collisions [2], so that they can be compared onthesamebasis.Itisseenthat R for0–10%centralityPb–Pb is

∼

5 fm,andissignificantlylargerthantheR

∼

1 fmmeasuredfor pp collisions. Thisisexpectedsince R reflectsthe geometric size oftheinteractionregionofthecollision.Itissomewhatsurprising that

λ

forppcollisionsisseentobesignificantlylessthanthatfor Pb–Pbcollisions.Therearetwomainfactorseffectingthevalueof the

λ

parameter:1)thedegreetowhichaGaussianfitsthe corre-lationfunction and2) theeffectoflong-livedresonancesdiluting thekaonsample. For1),itisseeninFig.3forppandinFig. 2of Ref. [2] forPb–PbthattheGaussianfunctionusedintheLedincky equation,Eqs. (10) and(11),fitsbothcollidingsystemswell, mini-mizingtheeffectof1).For2),theK∗ decay(



∼

50 MeV)hasthe largest influence on diluting the kaon sample, and it is unlikely that the multiplicity ratioof K

/

K∗ changes dramaticallyin going from2.76 TeV to7 TeV. From theseargumentswe mightnaively expect

λ

tobesimilarintheppandPb–Pbcases.

In order to properly compare the present results with the ALICE pp collision identical-kaon measurements, we must take the weighted average (weightedby their statistical uncertainties) over the multiplicity bins used in Refs. [4,5] since our present resultsaresummedoverallmultiplicity.Fig.6showsthe compar-ison betweenthepresentresultsfor R and

λ

andmeasurements fromtheidentical-kaon femtoscopyin7 TeVpp collisions.The R

values are seen to agree between the present analysis and the identical kaon analyses within the uncertainties. The

λ

param-eters shown in Fig. 6 are each divided by their respective pair purities. Going fromthe lowest to the highestkT points, for the neutral-kaon pairs thepuritiesare 0.88and0.84 [4], andforthe

Fig. 5. R andλparametersextractedinthepresentanalysisfromK0

SK±femtoscopy

averagedoverK0

SK+andK0SK−,alongwithacomparisonwithK0SK±resultsfrom

ALICE2.76TeVPb–Pbcollisionsfor0–10%centrality [2].Thequadraticsumofthe statisticalandsystematicuncertaintiesisplottedfor allresultsasboxesandthe statisticaluncertaintiesaregivenaslines.Theλparametershavebeendividedby theirrespectivepairpuritiestofacilitatetheircomparison.

Fig. 6. R andpurity-normalizedλparametersextractedinthepresentanalysisfrom K0

SK± femtoscopyaveraged overK0SK+ and K0SK−,along with comparisonswith

identicalkaonresultsfromALICE7TeVppcollisionsaveragedoverevent multiplic-ity.Thequadraticsumofthestatisticalandsystematicuncertaintiesisplottedfor allresultsasboxesandthestatisticaluncertaintiesaregivenaslines.Alsoplotted asabluedashedlineisthesimpleaverageoftheidentical-kaonpurity-normalized λparameters.

charge-kaon pairs the purities are 0.84, 0.61, 0.79 and 1.0 [5], respectively. The purity-normalized

λ

parameters for the identi-cal kaons are seen to scatter in a wide range betweenvalues of

0.3–0.7,whereas the K0_SK± valuesare seento liein thenarrower rangeof0.25–0.30.

Inordertohelpto clarifythecomparisonbetweenthe purity-normalized

λ

valuesfromK0_SK±andtheidentical-kaonresults,the simpleaverageovertheidenticalkaonpurity-normalized

λ

param-etersisplottedasa bluedashedlineinFig.6.As seen,theK0_SK± valuestendtobesmallerthantheaverageoftheidenticalkaons, as was more significantly the case for the comparison with the purity-normalized

λ

valuesfromPb–PbseeninFig.5,howeverthe large scatterofthe identicalkaonsmakes itdifficult todrawany strongconclusionsfromthiscomparison.

