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UC Berkeley Previously Published Works

Title

Muon flux measurements at the davis campus of the sanford underground research

facility with the MAJORANA DEMONSTRATOR veto system

Permalink

https://escholarship.org/uc/item/6db9f3tm

Journal

Astroparticle Physics, 93

ISSN

0927-6505

Authors

Abgrall, N

Aguayo, E

Avignone, FT

et al.

Publication Date

2017-07-01

DOI

10.1016/j.astropartphys.2017.01.013

Peer reviewed

eScholarship.org

Powered by the California Digital Library

ContentslistsavailableatScienceDirect

Astroparticle

Physics

journalhomepage:www.elsevier.com/locate/astropartphys

Muon

flux

measurements

at

the

davis

campus

of

the

sanford

underground

research

facility

with

the

majorana

demonstrator

veto

system

N.

Abgrall

a

_,

_E.

_Aguayo

b

_,

_F.T.

_Avignone

_III

c,d

_,

_A.S.

_Barabash

e

_,

_F.E.

_Bertrand

d

_,

_A.W.

_Bradley

a

_,

V.

Brudanin

f

_,

_M.

_Busch

g,h

_,

_M.

_Buuck

i

_,

_D.

_Byram

j

_,

_A.S.

_Caldwell

k

_,

_Y-D.

_Chan

a

_,

C.D.

Christofferson

k

_,

_P.-H.

_Chu

l

_,

_C.

_Cuesta

i

_,

_J.A.

_Detwiler

i

_,

_C.

_Dunagan

k

_,

_Yu.

_Efremenko

m,∗

_,

H.

Ejiri

n

_,

_S.R.

_Elliott

l

_,

_A.

_{Galindo-Uribarri}

d

_,

_T.

_Gilliss

o,h

_,

_G.K.

_Giovanetti

o,h

_,

_J.

_Goett

l

_,

M.P.

Green

p,d,h

_,

_J.

_Gruszko

i

_,

_I.S.

_Guinn

i

_,

_V.E.

_Guiseppe

c

_,

_R.

_Henning

o,h

_,

_E.W.

_Hoppe

b

_,

S.

Howard

k

_,

_M.A.

_Howe

o,h

_,

_B.R.

_Jasinski

j

_,

_K.J.

_Keeter

q

_,

_M.F.

_Kidd

r

_,

_S.I.

_Konovalov

e

_,

R.T.

Kouzes

b

_,

_B.D.

_LaFerriere

b

_,

_J.

_Leon

i

_,

_A.M.

_Lopez

m

_,

_J.

_MacMullin

o,h

_,

_R.D.

_Martin

j,u

_,

R.

Massarczyk

l

_,

_S.J.

_Meijer

o,h

_,

_S.

_Mertens

a

_,

_J.L.

_Orrell

b

_,

_C.

_{O’Shaughnessy}

o,h

_,

_N.R.

_Overman

b

_,

A.W.P.

Poon

a

_,

_D.C.

_Radford

d

_,

_J.

_Rager

o,h

_,

_K.

_Rielage

l

_,

_R.G.H.

_Robertson

i

_,

E.

Romero-Romero

m,d

_,

_M.C.

_Ronquest

l

_,

_C.

_Schmitt

a

_,

_B.

_Shanks

o,h

_,

_M.

_Shirchenko

f

_,

N.

Snyder

j

_,

_A.M.

_Suriano

k

_,

_D.

_Tedeschi

c

_,

_J.E.

_Trimble

o,h

_,

_R.L.

_Varner

d

_,

_S.

_Vasilyev

f

_,

K.

Vetter

a,s

_,

_K.

_Vorren

o,h

_,

_B.R.

_White

d

_,

_J.F.

_Wilkerson

o,h,d

_,

_C.

_Wiseman

c

_,

_W.

_Xu

l,t

_,

E.

Yakushev

f

_,

_C.-H.

_Yu

d

_,

_V.

_Yumatov

e

_,

_I.

