The transverse momentum dependence of charged kaon Bose-Einstein correlations in the SELEX experiment

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DOI: 10.1016/j.physletb.2015.12.041

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Contents lists available atScienceDirect

Physics

Letters

B

www.elsevier.com/locate/physletb

The

transverse

momentum

dependence

of

charged

kaon

Bose–Einstein

correlations

in

the

SELEX

experiment

The

SELEX

Collaboration

G.A. Nigmatkulov

i

,

∗

,

A.K. Ponosov

i

,

1

,

U. Akgun

n

,

G. Alkhazov

j

,

J. Amaro-Reyes

l

,

A. Asratyan

f

,

A.G. Atamantchouk

j

,

1

,

A.S. Ayan

n

,

M.Y. Balatz

f

,

1

,

A. Blanco-Covarrubias

l

,

N.F. Bondar

j

,

P.S. Cooper

d

,

L.J. Dauwe

o

,

1

,

G.V. Davidenko

f

,

U. Dersch

g

,

3

,

A.G. Dolgolenko

f

,

G.B. Dzyubenko

f

,

1

_,

_{R. Edelstein}

b

_,

_{L. Emediato}

q

_,

_{A.M.F. Endler}

c

_,

_{J. Engelfried}

l

_,

I. Eschrich

g

,

2

,

C.O. Escobar

q

,

4

,

N. Estrada

l

,

A.V. Evdokimov

f

,

I.S. Filimonov

h

,

1

,

A. Flores-Castillo

l

,

F.G. Garcia

q

,

d

,

I. Giller

k

,

V.L. Golovtsov

j

,

P. Gouffon

q

,

E. Gülmez

a

,

M. Iori

p

,

S.Y. Jun

b

,

M. Kaya

n

,

5

,

J. Kilmer

d

,

V.T. Kim

j

,

L.M. Kochenda

j

,

I. Konorov

g

,

6

,

A.P. Kozhevnikov

e

,

A.G. Krivshich

j

,

H. Krüger

g

,

7

,

M.A. Kubantsev

f

,

V.P. Kubarovsky

e

,

A.I. Kulyavtsev

b

,

d

,

N.P. Kuropatkin

j

,

d

,

V.F. Kurshetsov

e

,

A. Kushnirenko

b

,

e

,

J. Lach

d

,

L.G. Landsberg

e

,

1

,

I. Larin

f

,

E.M. Leikin

h

,

G. López-Hinojosa

l

,

T. Lungov

q

,

V.P. Maleev

j

,

D. Mao

b

,

8

_,

_{P. Mathew}

b

,

9

_,

_{M. Mattson}

b

_,

_{V. Matveev}

f

_,

_{E. McCliment}

n

_,

_{M.A. Moinester}

k

_,

V.V. Molchanov

e

,

A. Morelos

l

,

A.V. Nemitkin

h

,

P.V. Neoustroev

j

,

C. Newsom

n

,

A.P. Nilov

f

,

1

,

S.B. Nurushev

e

,

A. Ocherashvili

k

,

10

,

Y. Onel

n

,

S. Ozkorucuklu

n

,

11

,

A. Penzo

r

,

S.V. Petrenko

e

,

M. Procario

b

,

12

,

V.A. Prutskoi

f

,

B.V. Razmyslovich

j

,

13

,

D.A. Romanov

i

,

V.I. Rud

h

,

J. Russ

b

,

J.L. Sánchez-López

l

,

A.A. Savchenko

i

,

J. Simon

g

,

14

,

G.V. Sinev

i

,

15

,

A.I. Sitnikov

f

,

V.J. Smith

m

,

M. Srivastava

q

,

V. Steiner

k

,

V. Stepanov

j

,

13

,

L. Stutte

d

,

M. Svoiski

j

,

13

,

V.V. Tarasov

f

,

N.K. Terentyev

j

,

b

,

I. Torres

l

,

16

,

L.N. Uvarov

j

,

A.N. Vasiliev

e

,

D.V. Vavilov

e

,

E. Vázquez-Jáuregui

l

,

17

_,

_{V.S. Verebryusov}

f

,

1

_,

_{V.A. Victorov}

e

_,

V.E. Vishnyakov

f

,

A.A. Vorobyov

j

,

K. Vorwalter

g

,

18

,

J. You

b

,

d

,

R. Zukanovich-Funchal

q a_{BogaziciUniversity,Bebek80815Istanbul,Turkey}

*

Correspondingauthor.

E-mailaddress:nigmatkulov@gmail.com(G.A. Nigmatkulov).

1 _Deceased.

2 _{Presentaddress:UniversityofCaliforniaatIrvine,Irvine,CA92697,USA.} 3 _{Presentaddress:AdvancedMaskTechnologyCenter,Dresden,Germany.}

4 _{Presentaddress:InstitutodeFísicadaUniversidadeEstadualdeCampinas,UNICAMP,SP,Brazil.} 5 _{Presentaddress:KafkasUniversity,Kars,Turkey.}

6 _{Presentaddress:Physik-Department,TechnischeUniversitätMünchen,85748Garching,Germany.} 7 _{Presentaddress:TheBostonConsultingGroup,München,Germany.}

8 _{Presentaddress:LucentTechnologies,Naperville,IL,USA.} 9 _{Presentaddress:BaxterHealthcare,RoundLake,IL,USA.} 10 _{Presentaddress:NRCN,84190Beer-Sheva,Israel.}

11 _{Presentaddress:SüleymanDemirelUniversitesi,Isparta,Turkey.} 12 _{Presentaddress:DOE,Germantown,MD,USA.}

13 _{Presentaddress:Solidum,Ottawa,Ontario,Canada.} 14 _{Presentaddress:SiemensHealthcare,Erlangen,Germany.} 15 _{Presentaddress:DukeUniversity,Durham,NC27708,USA.}

