Production of inclusive Υ(1S) and Υ(2S) in p–Pb collisions at √sNN=5.02TeV

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Production of inclusive Υ(1S) and Υ(2S) in p–Pb

collisions at √sNN=5.02TeV

B. Abelev, A. Baldisseri, J. Castillo Castellanos, J. -L. Charvet, H. Pereira da

Costa, A. Rakotozafindrabe, For The Alice Collaboration

To cite this version:

B. Abelev, A. Baldisseri, J. Castillo Castellanos, J. -L. Charvet, H. Pereira da Costa, et al.. Production

of inclusive Υ(1S) and Υ(2S) in p–Pb collisions at √sNN=5.02TeV. Physics Letters B, Elsevier, 2015,

740, pp.105 - 117. �10.1016/j.physletb.2014.11.041�. �hal-01103948�

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ALICE

Collaboration

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Articlehistory:

Received9October2014

Receivedinrevisedform19November2014 Accepted19November2014

Availableonline22November2014 Editor:L.Rolandi

WereportontheproductionofinclusiveΥ(1S)andΥ(2S)inp–Pbcollisionsat√sNN=5.02 TeV atthe

LHC.ThemeasurementisperformedwiththeALICEdetectoratbackward(−4.46<ycms<−2.96)and

forward(2.03<ycms<3.53)rapiditydowntozerotransversemomentum.Theproductioncrosssections

oftheΥ(1S)and Υ(2S)arepresented,as wellas thenuclearmodiﬁcationfactorandthe ratioofthe forwardtobackwardyieldsofΥ(1S).AsuppressionoftheinclusiveΥ(1S)yieldinp–Pbcollisionswith respect tothe yield from ppcollisions scaled bythe number ofbinary nucleon–nucleon collisions is observedatforwardrapiditybutnotatbackwardrapidity.Theresultsarecomparedtotheoreticalmodel calculationsincludingnuclearshadowingorpartonicenergylosseffects.

1. Introduction

Quarkoniaareboundstatesofaheavyquarkanditsanti-quark. TheJ/

ψ

familyiscomprisedofcharmandanti-charmquarksand the

Υ

family ofbottom and anti-bottom quarks. The former are commonly called charmonia and the latter bottomonia. In ele-mentary pp collisions, the production of a quarkonium can be understood asthe creation of a heavy-quark pair (QQ )

¯

followed byitsbindingintoa quarkoniumstatewithgivenquantum num-bers

[1]

.Theﬁrststepis welldescribed byperturbative quantum chromo-dynamics(QCD)whilethesecond stepisinherently non-perturbative.Threemainapproachesareusedtodescribe quarko-nium production in hadronic collisions: the Colour Evaporation Model (CEM) [2,3], the Colour-Singlet Model (CSM) [4] and the Non-Relativistic QCD (NRQCD) framework [5]. However, none of those models is able to satisfactorily describe simultaneously all aspectsofquarkoniumproductioninppcollisions

[6]

.

In ultra-relativistic Pb–Pb collisions, quarkonia are important probestostudythepropertiesofthedeconﬁnedstateofpartonic matter, the quark–gluon plasma (QGP). Such a state ispredicted by QCD at high temperature andpressure [7,8]. Since quarkonia areproducedattheearlystage ofthecollision,theyareexpected tointeractwiththeQGPthroughoutitsevolution.Inparticular,in thecolour-screeningscenario

[9]

quarkoniumstatesaresuppressed intheQGPwithdifferentdissociationprobabilitiesforthevarious massstates,depending ontheir binding energy.The CMS Collab-oration at the Large Hadron Collider (LHC) has reported on the

_E-mail_address:_{alice-publications@cern.ch}_.

observation ofthe sequential suppression of bottomonium states in Pb–Pb collisions at

√

sNN

=

2

.

76 TeV [10,11]. However, other

hotnuclearmattereffectsbesidescolourscreening,aswellascold nuclear matter (CNM) effects, do complicate thissimple picture. Ontheonehand,recentmeasurementsbytheALICECollaboration arecompatiblewitharegenerationmechanismplayingan impor-tant role inthe productionofJ/

ψ

inPb–Pb collisions attheLHC [12–14].Additional J/

ψ

areexpectedtobe producedfrom decon-ﬁnedcharmquarksbykineticrecombinationintheQGP

[15,16]

or bystatisticalhadronizationatthephaseboundary

[17]

.This addi-tional,hotnuclearmattereffect,competeswiththesuppressionby colourscreening.Duetothelower productioncrosssection ofbb

¯

pairscomparedto cc pairs,

¯

theregeneration of

Υ

(1S)isexpected tobesmallerthanthatofJ/

ψ

[18].Ontheotherhand,effects re-latedto the presence ofCNM can also modifythe production of quarkoniainnucleus–nucleuscollisions.

Cold nuclear matter effects can be separated into initial and ﬁnal-state effects. Initial-state effects occur prior to the forma-tionoftheheavy-quarkpair.Theseincludethemodiﬁcationofthe kinematicaldistributionofthe partonsinthenucleicomparedto thatinfreenucleons

[19–22]

aswellaspartonenergyloss

[23–25]

. First,thenuclearPartonDistribution Functions(nPDF) differfrom those in free nucleons (PDF). Since the gluon fusion mechanism dominates the production of heavy-quark pairs in high energy collisions, quarkonium production is particularly sensitive to the gluonnPDF,whichispresently notwell known.Bjorken-x (xBj) is

deﬁned asthe fraction ofthe hadron momentum carried by the parton. The gluon nPDF includes a shadowing region at low xBj

(xBj

0

.

01)correspondingtoasuppressionofgluons,an

antishad-owingregion atintermediatexBj (0

.

01

xBj

0

.

3)corresponding

http://dx.doi.org/10.1016/j.physletb.2014.11.041

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toanenhancementofgluons,andanadditionalsuppressionof glu-onsknownasEMCeffectathigherxBj(0

.

35

xBj

0

.