4.5. Implicationsfromthepresentresultsforthea0tobeatetraquark state

The K0_SK± FSI is described well by assuming it is due to the

a0 resonancefor both pp and Pb–Pb collisions, asseen in Fig. 3

of the present work and in Fig. 2 of Ref. [2]. The R parameters

extracted fromthismethod are also seen toagree within uncer-tainties withthe identical-kaon measurements for each of these collisionsystems.ForPb–Pbcollisions,itwasfoundthatthe

λ

pa-rameters extractedfromK0_SK± alsoagree withthe corresponding identical-kaon measurements for Pb–Pb collisions indicating that the FSIbetweenthe kaonsgoes solelythrough thea0 resonance.

Thepresentppcollisionresultsfor

λ

,whicharesignificantlylower than the K0_SK± values from Pb–Pb collisions seen in Fig. 5 and whichtendtobelowerthanthecorrespondingidentical-kaon val-ues in pp collisions seen in Fig. 6, imply that the FSI for these collisions does not go solely through the a0 resonance, i.e. non-resonant elastic channels and/or free-streaming are also present. From the arguments given in the Introduction, this is the geo-metric effectthat wouldbe expectedin the caseof atetraquark

a0 since competing annihilation channels could open up in the

smallersystemandcompetewiththeFSIthroughthea0,whereas foradiquarka0 theFSIshouldstill gosolelythroughthea0.The pp collisionresultsare thuscompatiblewiththeconclusionfrom thePb–Pbcollisionmeasurement [2] thatfavorstheinterpretation ofthea0 resonancetobeatetraquarkstate.

5. Summary

In summary, femtoscopic correlations with the particle pair combinationsK0_SK± arestudiedinppcollisionsat

√

s

=

7 TeVfor the first time by the LHC ALICE experiment. Correlations in the K0_SK±pairsareproducedbyfinal-stateinteractionswhichproceed through the a0 resonance. It is found that the a0 final-state in-teraction describes the shape of the measured K0

SK± correlation

functionswell.Theextractedradiusand

λ

parametersforK0 SK−are

found tobe equalwithin the experimentaluncertainties to those for K0_SK+. Results of the presentstudy are compared with those from identical-kaon femtoscopic studies also performed withpp collisions at

√

s

=

7 TeVby ALICEandwitharecent ALICEK0_SK± measurementinPb–Pbcollisionsat

√

sNN

=

2

.

76 TeV.These com-parisonssuggest thatnon-resonant elasticscatteringchannelsare presentinppcollisions,unlikeinPb–Pbcollisions.Itisour conclu-sionthatthepresentresults,incombinationwiththeALICEPb–Pb collision measurements,favortheinterpretationofthea0 tobe a

tetraquarkstate.

Acknowledgements

The ALICECollaboration would like to thank all its engineers andtechniciansfortheirinvaluablecontributionstothe construc-tionoftheexperimentandtheCERNacceleratorteamsforthe out-standingperformanceoftheLHCcomplex.TheALICECollaboration