16 _{Presentaddress:InstitutoNacionaldeAstrofísica,ÓpticayElectrónica,Tonantzintla,Mexico.} 17 _{Presentaddress:SNOLAB,Canada.}

18 _{Presentaddress:AllianzInsuranceGroupIT,München,Germany.}

http://dx.doi.org/10.1016/j.physletb.2015.12.041

0370-2693/©2015TheAuthors.PublishedbyElsevierB.V.ThisisanopenaccessarticleundertheCCBYlicense(http://creativecommons.org/licenses/by/4.0/).Fundedby SCOAP3_.

b_{Carnegie–MellonUniversity,Pittsburgh,PA15213,USA} c_{CentroBrasileirodePesquisasFísicas,RiodeJaneiro,Brazil} d_{FermiNationalAcceleratorLaboratory,Batavia,IL60510,USA} e_{InstituteforHighEnergyPhysics,Protvino,Russia}

f_{InstituteofTheoreticalandExperimentalPhysics,Moscow,Russia} g_{Max-Planck-InstitutfürKernphysik,69117Heidelberg,Germany} h_{MoscowStateUniversity,Moscow,Russia}

i_{NationalResearchNuclearUniversityMEPhI(MoscowEngineeringPhysicsInstitute),Moscow,Russia} j_{PetersburgNuclearPhysicsInstitute,St.Petersburg,Russia}

k_{TelAvivUniversity,69978RamatAviv,Israel}

l_{UniversidadAutónomadeSanLuisPotosí,SanLuisPotosí,Mexico} m_{UniversityofBristol,BristolBS81TL,UnitedKingdom} n_{UniversityofIowa,IowaCity,IA52242,USA} o_{UniversityofMichigan-Flint,Flint,MI48502,USA} p_{UniversityofRome“LaSapienza”andINFN,Rome,Italy} q_{UniversityofSãoPaulo,SãoPaulo,Brazil}

r_{UniversityofTriesteandINFN,Trieste,Italy}

a

r

t

i

c

l

e

i

n

f

o

a

b

s

t

r

a

c

t

Articlehistory:

Received20January2015

Receivedinrevisedform14November2015 Accepted14December2015

Availableonline18December2015 Editor:M.Doser Keywords: Correlationfemtoscopy HBTintensityinterferometry Kaon–kaoninteractions Bose–Einsteincorrelations

We report the measurement of the one-dimensional charged kaon correlation functions using 600 GeV/c

−,

π

− and 540 GeV/c p beams

from the SELEX (E781) experiment at the Fermilab Tevatron.

K±K±

correlation functions are studied for three transverse pair momentum, kT, ranges and parameterized by a Gaussian form. The emission source radii, R,

and the correlation strength,

λ, are extracted. The analysis

shows a decrease of the source radii with increasing kaon transverse pair momentum for all beam types.

©2015 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/). Funded by SCOAP3_.

1. Introduction

Inthispaper we presentresultsfrom K±K± correlation fem-toscopy studyin600 GeV

/

c



−C

(

C u

)

,

π

−C

(

C u

)

and540GeV

/

c pC

(

C u

)

interactions fromtheSELEX (E781) experiment[1]atthe Fermilab Tevatron. The correlation femtoscopy method allows to studyspatio-temporalcharacteristicsoftheemissionsourceatthe levelof1fm

=

10−15_{m.ThemethodisbasedontheBose–Einstein}

enhancementof identicalboson productionatsmallrelative mo-mentum. The quantum statistics correlations were first observed asan enhanced productionofthe identicalpionpairswithsmall opening angles in proton–antiproton collisions [2]. In 1960 this

enhancement was explained by the symmetrization of the

two-particle wave function by G. Goldhaber, S. Goldhaber, W.-Y. Lee, and A. Pais (GGLP effect) [3]. Later, in the 1970s, Kopylov and Podgoretsky suggested studying the interference effect in terms ofthe correlation function. They proposed the mixing technique to constructthe uncorrelated referencesample, andclarified the roleofthespace–timecharacteristicsofparticleproduction[4–6]. Subsequently, two-particle correlations at small relative momen-tum were systematically studied for lepton–lepton [7], lepton-hadron[8],hadron–hadron[9],andheavy-ion[10,11]collisions.It was foundthat thesystemcreated inheavy-ioncollisions under-goesthecollectiveexpansionandmaybedescribedbyrelativistic fluid dynamics[12–15].By using thewidth of thequantum sta-tisticalenhancement,onecanmeasuretheradii R oftheemitting source.The decreaseofthe extractedradiiwithincreasing

trans-versepair momentummaybe interpreted asthedecrease ofthe

“homogeneitylengths”[16]duetocollectivetransverseflow.

A comparison of femtoscopic measurements in lepton and

hadron-induced[17,18] collisionswithheavy-ioncollisions shows similar systematics [19,20]. These studies usually performed for

pions. However, measurements of heavier particles may provide

additional information aboutthe size, orientation anddynamical timescalesoftheemissionregion.

2. Experimentalsetupanddataselection

TheSELEX(E781) detectorisathree-stage magnetic spectrom-eterdesignedforcharmhadroproductionstudyat xF

>

0

.

1 (xF

=

pZ

pZ max). We report the analysis of 1 billion events of 600 GeV

/

c



−C

(

C u

)

,

π

−C

(

C u

)

and540GeV

/

c p C

(

C u

)

interactionsrecorded duringthe1996–1997fixedtargetrun.About2

/

3,1

/

6 and1

/

6 of thedatawereobtainedon



−,

π

−andp beams,respectively.

