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Measurement of the spin-dependent structure function g1(x) of the proton [Phys. Lett. B 329 (1994) 399]

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Measurement of the spin-dependent structure function g1(x) of the proton [Phys. Lett. B 329 (1994) 399]
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  EUROPEANORGANIZATIONFORNUCLEARRESEARCH CERNPPE9347 8March1993  MEASUREMENTOFTHESPIN-DEPENDENTSTRUCTURE FUNCTION  g  1  x   OFTHEDEUTERON  TheSpinMuonCollaborationSMC Abstract Wereportontherstmeasurementofthespin-dependentstructurefunction  g  d 1 ofthedeuteroninthedeepinelasticscatteringofpolarisedmuonsopolariseddeuterons,inthekinematicalrange0  : 006  x  0  : 6,1GeV  2 Q  2   30GeV  2 .Therstmoment,  d 1 =  R  10 g  d 1 dx  =0  : 023    0  : 020 stat:    0  : 015 syst: ,issmallerthanthepredictionoftheEllis-Jaesumrules.Usingearliermeasurementsof g  p 1 ,weinfertherstmomentofthespin-dependentneutronstructurefunction  g  n 1 .Thedierence  p 1     n 1 =0  : 20    0  : 05 stat:    0  : 04 syst: agreeswiththepredictionoftheBjorken sumrule,  p 1     n 1 =0  : 191    0  : 002. SubmittedtoPhysicsLettersB   B.Adeva  20 ,S.Ahmad  18 ,A.Arvidson  23 ,B.Badelek  23 ; 25 ,M.K.Ballintijn  23 ; 15 ,G.Bardin  19 ,G.Baum  1 ,P.Berglund  4 ; 8 ,L.Betev  13 ,I.G.Bird  19 ;a ,R.Birsa  22 ,P.Bjorkholm  23 ,B.E.Bonner 18 ,N.deBotton  4 ; 19 ,M.Boutemeur 26 ;b ,F.Bradamante  22 ,A.Bressan  22 ,A.Brull 6 ,J.Buchanan  18 ,S.Bultmann  1 ,E.Burtin  19 ,C.Cavata  19 ,J.P.Chen  24 ,J.Clement 18 ,M.Clocchiatti 22 ,M.D.Corcoran  18 ,D.Crabb  24 ,J.Cranshaw  18 ,T.Cuhadar 4 ;c ,S.DallaTorre  22 ,R.vanDantzig  15 ,D.Day  24 ,S.Dhawan  26 ,C.Dulya  2 ,A.Dyring  23 ,S.Eichblatt 18 ,J.C.Faivre  19 ,D.Fasching  17 ,F.Feinstein  4 ;d ,C.Fernandez  20 ; 9 ,B.Frois 19 ,C.Garabatos 20 ;a ,J.A.Garzon  20 ; 9 ,L.Gatignon  4 T.Gaussiran  18 ,M.Giorgi 22 ,E.vonGoeler 16 ,I.A.Goloutvin  10 ,A.Gomez  20 ; 9 ,G.Gracia  20 ,M.GrossePerdekamp  2 ,W.Grubler 5 ,D.vonHarrach  11 ,T.Hasegawa  14 ;e ,P.Hautle  5 ,N.Hayashi 14 ,C.A.Heusch  3 ,N.Horikawa  14 ,V.W.Hughes 26 ,G.Igo  2 ,S.Ishimoto  14 ;f ,T.Iwata  14 ,M.deJong  11 ,E.M.Kabu  11 ,R.Kaiser 6 ,A.Karev  10 ,H.J.Kessler 6 ,T.J.Ketel 15 ,I.Kiryushin  10 ,A.Kishi 14 ,Yu.Kisselev  10 ,L.Klostermann  15 ,W.Knop  7 ,V.Krivokhijine  10 ,V.Kukhtin  10 ,J.Kyynarainen  8 ,M.Lamanna  22 ,U.Landgraf 6 ,K.Lau  9 ,T.Layda  3 ,F.Lehar 19 ,A.deLesquen  19 ,J.Lichtenstadt 21 ,T.Lindqvist 23 ,M.Litmaath  15 ,S.Lopez-Ponte  20 ; 9 ,M.Lowe  18 ,A.Magnon  4 ; 19 ,G.K.Mallot 4 ; 11 ,F.Marie  19 ,A.Martin  22 ,J.Martino  19 ,B.Mayes 9 ,J.S.McCarthy  24 ,G.vanMiddelkoop  15 ,D.Miller 17 ,J.Mitchell 24 ,K.Mori 14 ,J.Moromisato  16 ,G.S.Mutchler 18 ,J.Nassalski 25 ,L.Naumann  4 ,B.Neganov  10 ,T.O.Niinikoski 4 ,J.E.J.Oberski 15 ,S.Okumi 14 ,A.Penzo  22 ,G.Perez  3 ;g ,F.Perrot-Kunne  19 ,D.Peshekhonov  10 ,R.Piegaia  4 ;h ,L.Pinsky  9 ,S.Platchkov  19 ,M.Plo  20 ,D.Pose  10 ,H.Postma  15 ,T.Pussieux  19 ,J.Pyrlik  9 ,J.M.Rieubland  4 ,A.Rijllart 4 ,J.B.Roberts 18 ,M.Rodriguez  20 ,E.Rondio  25 ,L.Ropelewski 25 ,A.Rosado  13 ,I.Sabo  21 ,J.Saborido  20 ,G.Salvato  22 ,A.Sandacz  25 ,D.Sanders 9 ,I.Savin  10 ,P.Schiavon  22 ,P.Schuler 26 ;i ,R.Segel 17 ,R.Seitz  11 ,S.Sergeev  10 ,F.Sever 15 ;j ,P.Shanahan  17 ,G.Smirnov  