7).Secondly,

ifthequarkoniumproductionisdominatedbylowxBj gluons,then

theColourGlassCondensate(CGC)modelcanbeusedtodescribe the nucleus as a coherent gluonic system that saturates at very large density [26]. Finally, partons can lose energy before creat-ing the heavy-quark pair, thereforemodifying the kinematic dis-tributionsofquarkonia.Final-stateeffectsarethosethataffectthe heavy-quarkpairduringtheﬁnitetimeitneedstoforma quarko-nium state orafterthe state hasbeen formed

[27]

.The QQ pair

¯

caninteractwiththenuclearmatterandeventuallybreakup.The break-upcrosssection dependsonthenatureofthepre-resonant stateandisexpectedtobesmallfor

Υ

(1S)athighenergy

[27–29]

. The ﬁnal-state resonance can also interact with surrounding co-movers and lose energy or even break up [30–32]. Finally, in a recentapproachtopartonenergyloss

[25]

,itishypothesizedthat the partonenergyloss is coherentand cannot be factorizedinto initialandﬁnalstateeffects.

Cold nuclear matter effects can be studied in proton–nucleus (p–A) collisions, where the QGP is not expected to be formed. Charmonium states havebeen extensively measured in p–A col-lisions atvariouscollision energies up toLHC energies. Bottomo-niumproductionhasrecentlybeenstudiedthankstotheincreased energy and luminosity available in collider experiments at RHIC [33,34]andtheLHC

[35]

.Duetothelargermassofthe bottomo-niumstatescomparedtothecharmoniumones,themeasurement of

Υ

production in proton–nucleus collisions allows a study of coldnuclearmattereffectsinadifferentkinematicregime, there-forecomplementingtheJ/

ψ

studies

[36,37]

.Inaddition,therecent measurement bythe ALICECollaboration inPb–Pb collisions ofa stronger

Υ

(1S)suppression atforwardrapidity

[38]

than at mid-rapidityhasstressedtheimportanceofunderstandingCNMeffects on

Υ

production(sinceinthecolourscreeningscenariosucha be-haviourisnotexpectedastheenergydensityshouldbelarger or equalatmid-rapiditythanatforwardrapidity).

InthisLetter,wereportALICEresultsoninclusive

Υ

production in p–Pb collisions at

√

sNN

=

5

.

02 TeV, measured via the

μ

+

μ

−

decay channel. The ALICE measurement of the

Υ

(1S) and

Υ

(2S) productioncrosssectioninp–PbcollisionsatLHCenergiesis pre-sentedatbackward(

−

4

.

46

<

ycms

<

−

2

.

96)andforward(2

.

03

<

ycms

<

3

.

53)centre-of-massrapidities.Thepositiverapidityis

de-ﬁnedby the directionoftheprotonbeam. The

Υ

(1S) production crosssectionsinp–Pbcollisionsarecomparedtothoseinpp col-lisions scaled bythe Pb-nucleusatomic massnumber APb

=

208.

Thisnuclearmodiﬁcationfactorispresentedasafunctionof rapid-ity.Theratiooftheforwardtobackwardyieldsisalsodiscussed.

2. Experimentalapparatusanddatasample

TheALICEdetectordesignandperformanceareextensively de-scribedin

[39]

and

[40]

.Theanalysispresented hereisbasedon the detection of muons in the ALICE forward muon spectrome-ter,whichcoversthelaboratorypseudorapidityrange

−

4

<

η

lab

<

−

2

.

5.Inaddition,theSiliconPixelDetector(SPD)isusedto recon-structtheprimaryvertex,theVZEROdetectorprovidesaminimum biastriggerandtheVZEROandTZEROdetectorsare bothusedas luminometers.Ashortdescriptionofthesedetectorsisgiveninthe followingparagraphs.

Themuonspectrometerconsistsofasetofabsorbers,adipole magnet with a 3 T m field integral, five tracking stations and twotriggerstations.Thefront absorber,madeofcarbon,concrete andsteel and placed between0.9 and5 m fromthe Interaction Point (IP), filters out hadrons, thus decreasing the occupancy in thetrackingsystem. Muon trackingisperformedby fivestations, eachoneconsistingoftwoplanesofCathodePadChambers(CPC).

The ﬁrst two stations are located upstream of the dipole mag-net, the third one is embedded inside the magnet gap and the fourthandﬁfthareplaceddownstreamofthedipole,justbeforea 1.2 mthick ironwall(7.2interactionlengths),whichabsorbs sec-ondary hadronsescaping the front absorber andlow-momentum muons (having p

<

1

.

5 GeV

/

c at the exitof the front absorber). The muon trigger systemislocated downstream oftheiron wall andconsistsof twostations, eachone equippedwithtwo planes ofResistivePlateChambers(RPC).Thetimeresolutionisofthe or-der of2 ns andtheeﬃciencyisbetter than95%

[41]

.The muon trigger system delivers single muon anddimuon triggers with a programmable transverse momentum (pT) threshold.Throughout

itsentirelength,aconicalabsorberaroundthebeampipe(

θ <

2◦) made oftungsten, lead and steelshields themuon spectrometer againstsecondary particlesproducedbytheinteractionoflarge-

η

primaryparticlesinthebeampipe.

Primary vertexreconstruction isperformedusingtheSPD, the two innermostlayers oftheInner TrackingSystem[42].It covers thepseudo-rapidityranges

|

η

lab

|

<

2 and

|

η

lab

|

<

1

.

4,fortheinner

andouterlayers,respectively.

ThetwoVZEROhodoscopes

[43]

,with32scintillatortileseach, are placed on each side of the IP, covering the pseudo-rapidity ranges 2

.

8

<

η

lab

<

5

.

1 and

−

3

.

7

<

η

lab

<

−

1

.

7. Each hodoscope

issegmentedinto8sectorsofequalazimuthal coverageandfour equal pseudo-rapidity rings. The logical AND of the signalsfrom the two hodoscopes forms the Minimum Bias (MB) trigger, also usedasaluminositysignal.Asecond luminositysignalisdeﬁned asthe logical AND ofthe twoTZERO arrays, located onopposite sides of the IP (4

.

6

<

η

lab

<

4

.

9 and

−

3

.

3

<

η

lab

<

−

3

.

0). Each

arrayconsistsof12quartzCherenkovcounters,readby photomul-tipliertubes.

Thedatasamplesusedforthisanalysiswerecollectedin2013. The number of bunches colliding at the ALICE IP ranged from 72 to 288. The peak luminosity during data taking was about 1029 _s−1_cm−2_. _The _average _number _of _visible _interactions _per

bunch crossinginsuchconditionsisabout 0.06,corresponding to amultipleinteraction(pile-up)probabilityofabout3%.

Thetriggerconditionusedfordatatakingisadimuon-MB trig-gerformedbythelogicalANDoftheMBtriggerandanunlike-sign dimuontriggerwithatriggerprobabilityforeachofthetwomuon candidates that increases with pT and is 50% at 0

.