gratefully acknowledges the resources and support provided by allGrid centresandthe Worldwide LHCComputing Grid(WLCG) collaboration. The ALICE Collaboration acknowledges the follow-ingfundingagenciesfortheirsupportinbuildingandrunningthe ALICEdetector:A.I. AlikhanyanNationalScienceLaboratory (Yere-vanPhysicsInstitute)Foundation (ANSL),State Committeeof Sci-enceandWorldFederationofScientists (WFS),Armenia; Austrian AcademyofSciencesandNationalstiftungfürForschung, Technolo-gie und Entwicklung, Austria; Ministry of Communications and High Technologies, National Nuclear Research Center, Azerbaijan; Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), Universidade Federal do Rio Grande do Sul (UFRGS), Fi-nanciadoradeEstudoseProjetos(Finep)andFundaçãodeAmparo àPesquisadoEstadodeSãoPaulo(FAPESP),Brazil;Ministryof Sci-ence&TechnologyofChina(MSTC),NationalNaturalScience Foun-dationofChina(NSFC)andMinistryofEducationofChina(MOEC), China;MinistryofScienceandEducation,Croatia;Centrode Apli-cacionesTecnológicasyDesarrolloNuclear(CEADEN),Cubaenergía, Cuba;MinistryofEducation,YouthandSportsoftheCzech Repub-lic,CzechRepublic;The DanishCouncil forIndependentResearch NaturalSciences,theCarlsbergFoundationandDanishNational Re-search Foundation (DNRF), Denmark;Helsinki Institute ofPhysics (HIP),Finland;Commissariatàl’EnergieAtomique(CEA)and Insti-tut Nationalde Physique Nucléaire etde Physique des Particules (IN2P3)andCentre National de laRecherche Scientifique (CNRS), France; Bundesministerium für Bildung, Wissenschaft, Forschung und Technologie (BMBF) and GSI Helmholtzzentrum für Schw-erionenforschung GmbH, Germany; General Secretariat for Re-search and Technology, Ministry of Education, Research and Re-ligions, Greece; National Research, Development and Innovation Office,Hungary;DepartmentofAtomicEnergy,Governmentof In-dia (DAE),DepartmentofScience andTechnology,Governmentof India (DST), University Grants Commission, Government of India (UGC)andCouncil ofScientificandIndustrialResearch(CSIR), In-dia; Indonesian Institute of Sciences, Indonesia; Centro Fermi – MuseoStoricodellaFisica e CentroStudie RicercheEnricoFermi andIstitutoNazionalediFisicaNucleare(INFN),Italy;Institutefor InnovativeScience andTechnology, Nagasaki Institute of Applied Science (IIST), Japan Society for the Promotion of Science (JSPS) KAKENHIandJapanese MinistryofEducation,Culture,Sports, Sci-enceandTechnology (MEXT), Japan;Consejo Nacionalde Ciencia (CONACYT) yTecnología, through Fondode Cooperación Interna-cionalenCiencia yTecnología(FONCICYT)and DirecciónGeneral deAsuntosdelPersonalAcademico(DGAPA),Mexico;Nederlandse OrganisatievoorWetenschappelijkOnderzoek(NWO),Netherlands; TheResearchCouncilofNorway,Norway;CommissiononScience andTechnology forSustainableDevelopment inthe South (COM-SATS),Pakistan;PontificiaUniversidadCatólicadelPerú,Peru; Min-istryofScienceandHigherEducationandNationalScienceCentre, Poland;KoreaInstituteofScienceandTechnologyInformationand NationalResearch Foundation of Korea (NRF), Republic ofKorea; MinistryofEducation andScientific Research, Institute ofAtomic PhysicsandRomanianNationalAgencyforScience,Technologyand Innovation, Romania; Joint Institute for Nuclear Research (JINR), Ministryof Education andScience ofthe Russian Federation and NationalResearch Centre Kurchatov Institute, Russia; Ministry of Education,Science,ResearchandSportoftheSlovakRepublic, Slo-vakia;NationalResearchFoundationofSouthAfrica,SouthAfrica; SwedishResearchCouncil(VR)andKnut&AliceWallenberg Foun-dation (KAW), Sweden; European Organization for Nuclear

Re-search,Switzerland;NationalScienceandTechnologyDevelopment Agency(NSDTA),SuranareeUniversityofTechnology(SUT)and Of-fice of the Higher Education Commission under NRU project of Thailand,Thailand;TurkishAtomicEnergyAgency(TAEK),Turkey; National Academy of Sciences of Ukraine, Ukraine; Science and TechnologyFacilitiesCouncil(STFC),UnitedKingdom;National Sci-enceFoundationoftheUnitedStatesofAmerica(NSF)andUnited StatesDepartmentof Energy, OfficeofNuclear Physics (DOE NP), UnitedStatesofAmerica.