Thebeamparticlewasidentified asa mesonorabaryon bya transition radiation detector. Interactionsoccurred on segmented

targets, which consisted of 2 copper and 3 diamond foils

sep-arated by 1.5 cm clearance, and had a total thickness of 5% of an interaction length forprotons. Particles were tracked ina set of 20 vertex Silicon Strip Detectors (SSD) arranged in 4 sets of planeswithastrippitchof20–25μm,rotatedby45◦.Eachofthe detectors has a hit detection efficiency greater than 98%. Trans-versevertexpositionresolution (

σ

) was4 μm forthe600GeV

/

c beam tracks. The average longitudinal vertex position resolution

was 270 μm for primary vertex and560 μm forsecondary

ver-tex. The detector geometry covers the forward 150 m rad cone.

The particlemomentum wasmeasured by deflectionofthe track

positionby twomagnetsM1 andM2 inasystemofproportional

wire chambersand silicon strip detectors.Momentum resolution of a typical 100 GeV

/

c track was

σ

p

/

p

≈

0

.

5%. A Ring Imaging

Cherenkov detector (RICH) performed particle identification in a

wide momentum rangeandprovided 2

σ

K

/

π

separation up to

165GeV

/

c andsingletrackringradiusresolutionof1.4%[21].The kaonidentificationefficiencywasover90%abovethekaon thresh-old(

≈

43GeV

/

c).TheaveragenumberoftracksreachingtheRICH wasabout5perevent[22].Thelayoutofthespectrometeris de-scribedelsewhere[1].

Fig. 1. Single K± purityas afunctionofmomentum (a)andthe average trans-versepairmomentumdependenceoftheK±pairpurityforthe−(circles),π−

(squares)andp(crosses)beams(b).

In thisanalysis we used primary tracks that have vertex

sili-contracksegmentmatchedwithdownstreamsegmentsmeasured

in the M1 andM2 spectrometers, with the momentum from45

to160GeV

/

c.Inorderto reducethecontamination ofsecondary particles, it was required that the extrapolated trackdistance to theprimary vertexwas lessthan15 μm in thetransverse plane. OnlytracksthatmatchedtheRICHdetectorwereusedinthe anal-ysis. Charged kaons were identified with the likelihood to be a kaon at least three times exceeding any other particle hypothe-sis. Fig. 1(a) shows the single kaon purity as a function of the

momentum for the



−,

π

− and p beams. It is defined as the

fractionoftheacceptedkaontracks thatcorrespondtotruekaon particles.The single particle puritywas estimatedfromthe RICH ringradiusdistributions ofthedataandbystudyingPYTHIA[23]

simulationswiththeparticleembeddingthroughthedetector.The

main contamination for charged kaons in the momentum range

p

>

120GeV

/

c comesfrompions,becauseofthe closeringradii intheRICHdetector.

Theelectronswereeliminatedfromtheanalysisusingthe tran-sitionradiationdetector(ETRD)that wasplaced beforeRICH.The contaminationfromother particlespeciesinthestudied momen-tum range is negligible. Fig. 1(b) shows the charged kaon pair purityas afunction of theaverage transverse momentum ofthe pairobtained forthe



−,

π

− and p beams. The K± pair purity iscalculatedasaproductoftwosingle-particlepuritiesusingthe experimentalmomentumdistributions.

Afterapplyingthecuts 4 842 147,597 101and103 551 identi-cal charged kaon pairs were selected for



−,

π

− and p beams, respectively.

3. Correlationfemtoscopy

Thetwo-particle correlationfunction isdefinedasthe ratioof theprobabilitytomeasuretwoparticleswithmomenta



p1and



p2

totheirsingleparticleprobabilities:

C

(



p1

,

p



2

)

=

P

(



p1

,



p2

)

P

(



p1

)P

(



p2

)

.

(1)

Experimentally, one studies the correlation function C

(



q

,

K



)

in termsofrelativemomentum



q

= 

p1

− 

p2 andaveragemomentum



K

= (

p1

+ 

p2

)/

2 oftwoparticles: C

(



q, K

)

=

A(



q, K

)

B(q, 



K)

·

D(



q, K

),

(2)

where A

(

q



,

K



)

isthemeasureddistributionofrelativemomentum withinthesameevent,B

(



q

,

K



)

isthereferenceorbackground dis-tributionthatissimilar totheexperimentaldistributioninall

re-spectsexceptforthepresenceoffemtoscopiccorrelations.The ref-erencesampleisusuallyformedfromparticlesthatcomefrom dif-ferentevents(eventmixingtechnique[6]).Thequantity D

(



q

,

K



)

is a so-calledcorrelationbaseline thatdescribesallnon-femtoscopic correlations, such as, forinstance,the correlationscaused by the energyandmomentumconservation-inducedcorrelations[24].In order to eliminate possiblebiases dueto theconstruction of the reference samples, the measured correlation functionswere cor-rected on thesimulated distributions by constructing the double ratio: R

(Q

)

=



dNK±K±

/d Q

dNref

/d Q



/



dNMC,K±K±

/d Q

dNMC,ref

/d Q



,

(3)

wherethesubscripts“MC”and“MC

,

ref ”correspondtothe simu-lateddata.