5 GeV

/

c. In

an additional oﬄineselection, thetiming information ofthetwo VZERO arrays is used to reject beam-halo andbeam-gas events. The Zero DegreeCalorimeters (ZDC), positioned symmetricallyat 112.5 m fromthe IP,are usedoﬄine torejecteventswitha dis-placed vertex,originatingfromtheinteractionsofsatellite proton andleadbunches,asdescribedin

[40]

.

ThetwoLHCbeamshavethesamemagneticrigiditybut differ-entprojectilechargetomassratio,whichresultsinthetwobeams havingdifferentenergies: Ep

=

4 TeV and EPb

/

APb

=

1

.

58 TeV. As

aconsequence,thecentre-of-masssystemofnucleon–nucleon col-lisions is shifted in rapidity by

y

=

0

.

465 with respect to the laboratoryframe inthedirectionofthe protonbeam. Intermsof therapidityinthecentre-of-massframe ycms,themuon

spectrom-eter acceptance is 2

.

03

<

ycms

<

3

.

53 when the proton beam is

travellinginthedirectionofthespectrometer(p–Pbconﬁguration), and

−

4

.

46

<

ycms

<

−

2

.

96 inthe opposite case(Pb–p

conﬁgura-tion). Toaccessboth rapidity ranges,data were takeninthe two conﬁgurations.

About 9

.

3

×

106 (2

.

1

×

107)dimuon-MB-triggered eventswere analyzed for the p–Pb (Pb–p) conﬁguration, corresponding to an integratedluminosity

L

int

=

5

.

01

±

0

.

19 nb−1 (5

.

81

±

0

.

20 nb−1).

The determination of the integrated luminosities and associated uncertaintiesisdescribedlater.

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Fig. 1. Invariantmassdistributionofopposite-signdimuonsintherapidityregions−4.46<ycms<−2.96 (left)and2.03<ycms<3.53 (right)inp–Pbcollisions.Ineach

case,thefullcurveshowsthetotalﬁtfunctionandthedashedcurvesthesignalcomponentforthethreeΥ states(seetextfordetails).

3. Dataanalysis

Muon track candidates are reconstructed in the muon spec-trometer using the standard tracking algorithm [44]. The tracks are required to exit the front absorber at a radial distance from thebeamaxis, Rabs,in therange17

.

6

<

Rabs

<

89

.

5 cm toreject

trackscrossingtheregionoftheabsorberwiththehighestdensity material.Inthisregion,multiplescatteringandenergylosseffects arelargeandcanaffectthemassresolution.Thecontributionfrom fakeandbeam-gasinteractioninducedtracksisreducedby select-ingtrackspointingtotheinteractionvertex. Inaddition,tracksin thetrackingsystemarerequestedtomatchatracksegmentinthe triggersystem(triggertracklet).

The

Υ

signalisobtainedfromtheinvariant massdistributions of opposite-sign dimuons with a laboratory pair-rapidity in the range 2

.

5

<

|

ylab

|

<

4 down to zero transverse momentum. The

raw number of

Υ

is obtainedby ﬁtting the invariant mass dis-tributions.Asumoftwo exponentialfunctionsisusedto param-eterizethe background continuum, andeach

Υ

resonance shape is described by an extended Crystal Ball(CB) function [45]. The CB function ismade ofa Gaussian core anda power-law tailon each side and is found to reproduce the shape of the

Υ

peak obtainedinMonte Carlo(MC) simulations. Sincethe CB tails are poorlyconstrainedby thedata,theyare ﬁxedfromtheresultsof the MC simulations. It is also necessary to ﬁx the mass differ-ence between states by using the PDG values [46] and to force the width of the

Υ

(2S) and

Υ

(3S) to scale proportionally with the

Υ

(1S)width accordingto the ratioofthe resonance masses. MCsimulations validatedthese assumptions.The

Υ

(1S)signal to backgroundratio (S/B)1 _is _between_0.8_to _1.8, _allowing _the

posi-tion and width of the

Υ

(1S) peak to be free parameters in the ﬁt.Thesigniﬁcance(S/

√

S

+

B)for

Υ

(1S)isbetween6

.

3 and11

.

6 forthe rapidity bins considered in the analysis. The signiﬁcance of the

Υ

(2S) in the rapidity ranges

−

4

.

46

<

ycms

<

−

2

.

96 and

2

.

03

<

ycms

<

3

.

53 islargerthan 3,whichallows areliable

mea-surement. However, dueto the limited statistics,the signiﬁcance ofthe

Υ

(3S) stateis toolowto separate thesignalfromthe un-derlying background. Fig. 1 illustrates the ﬁttingmethod for the rapidity intervals

−

4

.

46

<

ycms

<

−

2

.

96 (left panel) and 2

.

03

<

ycms

<

3

.

53 (rightpanel).Themeasured

Υ

(1S)peakpositionisin

agreementwiththeresonancemassvaluefromPDG

[46]

andthe

1 _The_signal_to_background_ratio_and_{signiﬁcance}_numbers_are_always_evaluated

determiningthe number ofsignaland backgroundcounts inaninvariant mass rangecentredonthe Υ massand correspondingto±3 times thewidthofthe peak.

measured width(155

±

25 MeV

/

c2 in

−

4

.

46

<

ycms

<

−

2

.

96 and

160

±

22 MeV

/

c2 in 2

.

03

<

ycms

<

3

.

53) agrees with the results

fromMCsimulations.Asimilaragreementwasobservedforall ra-piditybinsconsideredinthisLetter.

Toinvestigatethesystematicuncertaintiesonthesignal extrac-tion procedure, different fits were performed parameterizing the backgroundcontinuum withthe sumoftwo power-lawfunctions andusingalternativeinvariantmassfittingranges.Sincesome pa-rametersare fixedinthefittingprocedure,therelatedsystematic uncertainties werealso studied.TheCB tailparameterswere var-ied according to their spreadobtained by several fits of the MC distributionsindifferentmassranges.Thewidthofthe

Υ

(2S)and

Υ

(3S) were varied according to the size of the uncertainties of the

Υ

(1S) width obtained from the ﬁt. The latter method was similarly used to estimate the systematic uncertainty related to the ﬁxing of the

Υ

(2S) and

Υ

(3S) peak position.The raw num-ber of

Υ

(1S) and

Υ

(2S) in the rapidity range

−

4

.

46

<

ycms

<

−

2

.