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ALICECollaboration

S. Acharya

139

,

F.T.-. Acosta

20

,

D. Adamová

93

,

A. Adler

74

,

J. Adolfsson

80

, M.M. Aggarwal

98

,

G. Aglieri Rinella

34

, M. Agnello

31

,

N. Agrawal

48

,

Z. Ahammed

139

,

S.U. Ahn

76

,

S. Aiola

144

,

A. Akindinov

64

,

M. Al-Turany

104

,

S.N. Alam

139

,

D.S.D. Albuquerque

121

, D. Aleksandrov

87

,

B. Alessandro

58

,

H.M. Alfanda

6

,

R. Alfaro Molina

72

,

Y. Ali

15

,

A. Alici

10,27,53

, A. Alkin

2

,

J. Alme

22

,

T. Alt

69

, L. Altenkamper

22

,

I. Altsybeev

111

, M.N. Anaam

6

,

C. Andrei

47

,

D. Andreou

34

,

H.A. Andrews

108

,

A. Andronic

104,142

,

M. Angeletti

34

,

V. Anguelov

102

, C. Anson

16

,

T. Antiˇci ´c

105

,

F. Antinori

56

,

P. Antonioli

53

, R. Anwar

125

,

N. Apadula

79

, L. Aphecetche

113

,

H. Appelshäuser

69

,

S. Arcelli

27

,

R. Arnaldi

58

,

M. Arratia

79

,

I.C. Arsene

21

,

M. Arslandok

102

,

A. Augustinus

34

, R. Averbeck

104

,

M.D. Azmi

17

,

A. Badalà

55

,

Y.W. Baek

40,60

,

S. Bagnasco

58

,

R. Bailhache

69

,

R. Bala

99

,

A. Baldisseri

135

,

M. Ball

42

, R.C. Baral

85

,

A.M. Barbano

26

,

R. Barbera

28

,

F. Barile

52

,

L. Barioglio

26

,

G.G. Barnaföldi

143

,

L.S. Barnby

92

,

V. Barret

132

,

P. Bartalini

6

,

K. Barth

34

, E. Bartsch

69

,

N. Bastid

132

, S. Basu

141

, G. Batigne

113

,

B. Batyunya

75

, P.C. Batzing

21

, J.L. Bazo Alba

109

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88

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102

,

C. Bedda

63

,

N.K. Behera

60

,

I. Belikov

134

,

F. Bellini

34

,

H. Bello Martinez

44

, R. Bellwied

125

,

L.G.E. Beltran

119

,

V. Belyaev

91

,

G. Bencedi

143

, S. Beole

26

,

A. Bercuci

47

,

Y. Berdnikov

96

,

D. Berenyi

143

,

R.A. Bertens

128

,

D. Berzano

34,58

,

L. Betev

34

,

P.P. Bhaduri

139

, A. Bhasin

99

, I.R. Bhat

99

,

H. Bhatt

48

, B. Bhattacharjee

41

,

J. Bhom

117

,

A. Bianchi

26

,

L. Bianchi

26,125

,

N. Bianchi

51

,

J. Bielˇcík

37

,

J. Bielˇcíková

93

, A. Bilandzic

103,116

,

G. Biro

143

,

R. Biswas

3

,

S. Biswas

3

,

J.T. Blair

118

,

D. Blau

87

, C. Blume

69

, G. Boca

137

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34

,

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91

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143

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91

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38

,

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138

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34

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104

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120

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69