_Zhitnikov

f

_,

(The

Majorana

Collaboration)

a_{NuclearScienceDivision,LawrenceBerkeleyNationalLaboratory,Berkeley,CA,USA} b_{PacificNorthwestNationalLaboratory,Richland,WA,USA}

c_{DepartmentofPhysicsandAstronomy,UniversityofSouthCarolina,Columbia,SC,USA} d_{OakRidgeNationalLaboratory,OakRidge,TN,USA}

e_{NationalResearchCenter“KurchatovInstitute” InstituteforTheoreticalandExperimentalPhysics,Moscow,Russia} f_{JointInstituteforNuclearResearch,Dubna,Russia}

g_{DepartmentofPhysics,DukeUniversity,Durham,NC,USA} h_{TriangleUniversitiesNuclearLaboratory,Durham,NC,USA}

i_{CenterforExperimentalNuclearPhysicsandAstrophysics,andDepartmentofPhysics,UniversityofWashington,Seattle,WA,USA} j_{DepartmentofPhysics,UniversityofSouthDakota,Vermillion,SD,USA}

k_{SouthDakotaSchoolofMinesandTechnology,RapidCity,SD,USA} l_{LosAlamosNationalLaboratory,LosAlamos,NM,USA}

m_{DepartmentofPhysicsandAstronomy,UniversityofTennessee,Knoxville,TN,USA}

n_{ResearchCenterforNuclearPhysicsandDepartmentofPhysics,OsakaUniversity,Ibaraki,Osaka,Japan} o_{DepartmentofPhysicsandAstronomy,UniversityofNorthCarolina,ChapelHill,NC,USA}

p_{DepartmentofPhysics,NorthCarolinaStateUniversity,Raleigh,NC,USA} q_{DepartmentofPhysics,BlackHillsStateUniversity,Spearfish,SD,USA} r_{TennesseeTechUniversity,Cookeville,TN,USA}

s_{DepartmentofNuclearEngineering,UniversityofCalifornia,Berkeley,CA94720,US} t_{DepartmentofPhysics,UniversityofSouthDakota,Vermillion,SD,USA}

u_{DepartmentofPhysics,EngineeringPhysicsandAstronomy,Queen’sUniversity,Kingston,Canada}

∗ _{Correspondingauthor.}

E-mailaddress:[email protected](Yu.Efremenko).

http://dx.doi.org/10.1016/j.astropartphys.2017.01.013

a

r

t

i

c

l

e

i

n

f

o

Articlehistory:

Received26February2016 Revised12December2016 Accepted3January2017 Availableonline16February2017

Keywords:

Cosmic Ray Flux

a

b

s

t

r

a

c

t

WereportthefirstmeasurementofthetotalmuonfluxundergroundattheDavisCampusoftheSanford UndergroundResearchFacilityatthe4850 ftlevel.MeasurementswereperformedusingtheMajorana Demonstrator_{muon vetosystemarrangedintwo differentconfigurations.Themeasuredtotalfluxis}

(5.31±0.17)×10−9 _μ/s/cm2 _.

© 2017ElsevierB.V.Allrightsreserved.

1. Introduction

The DavisCampusattheSanford UndergroundResearch Facil-ity(SURF)[1],locatedintheformerHomestakegoldmine,is sit-uated ata depthof4850 ftnearthecityofLead, SD,USA.SURF hasbecomeaprimesiteforlowbackgroundscienceintheUnited States since theinauguration ofits DavisCampus in 2012. Accu-rate characterization of the muon flux and average rock density is important for understanding cosmic-ray-induced backgrounds not only inexisting experimentspresently deployedat SURF, but also for future projects. A previous measurement of the vertical muon flux at the 4850-ft level has been reported [2], and the total muon flux was measured for the 800- and 2000-ft levels

[3]atSURF.Thetotalmuonfluxatthe4850-ftlevelwascalculated to be

(

4.4±0.1

)

×10−9

_μ

_/s/cm2 _{[4]. In this article,we presenta} first measurementofthetotal muonflux atthe4850-ft level

us-ingtheMajoranaDemonstratormuonvetosystem.Wecompare

ourmeasurementtopreviouswork,andtoourownsimulationof muon transportfromthesurfacetotheexperimentusing geolog-ical measurements ofthe average rockdensityofthe SURF over-burden.