96 are 161

±

21

(

stat

)

±

9

(

syst

)

and 42

±

14

(

stat

)

±

5

(

syst

)

, respectively. In the 2

.

03

<

ycms

<

3

.

53 rapidity range, they are

305

±

34

(

stat

)

±

13

(

syst

)

for

Υ

(1S) and 83

±

23

(

stat

)

±

10

(

syst

)

for

Υ

(2S).

The acceptance-times-eﬃciency ofthe muon spectrometer for themeasurementof

Υ

, A

×

ε

,iscalculatedwithMCsimulations. The pT and y distributionsofthegenerated

Υ

(1S)were

extrapo-lated,withaprocedureequivalentto theone adoptedfortheJ/

ψ

[47],to

√

sNN

=

5

.

02 TeV fromexistingppmeasurements

[48–50]

.

Nuclear shadowingcalculations

[51]

wereusedtoincludethe ex-pectedCNM effects.Thesystematicuncertaintywasestimatedby varying the pT and y input distributions by an amount

suﬃ-ciently large (based on theoretical estimations) to include the a priori unknown impact of CNM effects. Since the available data favoura zeroorsmallpolarization of

Υ

(1S) [52–54],an unpolar-izedproductionwas assumed. Particle transportisperformed us-ingGEANT3

[55]

andarealisticdetectorresponseisappliedtothe simulatedhitsinordertoreproducetheperformanceofthe appa-ratusduringdatataking.Thetimedependenceofthetrackingand trigger efficiencies is taken into account by incorporating in the MC simulationsthe deadchannelmaps obtainedfromthe online detectorinformationandthetriggerchamberefficienciesobtained fromarealdataanalysis.Inaddition,arealisticdescriptionofthe residualmisalignmentofthetrackingchambersisincludedinthe simulations. Thetrackingefficiencyis evaluatedwithdata by an-alyzing the clusterdistribution ofthe reconstructedtracks inthe detectionchamberswiththealgorithmdescribedin

[44]

.Thesame algorithmcanbeusedtoestimatethetrackingeﬃciencyfromMC data. The systematic uncertainties on thisvalue are obtained by

(5)

comparingthetrackingefficiencyestimatedfromrealandMCdata. The efficiency of the muon triggering system is calculated from dataandresultsfromtheanalysisoftriggertrackletdistributions reconstructed fromclustersin thefour planesof thetwo trigger stations.The corresponding systematic uncertainties are obtained by varying the trigger chamber efficiency in MC simulations by an amount equivalent to the statisticaluncertainties on the real dataestimation. The quality ofthe matching ofthe tracking and triggeringsysteminformationisensuredby a

χ

2 _cut._In_order_to

quantify the systematic uncertainties on the matching eﬃciency, thecut was varied inthesameproportions whileanalyzing both realandMCdata.Theobserveddifferenceinthematching proba-bilitiesprovidestheuncertainties.

The A

×

ε

valuesandthecorresponding systematic uncertain-tiesfor

Υ (

1S

)

measuredduringthep–PbandthePb–pdatataking periodsare

(

29

.

0

±

2

.

0

)

% and

(

20

.

1

±

1

.

6

)

%,respectively.Thevalue of A

×

ε

is lower for the Pb–p period mainly due to a reduced tracking eﬃciency. The

Υ

(2S) A

×

ε

and the corresponding sys-tematicuncertainties were evaluated withthe samemethod and thesameinputdistributionsasforthe

Υ

(1S).Theobserved differ-encesbetweenthe

Υ

(2S)and

Υ

(1S) A

×

ε

arelessthan0

.

5%.The shapevariations betweenthedifferentinputdistributionsusedin thestudyoftheA

×

ε

systematicuncertaintieswerelargeenough to cover the differences between the

Υ

(1S) and

Υ

(2S) distribu-tionsobservedbyLHCbintherapidityrange2

<

ycms

<

4

.

5 inpp

collisions

[49,56,57]

.

Therawnumberof

Υ

(1S)obtainedwiththeﬁtprocedure de-scribedpreviously,N

[Υ (

1S

)

]

,iscorrectedforthebranchingratioof thedimuondecaychannel, BRΥ (1S)→μ+μ−

=

0

.

0248

±

0

.

0005[46]

and for the acceptance-times-eﬃciency,

(

A

×

ε

)

Υ (1S). The

Υ

(1S)

crosssectionisobtainedas

σ

_pPbΥ (1S)

=

N

[Υ (

1S

)

]/(

A

×

ε

)

Υ (1S)

BR_{Υ (}_1S₎_→_μ+_μ−

×

L

,

(1)

where the integrated luminosity

L =

NMB

/

σ

MB is the ratio

be-tween the number of MB events and the MB trigger cross sec-tion.Sincetheanalyzed datasampleismadeofdimuontriggered events, it is necessary to use a scaling factor, F , to obtain the numberofMBeventsfromthenumberoftriggeredevents.The in-verseofthe F factor correspondstotheprobability ofhavingthe dimuontriggerconditionveriﬁedinan MBevent.Itsaveragevalue is F

=

1129

±

2

(

stat

)

±

11

(

syst

)

and F

=

589

±

2

(

stat

)

±

6

(

syst

)

forthep–PbandPb–pdatatakingperiods,respectively.These val-uesandthe corresponding statisticaluncertainties were obtained by averaging the resultsof two different methods,one basedon theratiooftriggerratesandtheotherbasedontheoﬄine selec-tionofdimuoneventsintheMBdatasample

[36]

.Thesystematic uncertainties reﬂect the difference between the results obtained withthetwomethods.TheMBtriggercrosssection

σ

MBwas

mea-suredwithavanderMeerscan

[58]

andfoundtobe2

.

09

±

0

.

07 b (2

.

12

±

0

.

07 b)forthep–Pb(Pb–p)conﬁguration,wherethe uncer-taintiesforthetwoconﬁgurationsarepartiallycorrelated

[59]

.The luminosity was also independently determined, ina similar way, by means of the TZERO-based luminosity signal. The two mea-surementsdifferbyatmost1%throughoutthewholedata-taking period.Suchasmallvariationwascombinedquadraticallywiththe

NMB and

σ

MB uncertainties, toget a total luminosity uncertainty

of3.8%forthep–Pbconﬁguration(forwardrapidities)and3.5%for thePb–pconﬁguration(backwardrapidities).

4. Results

The

Υ

(1S) production cross sections in p–Pb collisions at

√

sNN

=

5

.