,

M. Broz

37

,

E.J. Brucken

43

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58

, G.E. Bruno

33,34

, D. Budnikov

106

,

H. Buesching

69

,

S. Bufalino

31

,

P. Buhler

112

, P. Buncic

34

,

O. Busch

131,I

,

Z. Buthelezi

73

, J.B. Butt

15

,

J.T. Buxton

95

,

J. Cabala

115

,

D. Caffarri

89

,

H. Caines

144

,

A. Caliva

104

, E. Calvo Villar

109

,

R.S. Camacho

44

,

P. Camerini

25

,

A.A. Capon

112

,

W. Carena

34

,

F. Carnesecchi

10,27

,

J. Castillo Castellanos

135

,

A.J. Castro

128

,

E.A.R. Casula

54

,

C. Ceballos Sanchez

8

,

S. Chandra

139

, B. Chang

126

,

W. Chang

6

,

S. Chapeland

34

,

M. Chartier

127

,

S. Chattopadhyay

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,

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,

D.D. Chinellato

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,

T. Chowdhury

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,

P. Christakoglou

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C.H. Christensen

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80

,

T. Chujo

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,

S.U. Chung

18

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54

,

L. Cifarelli

10,27

,

F. Cindolo

53

,

J. Cleymans

124

,

F. Colamaria

52

,

D. Colella

52

, A. Collu

79

,

M. Colocci

27

,

M. Concas

58,II

,

G. Conesa Balbastre

78

, Z. Conesa del Valle

61

,

J.G. Contreras

37

,

T.M. Cormier

94

,

Y. Corrales Morales

58

,

P. Cortese

32

, M.R. Cosentino

122

,

F. Costa

34

,

S. Costanza

137

,

J. Crkovská

61

, P. Crochet

132

, E. Cuautle

70

,

L. Cunqueiro

94,142

,

D. Dabrowski

140

,

T. Dahms

103,116

, A. Dainese

56

, F.P.A. Damas

113,135

, S. Dani

66

,

M.C. Danisch

102

, A. Danu

68

, D. Das

107

,

I. Das

107

,

S. Das

3

,

A. Dash

85

,

S. Dash

48

,

S. De

49

,

A. De Caro

30

,

G. de Cataldo

52

,

C. de Conti

120

, J. de Cuveland

39

,

A. De Falco

24

,

D. De Gruttola

10,30

,

N. De Marco

58

,

S. De Pasquale

30

,

R.D. De Souza

121

,

H.F. Degenhardt

120

, A. Deisting

102,104

,

A. Deloff

84

,

S. Delsanto

26

,

C. Deplano

89

,

P. Dhankher

48

,

D. Di Bari

33

, A. Di Mauro

34

, B. Di Ruzza

56

, R.A. Diaz

8

, T. Dietel

124

,

P. Dillenseger

69

,

Y. Ding

6

,

R. Divià

34

, Ø. Djuvsland

22

, A. Dobrin

34

,

D. Domenicis Gimenez

120

,

B. Dönigus

69

,

O. Dordic

21

,

A.K. Dubey

139

, A. Dubla

104

,

L. Ducroux

133

,

S. Dudi

98

,

A.K. Duggal

98

,

M. Dukhishyam

85

,

P. Dupieux

132

, R.J. Ehlers

144

, D. Elia

52

,

E. Endress

109

,

H. Engel

74

,

E. Epple

144

,

B. Erazmus

113

,

F. Erhardt

97

,

A. Erokhin

111

,

M.R. Ersdal

22

,

B. Espagnon

61

, G. Eulisse

34

,

J. Eum

18

,

D. Evans