By virtue of thelimited statistics available for the

π

− and p beams,only theone-dimensionalfemtoscopicchargedkaon anal-ysisofcorrelationfunctionsintermsofinvariantrelative momen-tum, Q

=



(



p1

− 

p2

)

2

− (

E1

−

E2

)

2, was performed. In order to

extract thesize oftheemission region, R,one can usethe Gold-haber parametrization. This assumes that the emitting source of identicalbosonsisdescribedbyasphericalGaussiandensity func-tion: C(Q

)

=

N



1

+ λ

e−R2Q2



·

D(Q

),

(4)

where N is a normalization factor,

λ

describes the correlation strength, and D

(

Q

)

is the baseline distribution. In the current analysis,thesecondorderpolynomial,D

(

Q

)

=

1

+

a Q

+

b Q2_,was

used for estimation of the baseline distribution. The momentum correlations ofparticles emitted at nuclear distancesare also in-fluencedbytheeffectoffinal-stateinteraction(FSI),Coulomband stronginteractions[25–28].Foridenticalkaons,theeffectofstrong interactionsisnegligible[29].Thecorrelationfunctionofidentical bosonsshouldincreaseatlowrelativemomentum,exceptforsmall valueswhereCoulombinteractionbecomesdominant.Thismaybe takenintoaccountbymodifyingEq.(4):

C(Q

)

=

N



(

1

− λ) + λ

K

(Q

)



1

+

e−R2Q2



·

D(Q

),

(5)

wherethefactorK

(

Q

)

isthesquaredlike-signkaonpairCoulomb wavefunctionintegratedoverasphericalGaussiansource[30–32].

4. Resultsanddiscussions

The results discussed in this Letter were obtained with the same detector setup, cuts and fitting procedures, giving an op-portunity to compare the properties of the emission region for different hadron-induced collisions. The analysis was performed for three averagetransverse pair momentum kT

=



pT 1

+ 

pT 2



/

2

ranges:

(

0

.

00–0

.

30

),

(

0

.

30–0

.

55

),

(

0

.

55–1

.

00

)

GeV

/

c and forthe three beamtypes:



−,

π

−, p. The event mixing technique was used toconstruct theuncorrelatedreferencesample. Onlyevents withtwoormoreidenticalchargedkaons,groupedbyproduction target,wereusedintheeventmixing.Kaonsfromadjacentevents foreachtarget werecombinedtoprovideanuncorrelated experi-mentalbackground.Duetosmalldifferencesinthemeasured cor-relationfunctions,thepositiveandnegativekaonfour-momentum distributionswerecombinedinthenumeratorandthe denomina-tor beforeconstructing theratio.A puritycorrection was applied totheexperimentalcorrelationfunctionsaccordingtothe expres-sion:

C(Q

)

=

Cexperimental

(Q

)

−

1

P(Q

)

+

1

,

(6)

Fig. 2. Toprowshowstheexperimental(fullcircles)andPYTHIA-generated(open circles) correlation functions ofidentical kaonsobtained from using the event mixedreferencesamples.Thebottomrowshowsthefitstothedoubleratios ac-cordingtoEq.(5).Thesecondorderpolynomialwasusedforestimationofthe non-femtoscopiceffects.Thecorrelationfunctions aremeasured for0.30<kT<

0.55GeV/c rangeandcolumnsfromlefttorightrepresentthedataobtainedfor

−,π−andp beams,respectively.

The top rowofthe Fig. 2 showsthe experimental correlation functions(solidcircles) afterapplying thepurity correction mea-sured in the 0

.

30

<

kT

<

0

.

55 GeV

/

c region for



−,

π

− and

p beams. The correlation functions were normalized such that C

(

Q

)

=

1 for 0

.

5

<

Q

<

0

.

7GeV

/

c,where Bose–Einstein correla-tionsare absent andtheinfluenceofthe non-femtoscopiceffects issmall.The deviationof thecorrelation functionsfrom unityat Q

>

0

.

7 GeV

/

c corresponds to the non-femtoscopic correlations andthewell-definedenhancementatQ

<

0

.

4GeV

/

c isduetothe quantum statisticalcorrelations. The Coulomb repulsionbetween like-signkaons leads tothe decrease ofthe correlation functions atQ

<

0

.

1GeV

/

c.

Inordertocorrectfornon-femtoscopiceffects,theMonteCarlo event generator PYTHIA-6.4.28 [23] with different tunes

(Peru-gia 0, Perugia 2010 and Perugia 2011 [33]) was used. PYTHIA

contains neitherBose–Einstein correlationsnorthe final-state in-teractions. On the other hand, PYTHIA contains other kinematic effects,for instance,energyand momentum conservationeffects, that could lead to baseline correlations. The Perugia 2011 tune, which best describes charged-particle multiplicity, was used as

the main minimum-bias MC sample. The top row of the Fig. 2

showsthe comparison of simulatedcorrelation functions(empty circles), where PYTHIA events were filtered through the analysis cuts, withtheexperimental distributions (solid circles) measured for0

.

30

<

kT

<

0

.

55 GeV

/

c range. ThePYTHIA-generated

correla-tionfunctionswerenormalizedinthesamewayasthe experimen-talcorrelationfunctions.

It is seen that PYTHIA qualitatively describes the experimen-tal baseline in the region Q

>

0

.

5 GeV

/

c, where the effect of femtoscopic correlations is negligible. Since the MC calculation doesnotincludewavefunctionsymmetrizationforidentical parti-cles,thefemtoscopicpeakatlowrelativefour-momentumregion, Q

<

0

.

4GeV

/

c,isabsent.

Thebottom row ofthe Fig. 2showsdouble ratios, wherethe

experimental correlation functions are divided by the

PYTHIA-generated ones, obtained for the



−,

π

− and p beams in the 0

.

30

<

kT

<

0

.

55GeV

/

c region.Thedoubleratioswerefittedusing

Eq.(5).In the currentanalysis, theCoulomb function K

(

Q

)

was integratedoverasphericalsourceof1 fm.Duetoimperfectionsof thesimulationinthe Q

>

0

.

7GeV

/

c region,thenon-femtoscopic termD

(

Q

)

=

1

+

a Q

+

b Q2_wasused.

Fig. 3. Thecorrelationfunctionsconstructedwithrotatedparticles(toppanel)and opposite-chargepairs(bottompanel)for0.30<kT<0.55GeV/c range.Therange

0.19<Q<0.35GeV/c onthebottompanelisexcludedfromfitsduetothe contri-butionfromtheφ(1020)mesondecay.ThefitswereperformedusingEq.(5).The columnsrepresent−(left),π−(middle)andp (right)beams.