02 TeV are:

Table 1

Summaryoftherelativesystematicuncertaintiesoneachquantityenteringinthe calculations oftheresults.TypeI (II)standsfor uncertaintiescorrelated (uncor-related) with rapidity. Type IIuncertainties aregiven as arange including the smallest and the largest values observed inthe bins considered inthis analy-sis.Resultsarepresentedforthebackward(−4.46<ycms<−2.96)andforward

(2.03<ycms<3.53)rapidityregions.

Source Backward rapidity Forward rapidity Signal extraction:Υ(1S) 5%–6% (II) 4%–6% (II) Signal extraction:Υ(2S) 12% (II) 12% (II) Input MC parameterization:Υ(1S) 2%–5% (II) 4%–6% (II) Input MC parameterization:Υ(2S) 5% (II) 5% (II) Tracking efficiency 6% (II) 4% (II) Trigger efficiency 2% (II) 2% (II) Matching efficiency 1% (II) 1% (II)

σΥ (1S)

pp (interpolation) 11%–13% (II) 7%–12% (II) L (correlated) 1.6% (I) 1.6% (I)

L (uncorrelated) 3.1% (II) 3.4% (II)

σ

_pPbΥ (1S)

(

−

4

.

46

<

ycms

<

−

2

.

96

)

=

5

.

57

±

0

.

72

(

stat

)

±

0

.

60

(

syst

)

μb

,

σ

_pPbΥ (1S)

(

2

.

03

<

ycms

<

3

.

53

)

=

8

.

45

±

0

.

94

(

stat

)

±

0

.

77

(

syst

)

μb

.

The

Υ

(2S) production cross sections in p–Pb collisions at

√

sNN

=

5

.

02 TeV, obtained in a similar way but with

BR_{Υ (}2S)→μ+μ−

=

0

.

0193

±

0

.

0017[46],are:

σ

_pPbΥ (2S)

(

−

4

.

46

<

ycms

<

−

2

.

96

)

=

1

.

85

±

0

.

61

(

stat

)

±

0

.

32

(

syst

)

μb

,

σ

_pPbΥ (2S)

(

2

.

03

<

ycms

<

3

.

53

)

=

2

.

97

±

0

.

82

(

stat

)

±

0

.

50

(

syst

)

μb

.

Asummaryofthedifferentsourcesofsystematicuncertainties and their relative value is givenin Table 1. The uncertainties of typeIIarenotfullyuncorrelatedwithrapidityandnotrivial factor-ization incorrelated anduncorrelatedpartscan be made. Hence, theyarelabelledasuncorrelated,buttheycannotbequadratically combinedtoobtaintherapidityintegratedresult.

The

Υ

(1S) candidates were further divided in four rapidity ranges, namely

−

4

.

46

<

ycms

<

−

3

.

53,

−

3

.

53

<

ycms

<

−

2

.

96,

2

.

03

<

ycms

<

2

.

96 and2

.

96

<

ycms

<

3

.

53.Twoofthemare

sym-metricwithrespectto ycms

=

0.

Fig. 2

showstheinclusive

Υ

(1S)

differentialcrosssectiond

σ

/

d y asafunctionofrapidity.The ver-ticalerrorbarsrepresentthestatisticaluncertaintiesandtheopen boxestheuncorrelatedsystematicuncertainties.Alsoshownisthe inclusive

Υ (

1S

)

y-differentialinterpolated crosssection inpp col-lisions atthe samecentre-of-mass energy(obtained asexplained laterinthetext)scaledby APb.

The CNM effectscan bequantiﬁed withthenuclear modiﬁca-tionfactor, RΥ (_pPb1S)

=

σ

Υ (1S) pPb APb

×

σ

ppΥ (1S)

,

(2)

where

σ

ppΥ (1S) isthe

Υ

(1S)cross section inpp collisionsat

√

s

=

5

.

02 TeV.

Since

σ

ppΥ (1S) at

√

s

=

5

.

02 TeV has not yet been measured, it was computed using a data driven

√

s interpolation method. A detailed description of the adopted procedure is given in [60].The LHCb Collaboration hasmeasured the

Υ (

1S

)

cross sec-tion in pp collisions at

√

s

=

2

.

76

,

7 and 8 TeV, over the ranges

(6)

Fig. 2. InclusiveΥ(1S)productioncrosssectionasafunctionofrapidityinp–Pb collisionsat√sNN=5.02 TeV.Theverticalerrorbarsrepresentthestatistical

un-certaintiesandtheopenboxestheuncorrelatedsystematicuncertainties.The cor-relatedsystematicuncertaintyis 1.6% and isdirectly quotedinthe ﬁgure.It is obtainedbysumminginquadraturethecorrelateduncertaintyontheintegrated luminosityandthe uncertaintyonthebranching ratioofΥ(1S)todimuon.The bandscorrespondtotheinclusiveΥ(1S)ppcrosssectionobtainedwiththe proce-duredescribedinthetextandscaledbyAPb.

pT

<

15 GeV

/

c and 2

<

y

<

4

.

5, in 5rapidity bins of equal size

[49,56,57]. The LHCb results were re-binned to obtain the cross section in(approximately)the rapidity ranges ofinterest for this analysis: 2

<

y

<

3, 2

<

y

<

3

.

5, 3

<

y

<

3

.

5, 3

<

y

<

4

.

5, and 3

.

5

<

y

<

4

.

5.Foreach bin,thecrosssection asa functionof en-ergywasﬁttedaccordingto21differentshapes:15arebasedon LeadingOrderCEM(LO-CEM)calculationsfor

Υ

production, corre-spondingtovariouschoicesofPDFsandofthefactorizationscale; 3arebasedontheenergy-dependenceofbarebottom-quark pair production (FONLL) [61]; the remaining three are a power law, a linear and an exponential function. The obtained ﬁt parame-ters were used to compute the cross section at

√

s

=

5

.