108

,

S. Evdokimov

90

,

L. Fabbietti

103,116

, M. Faggin

29

,

J. Faivre

78

,

A. Fantoni

51

,

M. Fasel

94

,

L. Feldkamp

142

,

A. Feliciello

58

,

G. Feofilov

111

,

A. Fernández Téllez

44

, A. Ferretti

26

,

A. Festanti

34

,

V.J.G. Feuillard

102

, J. Figiel

117

,

M.A.S. Figueredo

120

,

S. Filchagin

106

, D. Finogeev

62

,

F.M. Fionda

22

,

G. Fiorenza

52

,

F. Flor

125

, M. Floris

34

,

S. Foertsch

73

, P. Foka

104

, S. Fokin

87

,

E. Fragiacomo

59

,

A. Francescon

34

,

A. Francisco

113

,

U. Frankenfeld

104

, G.G. Fronze

26

,

U. Fuchs

34

, C. Furget

78

,

A. Furs

62

,

M. Fusco Girard

30

,

J.J. Gaardhøje

88

,

M. Gagliardi

26

,

A.M. Gago

109

,

K. Gajdosova

88

, M. Gallio

26

,

C.D. Galvan

119

,

P. Ganoti

83

, C. Garabatos

104

, E. Garcia-Solis

11

, K. Garg

28

,

C. Gargiulo

34

,

K. Garner

142

,

P. Gasik

103,116

,

E.F. Gauger

118

, M.B. Gay Ducati

71

,

M. Germain

113

, J. Ghosh

107

, P. Ghosh

139

,

S.K. Ghosh

3

,

P. Gianotti

51

,

P. Giubellino

58,104

, P. Giubilato

29

, P. Glässel

102

,

D.M. Goméz Coral

72

,

A. Gomez Ramirez

74

,

V. Gonzalez

104

,

P. González-Zamora

44

,

S. Gorbunov

39

,

L. Görlich

117

,

S. Gotovac

35

,

V. Grabski

72

, L.K. Graczykowski

140

,

K.L. Graham

108

, L. Greiner

79

,

A. Grelli

63

,

C. Grigoras

34

,

V. Grigoriev

91

,

A. Grigoryan

1

,

S. Grigoryan

75

,

J.M. Gronefeld

104

,

F. Grosa

31

,

J.F. Grosse-Oetringhaus

34

,

R. Grosso

104

,

R. Guernane

78

,

B. Guerzoni

27

,

M. Guittiere

113

, K. Gulbrandsen

88

, T. Gunji

130

,

A. Gupta

99

,

R. Gupta

99

,

I.B. Guzman

44

,

R. Haake

34,144

, M.K. Habib

104

, C. Hadjidakis

61

, H. Hamagaki

81

,

G. Hamar

143

,

M. Hamid

6

,

J.C. Hamon

134

,

R. Hannigan

118

,

M.R. Haque

63

, A. Harlenderova

104

,

J.W. Harris

144

,

A. Harton

11

,

H. Hassan

78

,

D. Hatzifotiadou

10,53

,

P. Hauer

42

,

S. Hayashi

130

, S.T. Heckel

69

,

E. Hellbär

69

,

H. Helstrup

36

,

A. Herghelegiu

47

,

E.G. Hernandez

44

,

G. Herrera Corral

9

,

F. Herrmann

142

,

K.F. Hetland

36

,

T.E. Hilden

43

, H. Hillemanns

34

,

C. Hills

127

, B. Hippolyte

134

, B. Hohlweger

103

, D. Horak

37

,

S. Hornung

104

,

R. Hosokawa

78,131

, J. Hota

66

,

P. Hristov

34

,

C. Huang

61

, C. Hughes

128

, P. Huhn

69

,

T.J. Humanic

95

,

H. Hushnud

107

,

N. Hussain

41

,

T. Hussain

17

, D. Hutter

39

,

D.S. Hwang

19

,

J.P. Iddon

127

,

R. Ilkaev

106

, M. Inaba

131

,

M. Ippolitov

87

, M.S. Islam

107

, M. Ivanov

104

,

V. Ivanov

96

, V. Izucheev

90

,

B. Jacak

79

, N. Jacazio

27

,

P.M. Jacobs

79

,

M.B. Jadhav

48

,

S. Jadlovska

115

, J. Jadlovsky

115

,

S. Jaelani

63

,

C. Jahnke

116,120

, M.J. Jakubowska