10 ,A.Staude  13 ,A.Steinmetz  11 ,H.Stuhrmann  7 ,K.M.Teichert 13 ,F.Tessarotto  22 ,W.Thiel 1 ;k ,S.Trentalange  2 ,Y.Tzamouranis 9 ;l ,M.Velasco  17 ,J.Vogt 13 ,R.Voss 4 ,R.Weinstein  9 ,C.Whitten  2 ,R.Windmolders 12 ,W.Wislicki 25 ,A.Witzmann  6 ,A.Ya~ nez  20 ,N.I.Zamiatin  10 ,A.M.Zanetti 22  Inthepast15years,twoexperimentaldeterminationsofthespin-dependentstruc-turefunction  g  p 1  x  oftheprotonweremadefrommeasurementsofcrosssectionasym-metriesindeepinelasticscatteringoflongitudinallypolarisedleptonsbylongitudinally polarisedprotons.TherstwasanexperimentatSLAC1inwhichpolarisedelectronswithenergiesbetween6and21GeVwereusedandwhichcoveredthekinematicrange 0  : 1  x  0  : 7,where  x  istheBjorkenscalingvariable.ThesecondwasanexperimentatCERN2inwhichpolarisedmuonsof100,120and200GeVenergywereused,and whichcoveredthe  x  range0  : 01  x  0  : 7.Theresultoftheseexperimentsdisagrees 1 UniversityofBielefeld,PhysicsDepartment,4800Bielefeld1,Germany  m  2 UniversityofCalifornia,DepartmentofPhysics,LosAngeles,90024CA,USA  n 3 UniversityofCalifornia,InstituteofParticlePhysics,SantaCruz,95064CA,USA  4 CERN,1211Geneva23,Switzerland  5 ETH,8093Zurich,Switzerland  6 UniversityofFreiburg,PhysicsDepartment,7800Freiburg,Germany  m  7 GKSS,2054Geesthacht,Germany  m  8 HelsinkiUniversityofTechnology,LowTemperatureLaboratory,02150Espoo,Finland  9 UniversityofHouston,DepartmentofPhysics,Houston,77204-5504TX,andInstituteforBeam ParticleDynamics,Houston,77204-5506TX,USA  n;o 10 JINR,LaboratoryofSuperHighEnergyPhysics,Dubna,Russia  11 UniversityofMainz,InstituteforNuclearPhysics,6500Mainz,Germany  m  12 UniversityofMons,FacultyofScience,7000Mons,Belgium  13 UniversityofMunich,PhysicsDepartment,8000Munich,Germany  m  14 NagoyaUniversity,DepartmentofPhysics,Furo-Cho,Chikusa-Ku,464Nagoya,Japan  p 15 NIKHEF,FOMandFreeUniversity,1009AJAmsterdam,TheNetherlands q 16 NortheasternUniversity,DepartmentofPhysics,Boston,02115MA,USA  o 17 NorthwesternUniversity,DepartmentofPhysics,Evanston,60208IL,USA  n;o 18 RiceUniversity,BonnerLaboratory,Houston,77251-1892TX,USA  n 19 DAPNIA,CENSaclay,91191Gif-sur-Yvette,France 20 UniversityofSantiago,DepartmentofParticlePhysics,15706SantiagodeCompostela,Spain  r 21 TelAvivUniversity,SchoolofPhysics,69978TelAviv,Israel s 22 INFNTriesteandUniversityofTrieste,DepartmentofPhysics,34127Trieste,Italy  23 UppsalaUniversity,DepartmentofRadiationSciences,75121Uppsala,Sweden  24 UniversityofVirginia,DepartmentofPhysics,Charlottesville,22901VA,USA  o 25 WarsawUniversityandSoltanInstituteforNuclearStudies,00681Warsaw,Poland  t 26 YaleUniversity,DepartmentofPhysics,NewHaven,06511CT,USA  n a NowatCERN,1211Geneva23,Switzerland  b NowatUniversityofMontreal,PQ,H3C3J7,Montreal,Canada  c Permanentaddress:BogaziciUniversity,Bebek,Istanbul,Turkey  d Permanentaddress:DAPNIA,CENSaclay,91191Gif-sur-Yvette,France e Permanentaddress:MiyazakiUniversity,88921Miyazaki-Shi,Japan  f Permanentaddress:KEK,305Ibaraki-Ken,Japan  g Permanentaddress:UniversityofHonduras,PhysicsDepartment,Tegucigalpa,Honduras h Permanentaddress:UniversityofBuenosAires,PhysicsDepartment,1428BuenosAires,Argentina  i NowatSSCLaboratory,Dallas,75237TX,USA   j NowatESRF,38043Grenoble,France k NowatPhilipsKommunikations-IndustrieAG,8500Nurnberg10,Germany  l NowatUniversityofVirginia,Dept.ofPhysics,Charlottesville,22901VA,USA  