02 TeV. In order to take into account the rather poor agreement of the data with the ﬁtting functions (

χ

2

_/

_ndf

_>

_{2 for} _all _ﬁts, _where

ndf is the number of degrees of freedom), all the uncertainties on the ﬁt results were rescaled by

χ

2

_/

_{ndf .} _Fits _with

_χ

2

_/

_ndf

values larger than three times the minimum value obtained for the rapidity range considered were discarded. The weighted av-erage ofthe surviving results was computed (using the rescaled fit uncertainty as a weight) and retained as central value. The average(rescaled)fit-resultuncertaintywasevaluatedforeach ra-piditybin:itrangesfrom7%to12%.Asanadditionaluncertainty, the maximum difference between the average and the individ-ualfit results was computed: it ranges from 2% to 7%. Finally, a thirduncertaintywasconsidered,totakeintoaccounttheshiftof 0.035 rapidity units between the ranges adopted in the interpo-lationprocedure and those usedfor the measurement of RΥ (_pPb1S). Suchan uncertaintyisquantifiedbythe maximumdifference be-tween the cross sections in the two ranges, evaluated with the LO-CEMandFONLLmodels,andamountsto1%fortheforward ra-pidity region and3% forthe backward rapidity region. Since the interpolationis performedseparately foreach rapidity range,the associateduncertainties are assumedto be uncorrelatedwith ra-pidity.Fortheforwardandbackwardrapidity rangesusedforthe integratedresults, the obtainedinterpolated cross-sections times branchingratioare1451

±

114

(

syst

)

pb and770

±

87

(

syst

)

pb, re-spectively.

Usingthe interpolatedvalues of

σ

ppΥ (1S),the nuclear

modiﬁca-tionfactorsare

Fig. 3. NuclearmodiﬁcationfactorofinclusiveΥ(1S)inp–Pbcollisionsat√sNN=

5.02 TeV.TheresultsarecomparedtothoseforinclusiveJ/ψ[36].Thevertical er-rorbarsrepresentthestatisticaluncertaintiesandtheopenboxestheuncorrelated systematicuncertainties(fortheJ/ψ,theuncorrelatedandpartiallycorrelated un-certaintieshavebeenaddedinquadrature).ThefullboxesaroundRpPb=1 show

thesizeofthecorrelateduncertainties,whichinthecaseoftheΥincludeonlythe correlateduncertaintyontheluminosity(seeTable 1).

RΥ (_pPb1S)

(

−

4

.

46

<

ycms

<

−

2

.

96

)

=

0

.

86

±

0

.

11

(

stat

)

±

0

.

13

(

uncorr

)

±

0

.

01

(

corr

),

RΥ (_pPb1S)

(

2

.

03

<

ycms

<

3

.

53

)

=

0

.

70

±

0

.

08

(

stat

)

±

0

.

08

(

uncorr

)

±

0

.

01

(

corr

).

Undertheassumptionofa2

→

1 productionprocess(gg

→ Υ

), the sampledxBj rangesare 5

.

5

·

10−5

<

xBj

<

2

.

5

·

10−4 and3

.

6

·

10−2

_<

_x

Bj

<

1

.

6

·

10−1 atforwardandbackwardrapidity,

respec-tively.Thus, themeasurement atforwardrapidity teststhe shad-owingregionandtheoneatbackwardrapiditytheanti-shadowing region.Inthecaseofa 2

→

2 productionprocess (gg

→ Υ

g) the coveredxBj rangesarenaturally expectedtobeenlarged.In

Fig. 3

the inclusive

Υ

(1S)nuclear modiﬁcationfactor inp–Pbcollisions at

√

sNN

=

5

.

02 TeV isshowninfourclassesofrapidity.The

verti-cal errorbars representthestatisticaluncertainties andtheopen boxestheuncorrelatedsystematicuncertainties.Anadditional cor-related uncertaintyis indicated by the full box around RpPb

=

1.

The RpPb showsa suppression ofthe inclusive

Υ

(1S) production

yields atforward rapidity in p–Pbcompared to pp collisions. At backwardrapidity,the

Υ

(1S) RpPbiscompatiblewithunitywithin

uncertainties, and thereforedoesnot favoura strong gluon anti-shadowing.Alsoshownin

Fig. 3

istheALICEmeasurementofthe inclusive J/

ψ

RpPb [36]. Although the uncertainties are large, it

appears that at positive ycms the

Υ

(1S) andJ/

ψ

RpPb are rather

similar. It is worth notingthat dueto its larger mass,the

Υ

(1S)

RpPb atforward rapidity ishigher thanthe J/

ψ

one according to

all available model calculations [25,26,28,62]. At negative rapidi-ties, theJ/

ψ

RpPb aresystematically abovethe

Υ

(1S)onebutthe

twoRpPbareconsistentwithinuncertainties.Althoughtherapidity

rangesarenotidentical,the RpPbmeasuredbyLHCb

[63]

are

con-sistent with the ALICEmeasurements within uncertainties, albeit systematicallylarger

[60]

.

The ratio

[Υ (

2S

)/Υ (

1S

)

]

of the production cross section of

Υ (

2S

)

→

μ

+

μ

−to

Υ (

1S

)

→

μ

+

μ

−canbeobtainedas

Υ (

2S

)/Υ (

1S

)

=

N

[Υ (

2S

)

]/(

A

×

ε

)

Υ (2S) N

[Υ (

1S

)

]/(

A

×

ε

)

Υ (1S)

.

(3)

Thebranchingratioofthedimuondecaychannel doesnot en-ter the calculation. Additionally, since the same data sample is used,

L

cancelsout intheratio.Thesystematicuncertaintieson

(7)

Fig. 4. NuclearmodiﬁcationfactorofinclusiveΥ(1S)inp–Pbcollisionsat√sNN=5.02 TeV asafunctionofrapidity.Theverticalerrorbarsrepresentthestatistical

uncer-taintiesandtheopenboxestheuncorrelatedsystematicuncertainties.ThefullboxesaroundRpPb=1 showthesizeofthecorrelateduncertainties.Alsoshownareseveral

modelcalculations:(left)partonenergyloss[25]withandwithoutEPS09shadowingatNLOandCEMwithEPS09shadowingatNLO[62];(right)CGCbased[26]andCSM withEPS09shadowingatLO[28].ForthelattertheeffectofvariationintheshadowingandEMCcurvesishighlightedasdescribedinthetext.(Forinterpretationofthe coloursinthisﬁgure,thereaderisreferredtothewebversionofthisarticle.)

the ratioswere obtainedby quadratically combiningthe system-aticuncertaintiesenteringineachelementofEq.(3).Nevertheless, sincethedecaykinematicsofthetwo

Υ

statesareclose, the sys-tematicuncertaintieson tracking,trigger andmatchingeﬃciency, estimatedforthe samedetectorin thesame workingconditions, canceloutintheratio.Theresultsare:

Υ (

2S

)/Υ (

1S

)

_pPb

(

−

4

.