140

,

M.A. Janik

140

,

C. Jena

85

, M. Jercic

97

,

O. Jevons

108

,

R.T. Jimenez Bustamante

104

, M. Jin

125

,

P.G. Jones

108

,

A. Jusko

108

,

P. Kalinak

65

,

A. Kalweit

34

,

J.H. Kang

145

,

V. Kaplin

91

, S. Kar

6

, A. Karasu Uysal

77

,

O. Karavichev

62

, T. Karavicheva

62

,

P. Karczmarczyk

34

,

E. Karpechev

62

,

U. Kebschull

74

,

R. Keidel

46

,

D.L.D. Keijdener

63

,

M. Keil

34

,

B. Ketzer

42

, Z. Khabanova

89

,

A.M. Khan

6

,

S. Khan

17

,

S.A. Khan

139

,

A. Khanzadeev

96

,

Y. Kharlov

90

,

A. Khatun

17

,

A. Khuntia

49

,

M.M. Kielbowicz

117

,

B. Kileng

36

,

B. Kim

131

,

D. Kim

145

,

D.J. Kim

126

,

E.J. Kim

13

, H. Kim

145

,

J.S. Kim

40

,

J. Kim

102

,

J. Kim

13

,

M. Kim

60,102

, S. Kim

19

,

T. Kim

145

,

T. Kim

145

,

K. Kindra

98

,

S. Kirsch

39

, I. Kisel

39

,

S. Kiselev

64

,

A. Kisiel

140

,

J.L. Klay

5

,

C. Klein

69

,

J. Klein

58

,

C. Klein-Bösing

142

, S. Klewin

102

, A. Kluge

34

,

M.L. Knichel

34

,

A.G. Knospe

125

, C. Kobdaj

114

,

M. Kofarago

143

,

M.K. Köhler

102

,

T. Kollegger

104

, N. Kondratyeva

91

,

E. Kondratyuk

90

,

A. Konevskikh

62

,

P.J. Konopka

34

,

M. Konyushikhin

141

,

L. Koska

115

,

O. Kovalenko

84

,

V. Kovalenko

111

, M. Kowalski

117

,

I. Králik

65

, A. Kravˇcáková

38

,

L. Kreis

104

,

M. Krivda

65,108

,

F. Krizek

93

,

M. Krüger

69

,

E. Kryshen

96

,

M. Krzewicki

39

,

A.M. Kubera

95

, V. Kuˇcera

60,93

, C. Kuhn

134

,

P.G. Kuijer

89

,

J. Kumar

48

, L. Kumar

98

,

S. Kumar

48

,

S. Kundu

85

,

P. Kurashvili

84

,

A. Kurepin

62

, A.B. Kurepin

62

,

S. Kushpil

93

, J. Kvapil

108

,

M.J. Kweon

60

,

Y. Kwon

145

, S.L. La Pointe

39

,

P. La Rocca

28

,

Y.S. Lai

79

,

I. Lakomov

34

,

R. Langoy

123

,

K. Lapidus

144

,

A. Lardeux

21

,

P. Larionov

51

,

E. Laudi

34

,

R. Lavicka

37

,

R. Lea

25

,

L. Leardini

102

,

S. Lee

145

,

F. Lehas

89

, S. Lehner

112

, J. Lehrbach

39

,

R.C. Lemmon

92

, I. León Monzón

119

, P. Lévai

143

,

X. Li

12

,

X.L. Li

6

,

J. Lien

123

,

R. Lietava

108

,

B. Lim

18

, S. Lindal

21

,

V. Lindenstruth

39

,

S.W. Lindsay

127

, C. Lippmann

104

,

M.A. Lisa

95

, V. Litichevskyi

43

,

A. Liu

79

,

H.M. Ljunggren

80

, W.J. Llope

141

, D.F. Lodato

63

, V. Loginov

91

,

C. Loizides

79,94

,

P. Loncar

35

,

X. Lopez

132

,

E. López Torres

8

,

P. Luettig

69

, J.R. Luhder

142

,

M. Lunardon

29

,

G. Luparello

59

, M. Lupi

34

, A. Maevskaya

62

,

M. Mager

34

, S.M. Mahmood

21

, A. Maire

134

,

R.D. Majka

144

,

M. Malaev

96

,

Q.W. Malik

21

,

L. Malinina

75,III

,

D. Mal’Kevich

64

,

P. Malzacher

104

, A. Mamonov

106

,

V. Manko

87

,

F. Manso

132

,

V. Manzari