TheMajorana Demonstratorisanarray ofenriched and

nat-ural high-purity germanium (HPGe) detectors that are used to searchforthezeroneutrinodouble-beta(

ββ

(0

ν

))decayofthe iso-tope76_{Ge.Thedetailsoftheexperiment’sdesignaregiveninRef.}

[5]andonlykeyaspectsrequiredforthisresultarediscussedhere. ThespecificgoalsoftheMajoranaDemonstratorareto:

1. Demonstrateapathforwardtoachievingabackgroundrateat orbelow1count/(ROI-t-y)inthe4-keVregionofinterest(ROI) around the 2039-keV Q-value for76_Ge

ββ

₍₀

ν

_{) decay. This is} required for tonne-scale germanium-based searches that will probetheinverted-orderingneutrino-massparameterspacefor theeffectiveMajorananeutrinomassin

ββ

(0

ν

)decay. 2. Showtechnicalandengineeringscalabilitytowardatonne-scale

instrument.

3. Perform searches for additional physics beyond the Standard Model,suchasdarkmatterandaxions.

The Majorana _{Collaboration has designed a modular}

instru-ment composed of two cryostats built from ultra-pure electro-formedcopper,witheachcryostatcapableofhousingover20 kg ofHPGe detectors.The Majorana Demonstrator_{contains30 kg}

of detectorsfabricated fromGematerial enriched to 88%in 76_Ge and another 15 kg fabricated from natural Ge (7.8% 76_{Ge). The} modularapproachallows ustoassemble andoptimizeeach cryo-stat independently,providinga fastdeployment withminimal ef-fectonalready-operationaldetectors.

Startingfromtheinnermostcavity,thecryostatsaresurrounded by a compactgraded shield composed ofan inner layer of elec-troformedcopper,alayerofcommerciallysourcedC10100copper, high-purity lead, an active muon veto, borated polyethylene, and

purepolyethyleneshielding.Thecryostats,copper,andlead shield-ingareenclosedinaradonexclusionboxandrestonanover-floor table that has openings for the active muon veto and polyethy-lene shielding panels situatedbelow the detector. The entire ex-perimentislocatedina cleanroomatthe4850 ftlevelofSURF. Ahigh-levelsummaryofshieldcomponentsisshowninFig.1.

Alargefractionoftheplasticscintillatorpanelscomprisingthe activemuon-vetosystemwereoperatedindifferentconfigurations attheexperimentalsiteduringGedetectorconstructionsand com-missioning.Weusedtheresultingdatatomeasurethetotalmuon fluxattheDavisCampusatSURFforthefirsttime.

2. TheMAJORANA DEMONSTRATOR muonvetosystem

TheMajoranaDemonstrator_{muonvetosystemwasdesigned}

to completely enclose the passive copper and lead shield within twolayersofscintillatingpanelswhileminimizinggaps.Eachlayer is composed of 2.54-cm-thick EJ-204B scintillating acrylic sheets encapsulatedwithinAl cladding.Thesedetectorpanelshave vari-ousshapesanddimensionsresultinginatotal areaof ∼ 37 m2_.

TheDemonstratorusesatotalof32vetopanels,includingtwelve

thatresidewithinopeningsoftheoverfloortable intwo orthogo-nalorientations.The datapresentedinthispaperisbasedonthe operationoftwoconfigurations,onewith12vetopanelsrequiring two-foldcoincidence,andonewith14vetopanelsrequiring three-foldcoincidence.Thearrangementofthevetopanelsusedforeach configurationisshowninFig.2.Moredetailsoneachconfiguration aregiveninSections3and4below.

Lightfromeachindividualpanelwasreadoutbyasingle 1.27-cm photomultiplier tube (PMT) with wavelength shifting fibers embedded into grooves machined in the scintillator. The panel components were optimized to provide high light output, good lightcollectionuniformity,andexcellentmuon-detectionefficiency

Fig. 2. LayoutsoftheMajoranaDemonstratorvetopanelsusedinthisstudy.Thelayoutontheleftshowsthetwo-foldcoincidencearrangement,andontherightisthe three-foldcoincidencearrangement.Muonselectionrequireahitinatleastonepanelineachlayer.Forthethree-foldcoincidencearrangementmassiveleadshieldingwas presentbetweenthetoplayerandtheupperofthebottomtwolayersasshowninFig.1.Thebottomlayersresidewithinasteelsupportover-floortable,whichisnot shown.AllotherDemonstratorcomponentsarealsosuppressedinthisview.