Table 1

Systematicuncertainty(minimalandmaximal)valuesfordifferentsourcesof sys-tematicuncertainty(inpercent).Thevaluesofminimum(maximum)uncertainty canbefromdifferentaveragetransversepairmomentumrangeorthebeamtype, butfromaspecificsource.

The systematic uncertainty source λ(%) R (%)

Event/particle selection 1–7 1–9

PID and purity 0–4 0–6

Fit range 1–5 1–4 Momentum resolution 0–1 0–1 Two-track effects – – Non-femtoscopic form 0–4 1–11 Coulomb function – – Reference sample 1–8 5–13 Total 2–13 5–21

To estimate the influence of choice of the reference sample, thedifferentmethodsofconstructinguncorrelatedchargedparticle distributions wereused:opposite-chargepairs androtatedparticles, where pairs are constructed after inverting the x and y compo-nents ofthe three-momentum ofone ofthe twoparticles. Fig. 3

showsthedoubleratiosobtainedfromusingrotatedparticles(top panel) and opposite-charge pairs (bottom panel) reference sam-ples. The doubleratios were fittedusing Eq.(5);and thesecond orderpolynomial,D

(

Q

)

=

1

+

a Q

+

b Q2_{,wasusedtodescribethe}

non-femtoscopicterm.Itwasfoundthattheextractedfemtoscopic parameters,

λ

and R,obtainedfromusingrotated particles refer-encesamplesaresimilartothosefromtheeventmixedones.

The reference samples constructed from the opposite-charge

kaon pairs contain peaks coming from strong resonance decays;

andare influenced by the Coulomb attractionat Q

<

0

.

1 GeV

/

c. Themagnitudesoftheresonancepeaksmeasuredfortherealand simulated correlation functions were found to be different. This can be explained by the absence of the final-state rescattering ofparticles inPYTHIA.Thedoubleratios obtainedforunlike-sign kaonpairswerefittedthesamewayastheeventmixedones.The range 0

.

19

<

Q

<

0

.

35 GeV

/

c was excluded from fits dueto the

φ (

1020

)

mesondecayandbecausetheinfluenceofthefinal-state

interactions between opposite-charge kaon pairs was not taken

intoaccount.

The differentsources ofsystematicuncertainties werestudied foreachkT rangeandbeamtype.Table 1showsthemaximaland

minimal valuesofsystematicuncertaintythat correspondto spe-cific uncertainty sources. The values of the total uncertainty are

Table 2

K±K±sourceparametersfor−,π−andp beams.Statisticalandsystematicuncertaintiesarepresented.

Beam type kT(GeV/c) χ2/Ndof N λ R (fm) a (GeV/c−1) b (GeV/c−2)

− (0.00–0.30) 126/45 1.23±0.01 0.71±0.02±0.08 1.32±0.02±0.07 −0.59±0.02 0.38±0.02 (0.30–0.55) 85/45 1.18±0.01 0.66±0.02±0.08 1.18±0.02±0.05 −0.47±0.03 0.28±0.02 (0.55–1.00) 142/45 1.05±0.03 0.66±0.04±0.10 0.98±0.03±0.04 −0.22±0.08 0.13±0.05 π− (0.00–0.30) 62/45 1.19±0.03 0.67±0.06±0.09 1.25±0.06±0.06 −0.49±0.07 0.31±0.05 (0.30–0.55) 66/45 1.21±0.04 0.69±0.06±0.06 1.13±0.06±0.06 −0.46±0.09 0.24±0.07 (0.55–1.00) 58/45 1.34±0.07 0.44±0.10±0.11 1.16±0.19±0.14 −0.71±0.09 0.42±0.09 p (0.00–0.30) 65/45 1.51±0.06 0.98±0.17±0.13 1.54±0.16±0.17 −0.97±0.10 0.62±0.08 (0.30–0.55) 62/45 1.39±0.12 0.80±0.15±0.13 1.32±0.12±0.15 −0.72±0.13 0.40±0.11 (0.55–1.00) 43/44 1.26±0.16 0.91±0.24±0.11 1.13±0.17±0.11 −0.61±0.31 0.37±0.24

notnecessarilyequaltothequadraticsumofalltheuncertainties duetothe factthat they cancomefromdifferentbeamtypesor averagetransversepairmomentumranges.

Theuncertaintyduetothefitrangewas estimatedbyvarying theupperlimitofthefitfromQ

=

1GeV

/

c toQ

=

0

.

6GeV

/

c.The lowestvalueoftheupperlimitofthefitrangecorrespondstothe endofthecorrelationregion.ChangingtheradiusoftheCoulomb sourceintherangefrom0.5 fmto1.5 fmhasnegligibleeffecton theextractedemittingsourceparameters.

Different baseline shapes [34–36] were used to estimate the systematicuncertaintyduetothebaselinedetermination:

D(Q

)

=

1

,

(7)

D(Q

)

=

1

+

a Q

,

(8)

D(Q

)

=

1

+

e−a Q2

,

(9)

D(Q

)

=



1

+

a Q2

₊

_{b Q}4

_.

₍₁₀₎

The smearingof single particle momentawas studied by

em-beddingsimulatedkaontrackswithknownmomentathroughthe

detector. Experimental correlation functions were corrected for momentumresolutionusingtheexpression:

Ccorr

(

Q

)

=

Cuncorr

(Q

)C

unsmeared

(

Q

)

Csmeared

(

Q

)

,

(11)

whereCcorr(Q

)

isthecorrectedcorrelationfunctionandCuncorr(Q

)

represents the measured correlation function. The Cunsmeared(Q

)

and Csmeared(Q

)

are the correlation functions without and with takingintoaccountthemomentumresolutioneffect,respectively. Thesmearing ofthesingle particlemomenta leads tothe smear-ing ofthe correlation function inthe Q

<

0

.

