GudridMoortgat–Pick
DeutschesElektronen–SynchrotronDESY,Hamburg,Germany∗
(Dated:February1,2008)
Beampolarizationate+e−linearcolliderswillbeapowerfultoolforhighprecisionanalyses.Inthispaperwesummarizethepolarization-relatedresultsforHiggsandelectroweakphysics,QCD,SupersymmetryandalternativetheoriesbeyondtheStandardModel.Moststudiesweremadeforaplannedlinearcollideroperatingintheenergyrange
√2
(λ=−1
s=500−800GeV.Theresultsshowthattherearesixprincipaladvantagestobegainedwhen
bothbeamsarepolarized:(1)highereffectivepolarizationPeff=(Pe−−Pe+)/(1−Penhancementofrates(L)(4)increasedsensitivitytonon-standardcouplings,e−Pe+),(2)suppressionofbackground(3)(5)testofchiralquantumnumbersofSUSYscalarparticles,and(6)improvedaccuracyinmeasuringthepolarization.Thesefeatureswillbediscussedingreaterdetailinthefollowingsections.InparticularbothforSUSYandforhighprecisionstudiesinelectroweakphysicsthepolarizationofbothbeamsiscrucial.
II.
HIGGSPHYSICS
InordertoestablishexperimentallytheHiggsmechanismasthemechanismofelectroweaksymmetrybreakinganaccuratestudyoftheproductionanddecaypropertiesofHiggscandidatesisneeded.ThestudyofHiggsparticleswillthereforerepresentacentralthemeofthephysicsprogrammeofafutureLC.HiggsproductionataLCoccursmainlyviaWWfusion,e+e−→Hνν¯,andHiggsstrahlung,e+e−Polarizingbothbeamsenhancesthesignalandsuppressesbackground.Thescalingfactors,i.e.ratiosofpolarized→HZ.andunpolarizedcrosssection,aregiveninTableI[4,5].BeampolarizationcanhelptomeasuretheHZZandtheHWWcouplingseparatelye.g.viasuppressionoftheWWbackground(andthesignalofWWfusion)andenhancementoftheHZcontributionwithrightpolarizedelectronsandleftpolarizedpositrons.Further,variationoftherelativeamountsofHiggs-strahlungandWWfusionmakesitpossibletokeepthesystematicsarisingfromthecontributionstothefittedspectrumforthesetwoprocessessmallerthanthestatisticalaccuracy.MoreoverbeampolarizationreducesconsiderablytheerrorwhendeterminingtheHiggscouplings.Inan
2
TABLEI:HiggsproductioninStandardModel:Scalingfactors,i.e.ratiosofpolarizedandunpolarizedcrosssectionσpol/σunpol,aregiveninHiggsproductionandbackgroundprocessesfordifferentpolarizationconfigurationswith|Pe−|=80%,|Pe+|=60%[4,5].
Configuration(R0)(L0)
0.201.80
e+e−→HZe+e−→WW,e+e−→Zνν¯
0.76
1.25
1.261.700.102.85
Pe−=80%,Pe+=0
Re(bZ)Re(cZ)
0.000550.00065
0.000520.00011
Re(˜bZ)Re(˜bγ)
0.00104
0.00618
0.000320.00032
0.000780.001010.000230.00011
2
HZµZµ+
gZ
s=500GeVandL=300fb−1
[6].ItshowsthattheZZΦcouplingiswellconstrained.However,tofixtheZγΦcouplingbeampolarizationisessential,TableII.Simultaneousbeampolarization(±80,∓60)ofe−ande+beamsresultsinanfurtherreductionof20%–30%intheoptimalerrorscomparedtothecase(±80,0).
III.
ELECTROWEAKPHYSICS
√
AtTESLA[2]itispossibletotesttheSMwithunprecedentedaccuracy[7].Athigh
sanorder–of–magnitudeimprovementintheaccuracyofthe√2l
determinationofsinΘeffat
(σRR+σRL−σLR−σLL)(−σRR+σRL−σLR+σLL)
3
schemealsorequiressomeluminosityforthelessfavouredcombinations(LL)and(RR).Howeveronlyabout10%ofrunningtimewillbeneededforthesecombinationstoreachthedesiredaccuracyforthesehighprecisionmeasurements.TheBlondelSchemehastheadditionaladvantagethatthepolarizationmeasuredinthiswayistheluminosity-weightedvalueattheinteractionpoint,ratherthanthevalueatthelocationofthepolarimeter.√High
s=500GeVandwith|Pe−|=80%statisticalerrorsofO(10−4)canbe
reached.Moreover,usingsimultaneousbeampolarization(80,60)theerrorscanbefurtherreducedbyuptoafactor1.8comparedtothecasewith(80,0).[9].Anfurtheradvantageofusingpolarizede−ande+beamsisthatonecouldgainaboutafactortwoinrunningtimebyusingtheoptimalbeamconfiguration[8].
IV.
QCDPHYSICS
Strong–interactionmeasurementsatafutureLCwillformanimportantcomponentofthephysicsprogramme.Werestrictourselvesinthissectiontothestudyofpolarizationeffectsasatoolfordetermininga)thetopcouplingsandb)polarizedγstructurefunctions.