(

D > 99.9%) [6]. The details of the data acquisition system for

thevetosystemwere giveninRef.[5].Performanceofeachpanel isconstantlymonitoredwithLightEmittingDiodes(LED) embed-dedin the scintillator. Reconstructed LED events were also used tomeasurethelivetime ofthesystem. TheLEDsare pulsedata frequencyknownwithaprecisionof0.1%.

In a deep underground laboratory the muon flux is low, but

γ

rays fromthe experimentalapparatusandthe laboratory envi-ronmentare significant. As described in [6], the useof the rela-tively thin2.54-cm scintillator panels presents certain challenges forseparatingmuonsfrom

γ

rays andrandom

γ

-raycoincidences attheSURFdepth.Themostprobablemuon-energydeposition in theveto panels is∼ 5 MeV, which islow enough that the high energy tail of the

γ

-ray energy distribution can potentially en-croachupon themuon peak, potentiallyoverwhelming themuon contributiontothe spectrum.The designandconstruction ofthe vetopanelsachievedgoodlightcollectionandensuredthatthe

μ

peakremainedwell-separatedfromthe

γ

-raytailfortwo-foldor higher-multiplicitycoincidences,evenatthelowmuonfluxofthe DavisCampus.

3. Two-foldcoincidencemeasurement

For thefirst configurationwe used thetwelve narrowbottom panelsarrangedinsixpairs.Priortoinstallationintotheirfinal lo-cation,six panels,each with dimensionsof 32 _× 182 cm2_{, were} placedparallelto andontopofan additionalsixpanelswith di-mensions32×223cm2_{.Weselectedeventswherebothatopand} bottom panel simultaneously generated a signal above 1.8 MeV. Inthistwo-foldcoincidenceconfiguration,thelivetimeis1536h (5.53 × 106 _{s) betweenDecember 19, 2013 andMarch 11, 2014.} Thesumofenergydepositsinthetwo panelsisshowninFig.3. Fromthefigure, onecan seethatthe tailfromthe

γ

rays makes itdifficulttopreciselymeasurethemuonfluxfromthis configura-tion.Data werefit bycombinationof anexponential tail approx-imatingthe

γ

background(blue line), anda Landaudistribution formuons(redline).Thecharacterizationofthe

γ

backgroundtail withan exponential functionis justified throughan independent fittoaccidentaltwo-foldcoincidencesbetweenthebottompanels. Theextractednumberofmuonspassingthrough systemis912 ± 43.We note that becausethe pairs ofpanels were adjacent,this configurationissensitivetothetotalmuonfluxbutnotthemuon angulardistribution.

The individual data runswere 8hours andthe spread in the numberofdetectedeventsperrunfollowsPoissonstatistics.Allsix detectorpairshavesimilarmuonratesthatagreewithinstatistical fluctuations.

Sum energy of pairs, MeV

0 5 10 15 20 25 30

Counts / 0.39 MeV

0 10 20 30 40 50 60 70 80 90 100

Fig. 3. Theenergydepositionofselectedeventsforthetwo-foldcoincidence con-figuration(blacksolidhistogram).Thehorizontalscaleisthesummedenergy depo-sitionofthepairedpanels.Thetailfromtheenergydepositionoftheγ rays(blue dashedcurve)isfittedwithanexponentialdistribution.Thesignalfrommuonsis fittedbyaLandaudistribution(reddottedline).Thetotalfitisgivenbythesolid greencurve.Themostprobablesummedenergydepositvalueis10.7± 0.2MeV. (Forinterpretationofthereferencestocolorinthisfigurelegend,thereaderis re-ferredtothewebversionofthisarticle.)