2 GeV

/

c range. This decreasestheamplitudeofthepeak andmakesitwider.The sys-tematic uncertainty of this effect does not exceed 1%. The two-trackreconstructioneffects:“merging”,whentwotracksare recon-structedasone;and“splitting”,whenonetrackisreconstructedas two,werestudiedandfoundtobenegligible.

The main systematic uncertainty arises from using different methods of constructing the uncorrelated reference sample. The

dominant contribution comes from using opposite-charge kaon

pairs. The contamination of the “reference sample” uncertainty fromusingdifferentPYTHIAtunesdoesnotexceed5%.

Thesystematic errorson R and

λ

foreach beamtype andkT

rangeare takenasthe rmsspread ofthevaluesobtainedforthe differentsourcesofsystematicuncertainty.

The results of fits of R

(

Q

)

based on the parametrization of Eq.(5)with D

(

Q

)

=

1

+

a Q

+

b Q2 aregiveninTable 2.The ex-tractedsource radiiandcorrelation strengthfor



− (circles),

π

−

(squares)andp (stars)beamsasafunctionoftransversepair mo-mentumareshowninFigs. 4(a)and4(b),respectively.Thesource radii slightlydecrease withincreasing kT forall the beamtypes,

exceptthehighestaveragetransversepairmomentumintervalfor

Fig. 4. K±K± sourceparametersR (a)and λ(b)measuredfor− (circles),π−

(squares)andp (stars)beamsasafunctionoftransversepairmomentum,kT.

Sta-tistical(lines)andsystematic(boxes)uncertaintiesareshown.

the

π

−beam.The femtoscopicradiimeasuredfor



−,

π

−and p beamsareconsistentwithintheuncertainties.Thesmalldifference betweenmeasuredsourceparameters probablyarisesfrom differ-entcontaminationfromresonancedecays[37].

The decreaseofthe sourceradii withtransversepair momen-tum was previously observed in heavy-ion collisions and inter-pretedasacollectivehydrodynamicbehavior(collectiveflow)[38, 39].Thefirstdirectcomparisonofcorrelationfemtoscopyinp

+

p and heavy-ion collisions under the same detectorconditions, re-construction,analysisandfittingprocedureswasperformedbythe STAR collaboration [20]. It was shown that p

+

p collisions also have the transverse momentum scaling.Although the interpreta-tionoftheseresultsisstillunclear, thesimilaritiescould indicate aconnectionbetweentheunderlyingphysics.

The transverse momentum dependence was alsoobserved for

π π

ine+e−[40,41]andpp collisions[20,35,42].Forthefirsttime a similar analysis of chargedkaon Bose–Einstein correlations for

more thanone transversepairmomentumandmultiplicity range

was recently performed by the ALICE collaboration at the LHC

in pp collisions at

√

s

=

7 TeV [34]. It was shown that charged

kaon femtoscopicradii decrease withtransverse pair momentum

formiddleandhighmultiplicityranges.

There are several possible processes that maylead to the kT

dependenciesinthehadroniccollisions:

1. Thespace–momentum dependenceof thefemtoscopic radii

maybegeneratedbylong-livedresonances [43].Inparticularthis mayplayasignificantroleinhighmultiplicitybins,wherethebulk collectiveflowispredicted[44].

2. Humanic’s model [45], based on space–time geometry

of hadronization and effects of final-state rescattering between hadrons, reproducesbothmultiplicityandtransversemass depen-dencemeasuredattheTevatron[46].

3. In small systems,the string fragmentation should generate momentum andspacecorrelations,such askT dependenceofthe

source radii. However, there are almost no quantitative predic-tionsthatmaybedirectlycomparedwithdataexceptthe

τ

-model

in which space–time and momentum space are strongly

corre-lated[47].Moreover, the Lund stringmodelis not ableto repro-ducethemassdependenceoftheradii[17,48–50].

4.HydrodynamicbulkcollectiveflowmayleadtoakT

depen-dencethatisverysimilartothatfromheavy-ioncollisions. Takingtheaforementionedpossibilities,theoriginofthe

trans-verse pair momentum dependence of the femtoscopic radii in

hadroniccollisions is still unclear. Further theoretical studies are neededinordertounderstandtheunderlyingphysics.

5. Summary

Charged kaon Bose–Einstein correlations were measured in

the SELEX experiment. One-dimensional charged kaon

correla-tion functions in terms of the invariant four-momentum

dif-ference were constructed for



−,

π

− and p beams and three transversepair momentum ranges:

(

0

.

00–0

.

30

),

(

0

.

30–0

.

55

)

and

(

0

.

55–1

.

00

)

GeV

/

c.Thesourceparametersofcorrelationstrength,

λ

,andsource radii, R, wereextractedforall beamtypesandfor

the three average transverse pair momentum ranges. The slight

decreaseofthefemtoscopicradiiwithpairtransversemomentum was observedforall three beamtypes,exceptforthe highestkT

range of the

π

− beam. The values of the emitting source radii obtainedfor



−,

π

− and p beamsareconsistent withinthe un-certainties.