m SupportedbyBundesministeriumfurForschungundTechnologie n SupportedbytheDepartmentofEnergy  o SupportedbytheNationalScienceFoundation  p SupportedbyMonbushoInternationalScienceResearchProgram  q SupportedbytheNationalScienceFoundationoftheNetherlands r SupportedbyComisionInterministerialdeCienciayTecnologia  s SupportedbytheUS-IsraelBinationalScienceFoundation,Jerusalem,Israel t SupportedbyKBN  1   withthepredictionoftheEllis-Jaesumrule3fortheprotonandindicatesthatinthe quark-partonmodel,thespinsofquarksandantiquarkscontributelittletothespinoftheproton.Inalargenumberofpapers,avarietyoftheoreticalideaswereproposedto explainthisunexpectedresult4.SeveralexperimentsarepresentlybeingcarriedoutorpreparedatCERN5,SLAC6,andDESY7tomeasurethespinstructurefunction oftheneutronandtorepeattheprotonmeasurementwithimprovedaccuracy.Inthispaper,wepresentrstresultsfromameasurementofthecrosssection asymmetryforthedeuteron, A  d =    "#     ""   "# +    "" : 1Inthisexpression,   "#    "" arethecrosssectionsforinclusivedeepinelasticscattering oflongitudinallypolarisedmuonsolongitudinallypolariseddeuterons,forantiparallelparallelorientationofbeamandtargetpolarisations.Fromthisasymmetry,weevaluate thespin-dependentstructurefunction  g  d 1  x  ,whichwethenusetotestthepredictionoftheEllis-Jaesumrules3.Incombinationwiththeearlierresultsfrommeasurementswithprotontargets,ourdataallowustoevaluatetherstmomentofthestructure function  g  n  1  x  oftheneutronandtotesttheBjorkensumrule8.Theexperimentusesapolarisedmuonbeam,apolariseddeuterontarget,aspec-trometertomeasurethescatteredmuon,andabeampolarimeter.Thetargetandthe spectrometerarebasedontheapparatusbuiltbytheEMCcollaboration2,9,buthave beenupgradedtoreducesystematicuncertainties5,10.Thepolarimeterisnewandwillbedescribedinaforthcomingpublication11.Forthisexperiment,wehaveusedabeamofpositivemuonswithanaverageenergy of100GeV12,aspilltimeof2.4sandaperiodof14.4s.Thebeamintensitywas4    10  7 muonsperspill.Theincidentmuonmomentumismeasuredonanevent-by-eventbasis.ThepolarisedtargetinthepresentexperimentusesthesamecryogeniccomponentsastheEMCtarget2,13,14.Asuperconductingsolenoidprovidesamagneticeld of2.5Tparalleltothebeamdirection.Adilutionrefrigeratorcoolsthetargettoa temperatureofabout500mKduringpolarisation,andto50mKduringfrozenspin operation.Thetargetisdividedintwohalves,each40cmlongand5cmindiameter,separatedby20cm.Thelongitudinalpolarisationsinthetwohalvesareoppositeinsign sothatdatacanberecordedforbothpolarisationdirectionssimultaneously.Thetargetmaterialisdeuteratedbutanolwithanadmixtureofparamagnetic molecules.DynamicNuclearPolarisationDNPisobtainedbyapplyingmicrowavesatafrequencyclosetotheresonanceoftheparamagneticelectrons.Thetypicaldeuteron polarisationwasabout0.25untilitwasdiscoveredthatasubstantialincreaseinthepo-larisationcanbeobtainedbymodulatingrapidlythemicrowavefrequencyoverarange of30MHz15.Inthisway,deuteronpolarisationslargerthan0.40havebeenroutinely obtained.Thepolarisationismeasuredusing10NMRcoilsembeddedinthetargetma-terial.TheintegratedNMRabsorptionsignalswerecalibratedinthermalequilibriumat1.1K.Thisallowsustomeasurethepolarisationtoanaccuracyofabout0  : 02.Inordertominimisesystematicerrors,wereversedthepolarisationdirectionsin thetwotargethalvesatregulartimeintervals.Formostofourdatathespinswere