ProductionoftopsandFCNcouplings:HighprecisionmeasurementsofthepropertiesandtheinteractionoftopquarkswillbeanessentialpartoftheLCresearchprogramsincethetopasheaviestknownelementaryparticleprobablyplaysakeyroleinpinningdowntheoriginofelectroweaksymmetrybreaking.In[12]polarizationeffectswerestudiedatthetopthreshold.Themainbackgroundcomesfrome+e−→W+W−.ThescalingfactorsforsuppressingthisbackgroundareshowninTableI.Thegaininusingsimultaneouslypolarizede−ande+beams(80,60)isgivenbythehighereffectivepolarizationofPeff=0.946comparedtothecaseforonlypolarizedelectronssothatthetopvectorcouplingsvtcanbemeasuredupto1%withL=300fb−1.Theadvantageofusingpolarizede−ande+beamshasalsobeenstudiedforderivinglimitsontopflavourchangingneutralcouplings(FCN)fromsingletopproductionanditsFCNdecays[13].Withe−ande+polarization(80,45),limitsareimprovedbyaboutafactor2.5comparedtounpolarizedbeams,wherasineachcasethepositronpolarizationimprovesthelimitsobtainedwithonlyelectronpolarizationby30%–40%.Theseimprovementscorrespondtoanincreaseinrateofafactorof6–7.
Polarizedstructurefunctions(PSF)ofphotons:FortheLCγγ,γe−ande−e−modesareconceivable,andthesecouldbeusedtostudypolarizedstructurefunctionsofphotons.ForTESLAtheseoptionsarediscussedasapossibleupgrade,butitisalreadypossibletogetinformationaboutPSFeveninthenormale+e−modeifoneuseshighlypolarizede+ande−beamsintheprocesse+e−→γγ+e+e−→Di-jets+e+e−[14].Sincedepolarizationtendstobelargeattheeγvertexoneneedshighlypolarizede−ande+beamstogetfirstexperimentalhintsonpolarizedPSF.
V.
ALTERNATIVETHEORIES
SearchforadditionalgaugebosonsZ′,W′andforcontactinteractions:BeampolarizationisahelpfultooltoenlargethediscoveryreachofZ′,W′duetohighereffectivepolarizationandcorrespondinglyahigherluminosityforspecificchannels,butthepredictedeffectsarestronglymodeldependent.With(80,60)thediscoveryreachisincreasedby10%–20%comparedtothecasewhen(80,0)[15].Beampolarizationisalsoimportanttodistinguishbetweendifferentmodelsofcontactinteractions.Simulationstudiesaregivenin[15].Using(80,40)insteadofonly(80,0)couldenlargethediscoveryreachforthescaleΛofcontactinteractionsine+e−→b¯bbyupto40%forRRorRLinteractions.
Searchforlargeextradimensions:Inthedirectsearchforextradimensions,e+e−→γG,beampolarizationenlargesthediscoveryreachforthescaleMD[16],andisacrucialtoolforsuppressingthedominantbackgrounde+e−→νν¯γ[17].Inthecaseoftwoextradimensionsthereachisenlargedby16%withsimultaneousbeampolarization(80,60)comparedtothecasewithonlyelectronpolarization.Furthermorethebackgroundcanbesignificantlyreduced,theratioSisimprovedbyafactor2.2for(80,0)andbyafactor5for(80,60).ThisB
correspondstoanincreaseinratebyafactor5comparedtowhenonlyelectronsarepolarized,andafactor25whenbothbeamsarepolarized.
4
VI.
SUSYPHYSICS
PolarizationeffectsplayacrucialroleindiscoveringSUSYandinthedeterminationofsupersymmetricmodelparameters.Simultaneouspolarizationofbothbeamscouldleadtoanadditionalincreaseofthescalingfactoruptoanfactor1.6forrealisticpositronpolarizationscomparedtothecaseofonlypolarizedelectrons,dependingontheprocessandonthescenario[4].Thisenhancementcannotbeexpressedbytheeffectivepolarization,becausetheseratesdependexplicitlyonthepolarizationofbothbeams.Inthefollowing,however,wedonotfocusonthesestatisticaleffectsofbeampolarizationbutonthedeterminationoftheunderlyingSUSYmodel.InSUSYmodelsallcouplingstructuresconsistentwithLorentzinvarianceshouldbeconsidered.ThereforeitispossibletogetappreciableeventratesforpolarizationconfigurationsthatareunfavorableforSMprocesses.Allnumericalvaluesquotedbelow,ifnototherwisestated,aregivenfortheLC–referencescenarioforlowtanβwiththeSUSYparametersM2=152GeV,µ=316GeV,tanβ=3andm0=100GeV[18].