46

<

ycms

<

−

2

.

96

)

=

0

.

26

±

0

.

09

(

stat

)

±

0

.

04

(

syst

),

Υ (

2S

)/Υ (

1S

)

_pPb

(

2

.

03

<

ycms

<

3

.

53

)

=

0

.

27

±

0

.

08

(

stat

)

±

0

.

04

(

syst

).

The same ratio has been measured by ALICE in pp collisions at

√

s

=

7 TeV in the rapidity range 2

.

5

<

ycms

<

4

.

0 [64] and

is 0

.

26

±

0

.

08

(

tot

)

, where the uncertainty is the quadratic sum of the statistical and systematic uncertainties. The LHCb Collab-oration has measured the same ratio in pp collisions at

√

s

=

2

.

76

,

7 and 8 TeV andasafunctionofrapidityintherange2

.

0

<

ycms

<

4

.

5 [49,56,57]. The measured

[Υ (

2S

)/Υ (

1S

)

]

is found to

be, within uncertainties, independent of

√

s and rapidity. For

pT

<

15 GeV

/

c (14 GeV

/

c for 8 TeV) themeasured values inthe

range3

.

0

<

ycms

<

3

.

5 are 0

.

22

±

0

.

03

(

tot

)

,0

.

24

±

0

.

02

(

tot

)

and

0

.

25

±

0

.

01

(

tot

)

for

√

s

=

2

.

76

,

7 and 8 TeV,respectively.Our mea-sured ratio

[Υ (

2S

)/Υ (

1S

)

]

in p–Pbcollisions is compatible with thesameratio inpp collisions.Withinouruncertainties, thereis thereforenoevidenceofadifferentmagnitudeofCNMeffectsfor the

Υ

(2S) with respect to the

Υ (

1S

)

. At mid-rapidity, however, theCMSCollaboration has measured thedoubleratio,i.e. the ra-tio

[Υ (

2S

)/Υ (

1S

)

]

inp–Pbdividedby that inppcollisions, tobe 0

.

83

±

0

.

05

(

stat

)

±

0

.

05

(

syst

)

,suggestingastrongersuppressionof the

Υ

(2S)thanofthe

Υ

(1S)inp–Pbcollisions

[35]

.

Theinclusive

Υ

(1S) RpPb integratedoverthebackward or

for-wardrapidity ranges, arecompared toseveralmodel calculations in

Fig. 4

.Intheleft panel,theresultsarecompared toa next-to-leading order (NLO) CEM calculationusing the EPS09 parameter-ization ofthe nuclear modiﬁcation ofthe gluon PDF (commonly referred to asgluon shadowing) at NLO [62] (blue shaded band) andto a partonenergy loss calculation [25] with (green shaded band) or without (red band) EPS09 gluon shadowing at NLO. In thecaseoftheCEM

+

EPS09calculation,thebandreﬂectsthe un-certaintiesofthecalculation,dominatedbytheonesoftheEPS09 parameterization

[19]

.Inthecasesofthepartonenergylossmodel

calculations, the bandsrepresentthe uncertaintyfrom theEPS09 parameterizationorfromthepartontransportcoeﬃcient andthe parameterizationusedforthepp referencecrosssection.Noneof the calculationsfullydescribethe backwardandforwardrapidity data and all tend to overestimate the observed

Υ

(1S) RpPb. The

parton energy loss with EPS09calculation reproduces the

Υ

(1S)

RpPb at forwardrapidity buttendto overestimate itatbackward

rapidity.Theopposite trendisfoundifonlypartonenergylossis considered.

Intherightpanel,theresultsarecomparedtoacalculationof a 2

→

2 production model(gg

→ Υ

g) atleading order (LO) us-ing the EPS09 shadowing parameterization also at LO [28]. Two bandsare showntohighlighttheuncertainties linkedto two dif-ferent effects. The extent of the blue band shows the EPS09 LO relateduncertainties in theshadowing region,i.e. atlow xBj. The

redbandshowstheuncertaintyintheEMCregion,i.e. athighxBj.

As the authors of [28] discuss, the gluon nPDF is poorly known inthisregionandthe

Υ

(1S)RpPb atbackwardrapiditycouldadd

usefulconstraintstothemodelcalculations.Itisworthnotingthat thetwo bluebandsintheleft andrightpanelsof

Fig. 4

differby their central curve and the extent of the uncertainties. The two approachesare similar andalthoughthe productionmodels used are different,mostofthedifference comesfromtheusage ofthe NLOorLOEPS09gluonshadowingparameterizations.Itcanbe ar-guedthatusingan NLOparameterizationismoreappropriatethan an LO one,howeveritisworthremarking thatother gluon shad-owing parameterizations [20,21] (also at NLO) are available and that theuncertaintyband oftheEPS09LOparameterization prac-tically includesthem.Therefore, theblueuncertaintyband inthe rightpanelof

Fig. 4

canbeconsideredasincludingtheuncertainty duetodifferentgluonshadowingparameterizations.Thebackward rapidity

Υ

(1S)RpPbdisfavoursthestronggluonanti-shadowing

in-cludedintheEPS09parameterization.Intherightpanel of

Fig. 4

, a calculation based on the CGC framework coupled witha CEM productionmodel isalsoshown(green shadedband)forpositive

ycms.Itisworthnotingthatthiscalculation,althoughonlyslightly

underestimating the

Υ

(1S) RpPb,isnot abletoreproducetheJ/

ψ

RpPbinthesamerapidityrange

[36]

.

Thequantity RFBisdeﬁnedastheratioofthenuclear

modiﬁca-tionfactorsatforwardandatbackwardrapiditiesinarange sym-metricwithrespectto ycms

=

0.Itcanbecomputeddirectlyfrom

the ratio of the cross sections (see Eq. (1)) of

Υ

(1S) at forward and backward rapidities. RFB is therefore independent of

σ

ppΥ (1S).

(8)

Fig. 5. (Left)ForwardtobackwardratioRFBofinclusiveΥ(1S)yieldscomparedtotheJ/ψ RFB[36].Theverticalerrorbarsrepresentthestatisticaluncertaintiesandthe

openboxestheuncorrelatedsystematicuncertainties.(Right)InclusiveΥ(1S)RFBcomparedtotheoreticalmodelcalculations.Thestatisticalandsystematicuncertaintiesfor

theexperimentalvalueareaddedinquadrature.Forthecalculations,uncertaintiesarequotedwhenavailable.