4. Three-foldcoincidencemeasurement

Forthesecondconfigurationweusedthevetopanelsplacedin their planned final arrangement. Inthis configuration, data were selected for three-fold coincidences. Two of these signals came from each of the two layers of twelve panels (arrangedin their final sixby sixorthogonal configurationinthe over-floor,as indi-catedinFig. 2),andthethird signal camefromone oftwo large panelsmountedon thetopoftheexperiment’spassive shielding. A 1.6-mtall lead shield is situated betweenthe top and bottom panels witha small central cavity ofdimensions of (90 _× 50 _× 60cm3_{).Thetoppanelsarelocatedsidebysideandtheir} dimen-sionsareeach84×211cm2_.

un-E, MeV

0 2 4 6 8 10 12

Counts/0.5 MeV

0 10 20 30 40 50

E, MeV

0 2 4 6 8 10 12

Counts/0.5 MeV

0 10 20 30 40 50

Fig. 4. Energydistributionsinthetwolargetoplargepanelsforthesecond con-figurationduringathree-foldcoincidence,showingaclearmuonsignal.Theleft figureshowsdatafromtheupperleftpanelincoincidencewithbottompanelsand ontherightisdatafromtheupperrightpanelincoincidencewithbottompanels. Thesolidlineissimulation,whichhasmuchlargerstatistics.

Fig. 5. Thealtitudeinmofthesurfacedirectlyabovetheundergroundlaboratory, whichislocatedattheoriginoftheplotatanaltitudeof119 m.GeographicNorth isdirectedtowardsthetopofthefigure.Sourceforthisplotisfrom[11].

certainties.The run-to-runeventvariationsagreedwithinPoisson fluctuations.

5. Muonsimulationsandresults

To estimate the total muon flux we must estimate the effec-tive cross-sectional area ofourdetector configurationsrelative to themuonangulardistributionattheDavisCampus.Sincethetwo configurations have qualitatively different response to the muon angulardistribution,thedifferencebetweentheextractedflux val-uesprovides across-check onthesensitivitytothe detailsofthe assumed angulardistribution.To modelthe muon angular distri-butionandtheresponseofeachconfigurationtoit,wesimulated muonspropagatingfromthesurfacethroughtherocktotheDavis Campus, and then through the Majorana Demonstrator

labora-toryandthedetectors.

To understand muon propagation to the experimental site at 4850 ftbelowthesurfaceweperformeddetailedsimulationswith Geant4[7,8],version 4.96p04,usingtheQGSP_BIC_HPphysicslist withmuon-nuclearprocessesturnedon.Asurfacemapofthearea, 10 kminradius,surroundingthelaboratorywasimplementedin Geant4withagranularityof77x100 m,seeFig.5.Thislarge sim-ulated area allows entry angles between 0 and 78 degrees rela-tive tothe verticalaxisformuonsentering theunderground lab-oratory.Muonswithenergies between5 GeVand500TeVusing parametrizationfrom[9]weregeneratedrandomlyona100 km2 plane atan altitudeof 2500 m usingthe surfacemuon flux

en-ergyandangulardistributionfromRef.[10],andtheirpropagation throughtherockwasrecorded.

For the detector response component of the simulations we used both the GEANT3 package [12] in addition to Geant4 to check for consistency. We used energy andangular distributions ofmuonsenteringourlaboratoryfromthemuonpropagation sim-ulations inorderto determinethe effectivearea (A _eff) formuons detectedinbothcoincidenceconfigurations.Wegenerated271,000 muonsoveranareaof10×10m2_{,whichismuchlargerthanthat} ofthevetoarray.Thissurfaceatwhichthemuon pathswere ini-tiatedwassituated1 mabove therockceilingofthe laboratory, 2mabove theupperpanels.Thesemuonswere thenpropagated throughthe laboratory,andeventsin whichmorethan 1MeV is depositedin a panel by eitherthe muon orits secondarieswere recorded.AlldetailsoftheDemonstratorshieldingwereincluded

inthesimulationmodel.

For the two-fold-coincidence configuration simulation, 8779 muonswererecorded,resultinginaneffectivearea(A eff)of3.24 × 104 _cm2_{. For the three-fold-coincidenceconfiguration simulation,} 2876muonsweredetectedresultingin A _{eff =}1_.15_×104 _cm2_.

Themuonflux(F )(Eq.(1))iscalculatedusing A eff,thenumber ofmuonsobserved(N obs),andthelivetimeT ofeachconfiguration.

The statisticaluncertainties are large enough that the systematic uncertaintiesarenegligible.