Acknowledgements

TheauthorsareindebtedtothestaffofFermiNational Acceler-atorLaboratoryandforinvaluabletechnicalsupportfromthestaffs of collaborating institutions. This project was supported in part

by Bundesministerium für Bildung, Wissenschaft, Forschung und

Technologie,ConsejoNacionalde CienciayTecnología (CONACyT),

Conselho Nacional de Desenvolvimento Científico e Tecnológico,

FondodeApoyoalaInvestigación(UASLP),FundaçãodeAmparoà PesquisadoEstadodeSãoPaulo(FAPESP),theIsraelScience Foun-dationfoundedbytheIsraelAcademyofSciencesandHumanities, IstitutoNazionale diFisica Nucleare(INFN), theInternational Sci-enceFoundation(ISF),theNationalScienceFoundation,NATO,the RussianAcademyofSciences,theRussianMinistryofScienceand Technology, the Russian Foundation for Basic Research (research project No. 11-02-01302-a), the Secretaría de Educación Pública (Mexico),theTurkish Scientific andTechnological ResearchBoard (TÜB˙ITAK),andtheU.S.DepartmentofEnergy.WethankITEPand NationalResearchNuclear UniversityMEPhI(MoscowEngineering PhysicsInstitute)forprovidingcomputingpowersandsupportfor dataanalysisandsimulations.

TheauthorsalsowouldliketothankProf.MichaelLisaandProf. RichardLednickýforhelpfulcommentsandfruitfuldiscussions.

References

[1]J.S. Russ,N. Akchurin,V.A. Andreev,et al., Firstcharmhadroproduction re-sultsfromSELEX,in:ICHEP’98Proc.Int.Conf.onHighEnergyPhysicsII,1998, p. 1259,arXiv:hep-ex/9812031.

[2]G. Goldhaber, W.B. Fowler, S. Goldhaber, T.F. Hoang, T.E. Kalogeropoulos, W.M. Powell, Pion–pioncorrelations inantiprotonannihilation events,Phys. Rev.Lett.3(1959)181–183.

[3]G.Goldhaber,S.Goldhaber,W.Lee,A.Pais,InfluenceofBose–Einsteinstatistics ontheantiproton–protonannihilationprocess,Phys.Rev.120(1960)300–312.

[4]G.I.Kopylov, M.I.Podgoretsky,Correlationsofidentical particlesemittedby highlyexcitednuclei,Sov.J.Nucl.Phys.15(1972)219–223.

[5]G.I.Kopylov,M.I.Podgoretsky,Multipleproductionandinterferenceofparticles emittedbymovingsources,Sov.J.Nucl.Phys.18(1974)336–341.

[6]G.I.Kopylov,Likeparticlecorrelationsasatooltostudythemultiple produc-tionmechanism,Phys.Lett.B50(1974)472–474.

[7]G.Abbiendi,etal.,Transverseand longitudinalBose–Einsteincorrelationsin hadronicZ0_{decays,Eur.Phys.J.C16(2000)423–433,arXiv:hep-ex/0002062.} [8]S. Chekanov,et al., Bose–Einstein correlations in one and two dimensions

indeepinelasticscattering,Phys.Lett.B583(2004)231–246,arXiv:hep-ex/ 0311030.

[9]K.Aamodt,etal.,Two-pionBose–Einsteincorrelationsinpp collisionsat√s= 900GeV,Phys.Rev.D82(2010)052001,arXiv:1007.0516.

[10]H.Beker,etal.,mTdependenceofbosoninterferometryinheavyioncollisions attheCERNSPS,Phys.Rev.Lett.74(1995)3340–3343.

[11]L.Adamczyk,etal.,Beam-energy-dependenttwo-pioninterferometryandthe freeze-outeccentricityofpionsmeasuredinheavyioncollisionsattheSTAR detector,Phys.Rev.C92(2015)014904,arXiv:1403.4972[nucl-ex].

[12]J.Adams,etal.,Experimentalandtheoreticalchallengesinthesearchforthe quark–gluonplasma:theSTARCollaboration’scriticalassessmentofthe evi-dencefromRHICcollisions,Nucl.Phys.A757(2005)102–183,arXiv:nucl-ex/ 0501009.

[13]K. Adcox,et al.,Formation ofdensepartonicmatterinrelativisticnucleus– nucleuscollisionsatRHIC:experimentalevaluationbythePHENIX Collabora-tion,Nucl.Phys.A757(2005)184–283,arXiv:nucl-ex/0410003.

[14]B.B.Back,etal.,ThePHOBOSperspectiveondiscoveriesatRHIC,Nucl.Phys.A 757(2005)28–101,arXiv:nucl-ex/0410022.

[15]I.Arsene,etal.,Quark–gluonplasmaandcolorglasscondensateatRHIC?The perspective fromthe BRAHMS experiment, Nucl. Phys. A757 (2005)1–27, arXiv:nucl-ex/0410020.

[16]S.V.Akkelin,Y.M.Sinyukov,TheHBT-interferometryofexpandingsources,Phys. Lett.B356(1995)525–530.

[17]G.Alexander,I.Cohen,E.Levin,Thedependenceoftheemissionsizeonthe hadronmass,Phys.Lett.B452(1999)159–166,arXiv:hep-ph/9901341.

[18]W.Kittel,Bose–Einsteincorrelationsin Z fragmentationandotherreactions, ActaPhys.Pol.B32(2001)3927–3972,arXiv:hep-ph/0110088.

[19]Z.Chaje¸cki,Femtoscopyinhadronandleptoncollisions:RHICresultsandworld systematics,ActaPhys.Pol.B40(2009)1119–1136,arXiv:0901.4078.

[20]M.M.Aggarwal,etal.,Pionfemtoscopyinp+p collisionsat√s=200GeV, Phys.Rev.C83(2011)064905,arXiv:1004.0925.

[21]J.Engelfried,etal.,TheSELEXphototubeRICHdetector,Nucl.Instrum.Methods A431(1999)53–69,arXiv:hep-ex/9811001.

[22]J.Engelfried,etal.,TheE781(SELEX)RICHdetector,Nucl.Instrum.MethodsA 409(1998)439–442.

[23]T.Sjöstrand,S.Mrenna,P.Skands,PYTHIA6.4physicsandmanual,J.High En-ergyPhys.05(2006)026,arXiv:hep-ph/0603175v2.