52

,

Y. Mao

6

, M. Marchisone

129,133

,

J. Mareš

67

,

G.V. Margagliotti

25

,

A. Margotti

53

,

J. Margutti

63

,

A. Marín

104

,

C. Markert

118

, M. Marquard

69

,

N.A. Martin

102,104

,

P. Martinengo

34

,

J.L. Martinez

125

,

M.I. Martínez

44

,

G. Martínez García

113

, M. Martinez Pedreira

34

,

S. Masciocchi

104

,

M. Masera

26

, A. Masoni

54

,

L. Massacrier

61

,

E. Masson

113

,

A. Mastroserio

52,136

,

A.M. Mathis

103,116

,

P.F.T. Matuoka

120

,

A. Matyja

117,128

,

C. Mayer

117

,

M. Mazzilli

33

,

M.A. Mazzoni

57

,

F. Meddi

23

,

Y. Melikyan

91

,

A. Menchaca-Rocha

72

,

E. Meninno

30

,

M. Meres

14

, S. Mhlanga

124

,

Y. Miake

131

, L. Micheletti

26

, M.M. Mieskolainen

43

,

D.L. Mihaylov

103

,

K. Mikhaylov

64,75

,

A. Mischke

63

,

A.N. Mishra

70

,

D. Mi´skowiec

104

,

J. Mitra

139

, C.M. Mitu

68

,

N. Mohammadi

34

,

A.P. Mohanty

63

,

B. Mohanty

85

, M. Mohisin Khan

17,IV

,

D.A. Moreira De Godoy

142

,

L.A.P. Moreno

44

,

S. Moretto

29

,

A. Morreale

113

,

A. Morsch

34

,

T. Mrnjavac

34

,

V. Muccifora

51

,

E. Mudnic

35

,

D. Mühlheim

142

,

S. Muhuri

139

,

M. Mukherjee

3

,

J.D. Mulligan

144

,

M.G. Munhoz

120

,

K. Münning

42

,

R.H. Munzer

69

,

H. Murakami

130

,

S. Murray

73

,

L. Musa

34

,

J. Musinsky

65

,

C.J. Myers

125

, J.W. Myrcha

140

,

B. Naik

48

,

R. Nair

84

,

B.K. Nandi

48

, R. Nania

10,53

,

E. Nappi

52

,

A. Narayan

48

,

M.U. Naru

15

,

A.F. Nassirpour

80

,

H. Natal da Luz

120

,

C. Nattrass

128

,

S.R. Navarro

44

,

K. Nayak

85

,

R. Nayak

48

, T.K. Nayak

139

,

S. Nazarenko

106

,

R.A. Negrao De Oliveira

34,69

,

L. Nellen

70

, S.V. Nesbo

36

,

G. Neskovic

39

, F. Ng

125

,

M. Nicassio

104

,

J. Niedziela

34,140

,

B.S. Nielsen

88

,

S. Nikolaev

87

, S. Nikulin

87

, V. Nikulin

96

,

F. Noferini

10,53

,

P. Nomokonov

75

,

G. Nooren

63

,

J.C.C. Noris

44

,

J. Norman

78

,

A. Nyanin

87

, J. Nystrand

22

,

M. Ogino

81

,

H. Oh

145

, A. Ohlson

102

,

J. Oleniacz

140

,

A.C. Oliveira Da Silva

120

,

M.H. Oliver

144

,

J. Onderwaater

104

,

C. Oppedisano

58

, R. Orava

43

,

M. Oravec

115

,

A. Ortiz Velasquez

70

,

A. Oskarsson

80

,

J. Otwinowski

117

,

K. Oyama

81

, Y. Pachmayer

102

, V. Pacik

88

,

D. Pagano

138

,

G. Pai ´c

70

,

P. Palni

6

,

J. Pan

141

,

A.K. Pandey

48

,

S. Panebianco

135

,

V. Papikyan

1

,

P. Pareek

49

,

J. Park

60

, J.E. Parkkila

126

,

S. Parmar

98

,

A. Passfeld

142

,

S.P. Pathak

125

,

R.N. Patra

139

,

B. Paul

58

, H. Pei

6

,

T. Peitzmann

63

,

X. Peng

6

, L.G. Pereira

71

,

H. Pereira Da Costa

135

, D. Peresunko

87

,

E. Perez Lezama

69

,

V. Peskov

69

,

Y. Pestov

4

, V. Petráˇcek

37

,