F = Nobs

Aeff

T

(1)

The coincidence detectrion efficiency

is taken to be > 99.7% basedonthesingle-panelefficiency(

D)measured in[6].Forthe

first configuration with two-fold coincidence, the reconstructed flux was found to be

(

5.09±0.24

)

×10−9

_μ

_/s/cm2_{. Forthe} sec-ond configuration with three-fold coincidence, the reconstructed muonfluxwasfoundtobe

(

5.54±0.23

)

×10−9

_μ

_/s/cm2_.Although there were fewer muons registered for the second configuration, thestatisticalaccuracy issimilar tothe firstconfiguration dueto theabsenceoftherandomcoincidencebackgroundfrom

γ

rays.It shouldalsobe notedthatdatawere takenwiththe first configu-rationwhen themuon flux wasnearits annualminimum, while thesecond configurationdata were taken nearthe annual maxi-mumflux.The4-5%levelannualvariationofthemuon fluxison thesameorderasourpresentstatisticalsensitivity,andwillbethe subjectoffuturestudy.

Combiningresultsfrombothmeasurementsgivesatotalmuon fluxof

(

5.31±0.17

)

×10−9

_μ

_/s/cm2_{,takento be anaverage over} theseasonalvariation.Thesetworesultsderivefromtwovery dif-ferentgeometriesandangularacceptances.Withagreementbetter thanonesigma,weconcludethatthestatisticaluncertainty domi-nates.

1

2

3

4

5

6

0

20

40

60

80

100

120

Bottom parallel + Top left (data) Top left (MC) Top right (data) Top right (MC)

Number

of

events

Panel number

Fig. 6. Eventrateforthecoincidencebetweenthebottom6panelsandtheupper2 panelsforthethree-foldcoincidenceconfiguration.Thesimulationpredictionsare shownaslinesanddataaredisplayedwithstatisticalerrorbars.

6. Discussion

Our measured total flux is somewhat larger than the calcula-tioninRef.[4],althoughthetwoagreeatthe2-

σ

level.Reference

[4]approximatedtheSURFoverburdenwithaflatsurfaceprofile. An early measurement [2] of the vertical muon flux resulted in a value of

(

4_.91_±0_.06

)

_×10−9

_μ

_/s/cm2_{/sr.This measurement} employed large water Cherenkovtanks (200 × 200 × 120 cm3₎ stackedin3 layers.Events consistingofcoincidentsignalswithin 3tanksina vertical-pathtrajectory corresponding toan effective zenith angle < 18 degrees were selected for analysis. To com-pare our estimate for the total muon flux and that of Ref. [2], we integrate our total flux within an 18-degree cone. We calcu-lateaverticalmuonfluxof

(

4.42±0.15stat.

)

×10−9

μ

/s/cm2/sr us-ing our own muon model where the stated uncertainty is only thestatisticaluncertaintyfromourtotalflux measurement. How-ever, the vertical flux extracted from other muon models based on our measured total flux predict different values of

(

4.16± 0.12stat.

)

×10−9

_μ

_/s/cm2_{/sr usingRef. [13]and}

₍

_5.05±0.16

stat.

)

× 10−9

_μ

_/s/cm2_{/sr using a muon angular distribution [14] derived} from the MUSIC package [15]. The spread in the extracted ver-ticalfluxes is a result of differences in the angular distributions nearsmall zenith angle and is indicative of a systematic uncer-taintyintheoverburdenmodelandinthesimulations.Takingthe standard deviationof the three asan estimate of the systematic uncertainty, we calculate the vertical flux to be

(

4_.4_±0_.7syst.

)

× 10−9

_μ

_/s/cm2_{/sr.Thetotalmuonflux,ontheotherhand,is} insen-sitive to the choice of angular distribution model – the system-aticuncertaintyinthetotalfluxextractedusingthethreedifferent angulardistributions isnegligiblerelative tothe statistical uncer-tainty.