reversedevery8hoursbyrotatingtheelddirectionusingthe0.2Ttransverseeldofa newsuperconductingdipolecoilwoundonthemicrowavecavity.Inaddition,therelative orientationofthesolenoideldandthetargetpolarisationwaschangedatleastonceperweekwithDNP.2   Intherststageofthemuonspectrometer,chargedparticlesaremomentumanal-ysedwithaconventionallarge-aperturedipolemagnetandseveralsetsofproportionaland driftchambers.Hadronsareabsorbedinanironwall.Downstreamofthiswallstreamertubes,drifttubes,proportionalchambersandscintillatorhodoscopesareusedformuon identicationandtriggering.Thebeampolarisationisdeterminedfromtheshapeoftheenergyspectrumofthe positronsfromthedecay    +  !  e  +    e       .Downstreamofthemuonspectrometer,a30m longmuondecaypathisdenedbetweenashowervetohodoscopewhichidentiesthe    +  andadipolemagnetwherethemomentumofthe  e  +  ismeasuredusingmultiwire proportionalchambers.Identicationofthedecaypositronsisdoneusingtheenergy depositedinaleadglasscalorimeter.Radiativecorrectionsaretakenintoaccount.For100GeVpositivemuons,thebeampolarisationisfoundtobe  P    =    0  : 82    0  : 06,ingood agreementwithMonteCarlosimulationsofthebeamtransport12.O-lineeventreconstructionprogramsdeterminethekinematicsoftheincidentandscatteredmuonandthevertexposition.Startingfromthescatteredmuonidentied downstreamoftheabsorberwallinthemuonspectrometer,theupstreamtrajectory isreconstructeduptotheinteractionpoint.Theaveragevertexresolutionis3cmin thedirectionofthebeamand0.3mminthetransverseplane.Thispermitsagood identicationoftheeventsoriginatingfromtheupstreamanddownstreamtargetcells.AMonteCarlosimulationwasdevelopedforourexperimentalset-upusingthe GEANTprogram16.Thedetaileddescriptionoftheapparatusincludestheresolutionsandecienciesofalldetectors.Thesimulationusesthedistributionofincidentmuonsrecordedduringthedatataking.TheMonteCarloprogramhasbeenusedtotesttheeventreconstruction,todeterminesmearingduetoniteresolutionandtoestimatesystematic errors.Wereporthereondatatakenin1992,coveringthekinematicrange1GeV  2 Q  2   30GeV  2 and0  : 006  x  0  : 6.Cutswereappliedonkinematicvariablesinorderto minimisesmearingeects,tolimitthesizeofradiativecorrections,andtorejectmuonsoriginatingfromthedecayofpionsproducedinthetarget.Aftercuts,thedatasample amountsto3  : 2    10  6 eventswithanaveragedeuteronpolarisation  P  T  =0  : 35.Themeasuredeventyieldsfromthetwotargetcellscanbeexpressedintermsofthecrosssectionasymmetry  A  d : N  u =  n  u   a  u   0 1    fP    P  u A  d 2 N  d =  n  d   a  d   0 1    fP    P  d A  d  ; 3wherethesubscripts u  and  d  refertotheupstreamanddownstreamtargetcells, n  isthenumberoftargetnucleons,thebeamux, a  theapparatusacceptance,   0 the unpolarisedcrosssection, f  thefractionoftheeventyieldfromthedeuteronsinthe targetmaterialdilutionfactor,and  P    and  P  u;d arethebeamandtargetpolarisations.Thesignofthepolarisationofboththetargetandtheincidentmuonisdenedtobe positivewhenparalleltothebeamdirection.Withthisdenition, P    isnegativeforthe    +  beam,and  P  u and  P  d areofoppositesign.Cutsareappliedtoensurethatthebeam uxisthesameforbothtargetcells.Thedilutionfactoris f  '  0  : 19,andtheraw asymmetry  fP    P  T  A  d isoforder10    3 .Thelongitudinalvirtualphotonasymmetry  A  d 1 isrelatedtothemuon-deuteron 3 
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