Fluxes of atmospheric muons underwater depending on the smal

The prompt muon contribution to the deep-sea atmospheric muon flux can serve as a tool for probing into the small-x feature of the gluon density inside of a nucleon, if the muon energy threshold could be lifted to 100 TeV. The prompt muon flux underwater i

3

002 ebF 02 1v3812030/hp-pe:hviXraFluxesofatmosphericmuonsunderwaterdependingonthesmall-xgluondensity

AMisaki1,TSSinegovskaya2,SISinegovsky2andNTakahashi3

1WasedaUniversity,Okubo3-4-1,Shinjuku-ku,Tokyo,169-8555Japan2IrkutskStateUniversity,664003Russia3

HirosakiUniversity,036-8561Japan

E-mail:sinegovsky@api.isu.runnet.ru

Abstract.Thepromptmuoncontributiontothedeep-seaatmosphericmuon uxcanserveasatoolforprobingintothesmall-xfeatureofthegluondensityinsideofanucleon,ifthemuonenergythresholdcouldbeliftedto100TeV.Thepromptmuon uxunderwateriscalculatedtakingintoconsiderationpredictionsofrecentcharmproductionmodelsinwhichthesmall-xbehaviourofthegluondistributionisprobed.WediscussthepossibilityofdistinguishingthePQCDmodelsofthecharmproductiondi eringinthesmall-xexponentofthegluondistribution,inmeasurementsofthemuon uxatenergies10100TeVwithneutrinotelescopes.

Submittedto:J.Phys.G:Nucl.Phys.

1.Introduction

Acorrecttreatmentofthecharmhadroproductionisimportanttotheatmosphericmuonandneutrinostudies,sinceshort-livedcharmedparticles,D±,D0,

The prompt muon contribution to the deep-sea atmospheric muon flux can serve as a tool for probing into the small-x feature of the gluon density inside of a nucleon, if the muon energy threshold could be lifted to 100 TeV. The prompt muon flux underwater i

uxesatthegroundleveldependingstronglyonprotongluondistributionsatsmallxscale,x<10 5.

ThemuonspectraunderwatercomputedwiththemodelofPasqualietal.[2],inwhichusedweretheMRSD [5]andtheCTEQ3M[6]setsofPDFs,wererecentlydiscussed[7,8,9].Inthisnote,usingpredictionsofthePQCDmodel[3,4]forthecharmproduction,wediscussthePMcontributiontothedeep-seamuon uxatdepthstypicalforoperatingandconstructingneutrinotelescopes,AMANDA[10],ANTARES[11],Baikal[12],NESTOR[13].Duetolargedetectorvolumeandefectivearea(104 105m2)andhomogeneityofsurroundingmattertheseundericeanddeep-seainstallationshaveconsiderableadvantagesoverundergrounddetectorsforprobingveryhigh-energyatmosphericmuons.

Namely,herewetrytostudyaPM uxunderwaterdependenceonthepowerλofthesmall-xgluondistributionfunction:xg(x,Q2)∝x λ.Thenatureofthesmall-xbehaviourofthegluondensityisnowunderextensivediscussion(see,forexample,[14,15,16,17,18,19]).Thesmall-xbehaviourofthePDFsisthesubjectofthedeepinterestbecauseanunderstandingoftheunderlyingdynamicsisfaryetfrombeingclear.2.PDFsandcharmproductionmodels

Duetodominantsubprocessinheavyquarkshadroproduction,gg→

c

The prompt muon contribution to the deep-sea atmospheric muon flux can serve as a tool for probing into the small-x feature of the gluon density inside of a nucleon, if the muon energy threshold could be lifted to 100 TeV. The prompt muon flux underwater i

1

-V

eG1

-rs1

-s2-mc ,)θ ,µE(µφ)V3

eG / µE(10

10

10

10108

Eµ , GeV

Figure1.Verticalsea-levelmuon uxdataandpredictions.Experiments: –

Artyomovsk[24],△–Baksan[25], –MSU[26], –Frejus[27],

–MACRO[28],–LVD[29].Thelowersolidlinestandsforconventionalmuons.Therestofcurvesrepresentthetotalmuon ux,sumofpromptmuonsandconventionalones.

Pasquali,RenoandSarcevic[2](hereafterPRS–dottedlineswithnumbers1,2,3)andmodelsbyGelmini,GondoloandVarieschi[3,4](GGV–thincurveswithnumbers0.1–0.5).Thesemodelsareusedfurtherincalculationsofthedeep-seamuon ux.LetussketchoutPQCDmodels.

2.1.ThemodelbyPasquali,RenoandSarcevic

2.1.1.PRS-1.ThePRS-1model(dottedlinesin gures1,2)(identicalwiththePQCD-1inreference[9])isbasedontheMRSD set[5].ThePDFinputparametersare

thefollowings:xg(x,Q2 0.50)～xasx→0,4-momentumtransfersquaredQ20=4GeV2

;

thesealightquarkasymmetry,

d,istakingintoconsideration;theQCDscaleintheminimalsubtractionscheme(MS

4

=0.215GeV,correspondstothee ectivecouplingattheZbosonmassscaleαs(MZ2

)=0.111.ThefactorizationscaleisµF=2mc,therenormalizationoneisµR=mc,wherethecharmquarkmass,mc,ischosentobeequal1.3.Thesea-levelpromptmuon uxhasbeenparameterizedbyauthors[2]withtheequation:

lg[E3D,Λc

1µφµ(Eµ)·(cm 2ssr 1GeV2) 1]= 5.91+0.290y+0.143y2 0.0147y3,

(1)

wherey=lg(

Eµ

The prompt muon contribution to the deep-sea atmospheric muon flux can serve as a tool for probing into the small-x feature of the gluon density inside of a nucleon, if the muon energy threshold could be lifted to 100 TeV. The prompt muon flux underwater i

2.1.2.PRS-2.InthePRS-2model(thesameasthePQCD-2inreference[9])CTEQ3Mset[6]wasused.CorrespondinginputswhichwereutilizedinthismodelareΛ

(γ0+γ1y+γ2y2+γ3y3)

1GeV

cm 2s 1sr 1GeV 1.

(4)

Intable1 vesetsoftheparameterstoequation(4)arepresentedfordi erentvaluesoftheindexλofthesmall-xgluondestribution.

Table1.Parametersofthepromptmuonspectrumatsealevel(4).

0.13.122.70 0.0951.49 0.21480.23.542.71 0.0821.12 0.02850.31.802.380.045 0.820.9110.40.972.090.160 2.571.7490.50.581.840.257 4.052.455

The prompt muon contribution to the deep-sea atmospheric muon flux can serve as a tool for probing into the small-x feature of the gluon density inside of a nucleon, if the muon energy threshold could be lifted to 100 TeV. The prompt muon flux underwater i

3.Theconventionalmuon ux

Themainsourceoftheatmosphericmuonsupto～50TeVaredecayscosmicraypionsandkaons.The ux(conventional)of(π,K)-muonsbasedonthenuclearcascademodelby[33](seealso[32,34]).partofthisspectrumfortheverticalmaybeapproximatedwiththecm 2s 1sr 1GeV 1):

3.672

14.35EµforE1<Eµ E2,π,K

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