+−˜˜StopSector:In[19]thefeasibilityofdetermining√thestopmixingangleintheprocessee→t1t1atTESLA
hasbeeninvestigated.Thestudywasmadeat
s=450GeV.ForP(e−)=−80%andvariableP(e+)oneseesfromFig.2athatforP(e+)<40%thesignificantlyhighestratesarethoseforthepaire˜−˜+LeR,atleasttwotimeslargerthanforallotherpairs.Thiscleardistinctionbetweenthedifferentproductionchannelsisonlypossibleforenergiesclosetothethresholdsinceforhigherenergiestheeffectsarecoveredbykinematicalreasons.
Atane−e−collidersleptonproductionoccursviat–channelexchange.Itisonlypossibletoverifytheassociationbetweene−˜−L,RandeL,R.
Charginosector:IntheMSSMthecharginoproductiondependsonthefundamentalparametersM2,µ,tanβ,mν˜e.Forcompletelylongitudinallypolarizedbeamsandassumingthatthemassesoftheexchangedsneutrinosmν˜eareknown,ithasbeenshown[22]thattheseparameterscanbedeterminedquitewell.Furthermoreamethodhasbeenshowntoconstrainmν˜eisbeyondthekinematical˜eindirectlyevenifthedirectproductionofmν
+−−
reach[23],sincetheforward–backward–asymmetryofthedecayelectroninee→χ˜+˜−˜−˜0¯,is1eν1χ1,χ1→χverysensitivetomν˜e.Withadditionalpositronbeampolarizationonegetsfurtherincreaseintheratesbyafactorofabout1.6,sothatthestatisticalerrorin∆AFBisreducedby20%.Insinglecharginoproduction,e+e−→e˜χ˜−νe,e+e−→e˜χ˜+ν¯e[3]thepreferredbeampolarizationconfig-urationsare(RR)and(LL),whicharedisfavouredintheSM.Sinceoneexpectssmalleventratespositronpolarizationcouldplayamajorroleinthemeasurementandanalysisofthisprocess.
Neutralinosector:Asinthecasesstudiedbefore,beampolarizationiscrucialforacomprehensivedeter-minationofthefundamentalparameters,andinparticularofM1[24].FurthermoreneutralinoproductioninlowestorderoccursviaZ,e˜Lande˜Rexchangeandissensitivetothechiralcouplingsandthemassesofe˜L,e˜R.Thereforetheorderingofmagnitudeofthecrosssectionsfordifferentpolarizationconfigurationsdependssignificantlyonthecharacteroftheneutralinos[23].
AlinearcolliderwithpolarizedbeamsofferseventhepossibilitytoverifyveryaccuratelythefundamentalSUSYassumptionthattheYukawacouplings,gW˜andg˜areindenticaltotheSU(2)andU(1)gaugecouplingsB
′
gandg.Varyingtheleft–handedandright–handedYukawacouplingsleadstoasignificantchangeinthecorrespondingleft–handedandright–handedproductioncrosssections.CombiningthemeasurementsofthepolarizedcrosssectionsσRwith(+90,−60)andσLwith(−90,+60)fortheprocesse+e−→χ˜0˜01χ2,theYukawa
asdemonstratedinFig.2b.The1σstatisticalcouplingsgW˜canbedeterminedtoquiteahighprecision˜andgB
errorshavebeenderivedforanintegratedluminosityofLdt=100and500fb−1andforP(e−)=±90%,P(e+)=∓60%.
Analoguestothecharginocaseandtheindirectconstrainingofthesneutrinomassitispossibletoconstraintheselectronmassesindirectlyviatheanalysisofforward–backwardasymmetriesofneutralinodecayleptons[23].SinceneutralinosareMajoranafermionstheneutralinoproductionisexactlyforward–backwardsymmetricifCPisconserved.However,duetospincorrelationsbetweenproductionanddecay,nonvanishingasymmetries
∆ALR 10-5201816141210864200.10.20.3¯e+e−→Z→ℓℓ
P=0.8-5
0.40.50.60.70.80.9¯atGigaZFIG.1:TestofElectroweakTheory:Thestatisticalerrorontheleft–rightasymmetryALRofe+e−→Z→ℓℓ
asafunctionofthepositronpolarizationP(e+)forfixedelectronpolarizationPe−=±80%[8].
1P++1000a)σ(ee−→e˜+˜−R,LeR,L)/fb
1000500500e˜−L˜e+R
100e˜−L˜e+L
10050e˜−R˜e
+R5010e˜−R˜e+L
1055-1-0.500.511Pe+
FIG.2:a)ProductioncrosssectionsasafunctionofPe+for
√
b)e+e−10.2
→χ˜0χ˜012
-RY0.15
Pe-=-0.9, Pe+ =+0.6
0.1
0.05
0
500 fb-1-0.05
61.0100 fb--= +eP ,-0.1
9.0+=-eP-0.15
-0.04-0.03-0.02-0.0100.010.020.03
0.040.05
YL-1
6
Pe+
1+−
a)e+e−→χ˜0˜0χ01χ2→2˜1ee
b)
−12%0.5−8%0−4%-0.50%4%8%10%-1-1-0.500.51Pe−
+−+−
FIG.˜0˜0˜0˜01χ2,χ2→χ1ee√3:a)Contourlinesoftheforward–backwardasymmetryofthedecayelectronAFB/%ofee→χat
7
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