We wouldliketo note twothings, however,incomparing our extractedverticalfluxrelativetotheverticalfluxmeasurementof Ref.[2].First,thequoteduncertaintiesinRef.[2]areentirely statis-ticalandnosystematicuncertaintywasestimated.Wewereunable toobtainfromtheauthorsadditionaldetailsabouttheRef.[2] ge-ometryand thresholds inorder to simulatetheir apparatus with thedifferent muon flux angularprofiles. Second, while the mea-surementof[2]wasperformedatthesameundergroundlevel,the separate location ofthe two experiments beneaththe sharp sur-faceprofileresultsinslightlydifferentoverburdensandazimuthal muonfluxdistributions.Nonetheless, whenincludingthe system-aticuncertaintyinthemuonmodelsduetodifferingrockdensity andangulardistribution,ourcalculatedverticalmuonfluxis con-sistentwithRef.[2].

Tostudythe effectofrockdensityfurther,thetotal simulated muonfluxattheDavisCampuswasevaluatedoverarangeofrock

Fig. 7. Thepredictedmuonfluxat4850 ftbasedontheGeant4simulation de-scribedinthetextforseveralvaluesoftheaveragerockdensity.Thedashed(red) curveisanexponentialfittothosesimulateddatapoints.Thetotalsimulation un-certaintiesareindicatedbytheerrorbarsandarecorrelatedbetweenneighboring points.Thehorizontal(gray)shadedregionrepresentsourmeasurementconfidence intervalwiththecentralvalueindicatedbytheblackline.Thevertical(green)band showsrockdensityrangefromgeologicalstudies.(Forinterpretationofthe refer-encestocolorinthisfigurelegend,thereaderisreferredtothewebversionofthis article.)

densities. The simulatedflux has to be normalized to the muon fluxatthe surface,so experimentaldatais usedtoderive a scal-ing factor. A surface muon flux [10] of 2.0±0.2

μ

/s/cm2 _{is used} asreference.Theuncertaintiesinthisvaluetake intoaccountthe uncertainty in altitude as well as possible seasonal variations of theatmospherictemperatureresultingina variationofthemuon flux[16,17].Thedependanceofrockdensityonthetotalflux can beseeninFig.7.Wefindthatarockdensityof2.89_±0.06g/cm3 yieldsatotalmuonfluxconsistentwithourmeasurement.This re-sultagreesverywellwithgeologicalstudiesatSURFthatfoundan averagerockdensityof2.86_±0.11 g/cm3_{[18](takingthenominal} 4%uncertainty)basedoncone45degreesfromvertical.

7. Conclusion

We report for the first time a measurement of the total flux of muons at the SURF Davis Campus. This flux is necessary for presentandfutureexperimentstoassesscosmic-rayinduced back-groundsat thisunderground location.A measured total flux per-mits such an assessment with less interpretation than would be requiredto incorporate effectsof therock density,surface topol-ogy,andmuonangulardistribution. Previousmeasurementswere done at the800 and 2000 ftlevels [3]. The measured flux was foundtobeingoodagreementwiththatpredictedin[4]andwith our ownsimulations using a rockdensitysimilar to values mea-sured in geological studies. A comparison of our result with an oldermeasurement oftheverticalflux [2]isconsistent when in-cludingasystematicuncertaintyonthemuonangulardistribution neededtoconvertourtotalfluxintoaverticalflux.TheMajorana

Demonstratorvetosystemisoperatingintheunderground

envi-ronmentandidentifiesmuonsasexpected.

Acknowledgments

ThismaterialisbaseduponworksupportedbytheU.S. Depart-ment ofEnergy,OfficeofScience,Office ofNuclearPhysicsunder Award Numbers DE-AC02-05CH11231, DE-AC52-06NA25396, DE-FG02-97ER41041, DE-FG02-97ER41033, DE-FG02-97ER41042, DE-SC0012612, DE-FG02-10ER41715, DE-SC0010254, and DE-FG02-97ER41020. We acknowledge support from the Particle Astro-physics Program and Nuclear Physics Program of the National Science Foundation through grant numbers PHY-0919270, PHY-1003940, 0855314,PHY-1202950, MRI 0923142and 1003399.We acknowledge support from the Russian Foundationfor Basic Re-search,grantNo.15-02-02919.Weacknowledgethesupportofthe U.S. Department of Energy through the LANL/LDRD Program. We thank our hosts and colleagues at the Sanford Underground Re-searchFacilityfortheirsupport.

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