The drawback of the RFB ratio is that it can only be measured

in the restricted rapidity range 2

.

96

<

|

ycms

|

<

3

.

53, hence

los-ing about two thirds of the number of measured

Υ

. The mea-sured forward to backward ratio is RFB

(

2

.

96

<

|

ycms

|

<

3

.

53

)

=

0

.

95

±

0

.

24

(

stat

)

±

0

.

14

(

syst

)

.Uncertaintiesareobtainedby sum-ming in quadrature the contribution of each individual element enteringtheratio.Theinclusive

Υ

(1S) RFBiscomparedin

Fig. 5

to

theinclusiveJ/

ψ

RFB [36] inthe samerapidity range(leftpanel)

and to several model calculations (right panel). In the rapidity range2

.

96

<

|

ycms

|

<

3

.

53 the

Υ

(1S)RFB iscompatiblewithunity

andis larger than that of the J/

ψ

. All models describe the data withinthepresentuncertaintiesofthemeasurement.

5. Conclusion

In summary, we reported the ALICE measurement of

Υ

pro-duction in p–Pb collisions at

√

sNN

=

5

.

02 TeV at the LHC. The

Υ

(1S) production cross section and nuclear modiﬁcation factor werepresentedinthe rapidityranges

−

4

.

46

<

ycms

<

−

2

.

96 and

2

.

03

<

ycms

<

3

.

53 down to zero transverse momentum. At

for-ward rapidity, RpPb shows a suppression of

Υ

(1S) production in

p–Pbcompared to pp collisions. At backward rapidity,the

Υ

(1S)

RpPbisconsistentwithunity,suggestingthatgluonanti-shadowing

is smaller than expected in the EPS09 parameterization. Models includingthe nuclear modiﬁcationof thegluon PDF

[28,62]

ora contributionfromcoherentpartonenergyloss

[25]

tendto overes-timateourmeasured RpPbandcannotsimultaneouslydescribethe

forwardandbackward rapiditysuppressions. ACGC basedmodel [26] is in agreement withour

Υ

results atforward rapidity but cannot describe the J/

ψ

RpPb [36]. The forward to backward

ra-tio RFB of the inclusive

Υ

(1S) yields in 2

.

96

<

|

ycms

|

<

3

.

53 is

compatiblewithunity within largeuncertainties. Withinour un-certainties,the

[Υ (

2S

)/Υ (

1S

)

]

ratioshows noevidence of differ-entCNMeffectsonthetwostates.Additionalmeasurementswith higherstatistics are needed to further constrain the models and extrapolatetheCNMeffectstoPb–Pbcollisions.

Acknowledgements

The ALICECollaboration wouldlike to thank all its engineers andtechniciansfortheirinvaluablecontributionstothe construc-tion of the experiment and the CERN accelerator teams for the outstandingperformanceoftheLHCcomplex.

The ALICECollaborationgratefullyacknowledges theresources andsupportprovidedby allGridcentresandtheWorldwide LHC ComputingGrid(WLCG)Collaboration.

The ALICE Collaboration acknowledges the following funding agencies fortheir supportin buildingandrunning theALICE de-tector: StateCommitteeofScience,World FederationofScientists (WFS) and Swiss Fonds Kidagan, Armenia, Conselho Nacional de DesenvolvimentoCientíﬁco eTecnológico (CNPq),Financiadorade EstudoseProjetos(FINEP),FundaçãodeAmparoàPesquisado Es-tadodeSãoPaulo(FAPESP);NationalNaturalScienceFoundationof China(NSFC),theChineseMinistryofEducation(CMOE)and Min-istryofScience andTechnology ofthePeople’sRepublicofChina (MSTC); Ministry of Education andYouth ofthe Czech Republic; Danish Natural Science Research Council, the Carlsberg Founda-tion andthe DanishNationalResearch Foundation;TheEuropean ResearchCouncilundertheEuropeanCommunity’sSeventh Frame-workProgramme;HelsinkiInstituteofPhysicsandtheAcademyof Finland;FrenchCNRS-IN2P3,the‘RegionPaysdeLoire’,‘Region Al-sace’, ‘Region Auvergne’ andCEA, France; German BMBFand the HelmholtzAssociation;GeneralSecretariatforResearchand Tech-nology,MinistryofDevelopment,Greece;HungarianOTKAand Na-tionalOﬃceforResearch andTechnology (NKTH); Departmentof Atomic Energy, Government of India and Department of Science and Technology,Ministry of Science and Technology of the Gov-ernment ofIndia; IstitutoNazionale diFisicaNucleare(INFN)and CentroFermi–MuseoStoricodellaFisicaeCentroStudieRicerche “Enrico Fermi”, Italy; MEXT Grant-in-Aid for Specially Promoted Research, Japan; JointInstitute forNuclear Research, Dubna; Na-tionalResearchFoundationofKorea(NRF);CONACYT,DGAPA, Méx-ico,ALFA-ECandtheEPLANETProgram(EuropeanParticlePhysics LatinAmericanNetwork); StichtingvoorFundamenteelOnderzoek der Materie(FOM) andtheNederlandse Organisatievoor Weten-schappelijk Onderzoek (NWO), Netherlands; Research Council of Norway (NFR); Polish Ministry of Science and Higher Education; NationalScienceCentre,Poland;MinistryofNational Education/In-stitute forAtomic PhysicsandCNCS-UEFISCDI, Romania; Ministry ofEducationandScience ofRussianFederation, RussianAcademy ofSciences,RussianFederalAgencyofAtomicEnergy,Russian Fed-eralAgency forScience andInnovationsandthe Russian Founda-tionforBasicResearch;MinistryofEducationofSlovakia; Depart-mentofScienceandTechnology,RepublicofSouthAfrica;CIEMAT, EELA,MinisteriodeEconomíayCompetitividad(MINECO)ofSpain, XuntadeGalicia(ConselleríadeEducación),CEADEN,Cubaenergía, Cuba,andIAEA(InternationalAtomicEnergyAgency);Swedish Re-search Council (VR) and Knut and Alice Wallenberg Foundation

(9)

(KAW); Ukraine Ministry of Education andScience; United King-domScienceandTechnologyFacilitiesCouncil(STFC);TheU.S. De-partmentofEnergy,theUnitedStatesNationalScienceFoundation, theStateofTexas,andtheState ofOhio;MinistryofScience, Ed-ucationandSportsofCroatiaandUnitythroughKnowledgeFund, Croatia.

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