[24]Z.Chaje¸cki,M.Lisa,Globalconservationlawsandfemtoscopyofsmallsystems, Phys.Rev.C78(2008)064903,arXiv:0803.0022.

[25]R.Lednický,V.L.Lyuboshitz,B.Erazmus,D.Nouais,Howtomeasurewhichsort ofparticleswasemittedearlierandwhichlater,Phys.Lett.B373(1996)30–34.

[26]S.Voloshin,R.Lednický,S.Panitkin,N.Xu,Relativespace–timeasymmetriesin pionandnucleonproductioninnoncentralnucleus–nucleuscollisionsat high-energies,Phys.Rev.Lett.79(1997)4766–4769,arXiv:nucl-th/9708044.

[27]S.Pratt,Shapesandsizesfromnon-identical-particlecorrelations,Braz.J.Phys. 37(2007)871–876,arXiv:nucl-th/0612006.

[28]R.Lednický,Finite-sizeeffectontwo-particleproduction,J.Phys.G,Nucl.Part. Phys.35(2008)125109.

[29]R.Lednický,V.V.Lyuboshitz,V.L.Lyuboshitz,Final-stateinteractionsin multi-channelquantumsystemsandpaircorrelationsofnonidenticalandidentical particlesatlowrelativevelocities,Phys.At.Nucl.61(1998)2050–2063.

[30]M.G.Bowler,CoulombcorrectionstoBose–Einsteincorrectionshavegreatly ex-aggerated,Phys.Lett.B270(1991)69–74.

[31]Y.Sinyukov,R.Lednický,S.V.Akkelin,J.Pluta,B.Erazmus,Coulombcorrections toBose–Einsteincorrectionshavegreatlyexaggerated,Phys.Lett.B432(1998) 248–257.

[32]J.Adams,etal.,PioninterferometryinAu+Au collisionsat√sN N=200GeV, Phys.Rev.C71(2005)044906,arXiv:nucl-ex/0411036.

[33]P.Z.Skands,TuningMonteCarlogenerators:thePerugiatunes,Phys.Rev.D82 (2010)074018,arXiv:1005.3457.

[34]B.Abelev,etal.,Chargedkaonfemtoscopiccorrelationsinpp collisionsat√s= 7TeV,Phys.Rev.D87(2013)052016,arXiv:1212.5958v2.

[35]V.Khachatryan,etal.,MeasurementofBose–Einsteincorrelationsinpp col-lisions at √s= 0.9and 7TeV,J. HighEnergyPhys. 05(2011)029,arXiv: 1101.3518.

[36]S.V.Akkelin,Y.M.Sinyukov,Decipheringnonfemtoscopictwo-pioncorrelations in p+p collisionswith simple analytical models, Phys. Rev.D 85 (2012) 074023,arXiv:1106.5120.

[37]R.Lednický,T.B.Progulova,InfluenceofresonancesonBose–Einstein correla-tionsofidenticalpions,Z.Phys.C55(1992)295–305.

[38]M. Lisa, S. Pratt, R. Soltz,U. Wiedemann, Femtoscopy inrelativistic heavy ioncollisions:twodecadesofprogress,Annu.Rev.Nucl.Part.Sci.55(2005) 357–402,arXiv:nucl-ex/0505014.

[39]S.Pratt,Pioninterferometryforexplodingsources,Phys.Rev.Lett.53(1984) 1219–1221.

[40]G. Abbiendi,et al.,Bose–Einstein study ofposition–momentum correlations ofchargedpionsinhadronic Z0 _{decays,Eur.Phys. J.C52(2007)787–803,}

arXiv:0708.1122.

[41]P.Achard,etal.,Testoftheτ-modelofBose–Einsteincorrelationsand recon-structionofthesourcefunctioninhadronicZ -bosondecayatLEP,Eur.Phys.J. C71(2011)1648,arXiv:1105.4788.

[42]K.Aamodt,etal.,Femtoscopyofpp collisionsat√s=0.9and7TeVatthe LHCwithtwo-pionBose–Einsteincorrelations,Phys.Rev.D84(2011)112004, arXiv:1101.3665.

[43]U.A. Wiedemann, U.W. Heinz, Resonance contributions to Hanbury-Brown– Twiss correlation radii, Phys. Rev. C 56 (1997) 3265–3286, arXiv:nucl-th/ 9611031.

[44]K.Werner,I.Karpenko,T.Pierog,M.Bleicher,K.Mikhailov,Evidencefor hy-drodynamicevolutioninproton–protonscatteringat900GeV,Phys.Rev.C83 (2011)044915,arXiv:1010.0400.

[45]T.J. Humanic, Predictions for two-pion correlations for √s= 14 TeV proton–proton collisions, Phys. Rev. C 76 (2007) 025205, arXiv:nucl-th/ 0612098.

[46]T.Alexopoulos,et al.,Studyofsourcesizein pp collisions¯ at √s=1.8TeV usingpioninterferometry,Phys.Rev.D48(1993)1931–1942.

[47]T.Csorg ˝o,W.Kittel,W.J.Metzger,T.Novák,ParametrizationofBose–Einstein correlationsandreconstructionofthespace–timeevolutionofpionproduction ine+e−annihilation,Phys.Lett.B663(2008)214–216,arXiv:0803.3528.

[48]A.Bialas,M.Kucharczyk,H.Palka,K.Zalewski,MassdependenceofHBT cor-relationsine+e−annihilation,Phys.Rev.D62(2000)114007,arXiv:hep-ph/ 0006290.

[49]G.Alexander,OpenquestionsrelatedtoBose–Einsteincorrelationsine+e−→ hadrons,ActaPhys.Pol.B35(2004)69–76,arXiv:hep-ph/0311114.

[50]G.Alexander,Massand transversemass effectson thehadronemittersize, Phys.Lett.B506(2001)45–51,arXiv:hep-ph/0101319.