Fixedparameterdirection

Eur.
Phys.
J.
C(2012)72:2178DOI10.
1140/epjc/s10052-012-2178-8SpecialArticle-ToolsforExperimentandTheoryInvestigationofMonteCarlouncertaintiesonHiggsbosonsearchesusingjetsubstructurePeterRichardsona,DavidWinnbInstituteofParticlePhysicsPhenomenology,DepartmentofPhysics,UniversityofDurham,DurhamDH13LE,UKReceived:30July2012/Revised:20September2012/Publishedonline:17October2012TheAuthor(s)2012.
ThisarticleispublishedwithopenaccessatSpringerlink.
comAbstractWepresentaninvestigationofthedependenceofsearchesforboostedHiggsbosonsusingjetsubstructureontheperturbativeandnon-perturbativeparametersoftheHer-wig++MonteCarloeventgenerator.
Valuesarepresentedforanewtuneoftheparametersoftheeventgenerator,togetherwiththeanestimateoftheuncertaintiesbasedonvaryingtheparametersaroundthebest-tvalues.
1IntroductionMonteCarlosimulationsareanessentialtoolintheanal-ysisofmoderncolliderexperiments.
Theseeventgenera-torscontainalargenumberofbothperturbativeandnon-perturbativeparameterswhicharetunedtoawiderangeofexperimentaldata.
Whilesignicantefforthasbeendevotedtothetuningoftheparameterstoproduceabestttherehasbeenmuchlesseffortunderstandingtheuncertaintiesintheseresults.
Historicallyabesttresult,oratbestasmallnumberoftunes,areproducedandusedtopredictobserv-ablesmakingitdifculttoassesstheuncertaintyonanypre-diction.
The"Perugia"tunes[1,2]haveaddressedthisbyproducingarangeoftunesbyvaryingspecicparametersinthePYTHIA[3]eventgeneratortoproduceanuncertainty.
HerewemakeuseoftheProfessorMonteCarlotuningsystem[4]togiveanassessmentoftheuncertaintybyvary-ingalltheparameterssimultaneouslyaboutthebest-tval-uesbydiagonalizingtheerrormatrix.
ThisthenallowsustosystematicallyestimatetheuncertaintyonanyMonteCarlopredictionfromthetuningoftheeventgenerator.
Wewillillustratethisbyconsideringtheuncertaintyonjetsubstruc-turesearchesfortheHiggsbosonattheLHC.
AstheLHCtakesincreasingamountsofdatathediscov-eryoftheHiggsbosonislikelyinthenearfuture.
Onceweae-mail:peter.
richardson@durham.
ac.
ukbe-mail:d.
e.
winn@durham.
ac.
ukhavediscoveredtheHiggsboson,mostlikelyinthedipho-tonchannel,itwillbevitaltoexploreotherchannelsanddetermineifthepropertiesoftheobservedHiggsbosonareconsistentwiththeStandardModel.
Formanyyearsitwasbelievedthatitwouldbedifcult,ifnotimpossible,toob-servethedominanth0→bbdecaymodeofalightHiggsboson.
However,inrecentyearstheuseofjetsubstructure[5–20]offersthepossibilityofobservingthismode.
Jetsub-structureforh0→bbasaHiggsbosonsearchchannel,wasrststudiedinRef.
[5]buildingonpreviousworkofaheavyHiggsbosondecayingtoW±bosons[16],high-energyWWscattering[21]andSUSYdecaychains[22],andsubsequentlyreexaminedinRefs.
[8,15].
Recentstud-iesattheLHC[23–25]havealsoshownthisapproachtobepromising.
ThestudyinRef.
[5]wascarriedoutusingthe(FOR-TRAN)HERWIG6.
510eventgenerator[26,27]togetherwiththesimulationoftheunderlyingeventusingJIMMY4.
31[28].
Inordertoallowtheinclusionofnewtheoreticaldevelopmentsandimprovementsinnon-perturbativemod-ellinganewsimulationbasedonthesamephysicsphilos-ophyHerwig++,currentlyversion2.
6[29,30],isnowpre-ferredforthesimulationofhadron–hadroncollisions.
Herwig++includesbothanimprovedtheoreticaldescrip-tionofperturbativeQCDradiation,inparticularforradia-tionfromheavyquarks,suchasbottom,togetherwithim-provednon-perturbativemodeling,especiallyofmultipleparton–partonscatteringandtheunderlyingevent.
InFOR-TRANHERWIGacrudeimplementationofthedead-coneeffect[31]meantthattherewasnoradiationfromheavyquarksforevolutionscalesbelowthequarkmass,ratherthanasmoothsuppressionofsoftcollinearradiation.
InHerwig++animprovedchoiceofevolutionvariable[32]allowsevolutiondowntozerotransversemomentumforradiationfromheavyparticlesandreproducesthecorrectsoftlimit.
Therehavealsobeensignicantdevelopmentsofthemultiple-partonscatteringmodeloftheunderlyingPage2of13Eur.
Phys.
J.
C(2012)72:2178event[33,34],includingcolourreconnections[35]andtun-ingtoLHCdata[36].
ThebackgroundtojetsubstructuresearchesfortheHiggsbosoncomesfromQCDjetswhichmimicthedecayofaboostedheavyparticle.
AlthoughHerwig++hasperformedwellinsomeearlystudiesofjetsubstructure[25,37,38],itisimportantthatweunderstandtheuncertaintiesinourmodellingofthebackgroundjetswhichlieatthetailofthejetmassdistribution.
InadditionweimprovethesimulationofHiggsbosondecaybyimplementingthenext-to-leading-order(NLO)correctionstoHiggsbosondecaytoheavyquarksinthePOWHEG[39,40]formalism.
Inthenextsectionwepresentourapproachforthetun-ingoftheparameters,whicheffectQCDradiationandhadronization,inHerwig++togetherwiththeresultsofournewtune.
WethenrecapthekeyfeaturesoftheButterworth,Davison,RubinandSalam(BDRS)jetsubstructuretech-niqueofRef.
[5].
Thisisfollowedbyourresultsusingboththeleadingandnext-to-leading-ordermatrixelementsinHerwig++withimplementationofthenext-to-leading-orderHiggsbosondecaysandourestimateontheuncertainties.
2TuningHerwig++Anyjetsubstructureanalysisissensitivetochangesinthesimulationofinitial-andnal-stateradiation,andhadronization.
Inparticularthenon-perturbativenatureofthephenomenologicalhadronizationmodelmeansthereareanumberofparameterswhicharetunedtoexperimentalresults.
Herwig++usesanimprovedangular-orderedpartonshoweralgorithm[29,32]todescribeperturbativeQCDra-diationtogetherwithaclusterhadronizationmodel[29,41].
TheHerwig++clustermodelisbasedontheconceptofpreconnement[42].
Attheendoftheparton-showerevo-lutionallgluonsarenon-perturbativelysplitintoquark–antiquarkpairs.
Allthepartonscanthenbeformedintocolour-singletclusterswhichareassumedtobehadronpre-cursorsanddecayaccordingtophasespaceintotheob-servedhadrons.
Thereisasmallfractionofheavyclus-tersforwhichthisisnotareasonableapproximationwhicharethereforerstssionedintolighterclusters.
Themainadvantageofthismodel,whencoupledwiththeangular-orderedpartonshoweristhatithasfewerparametersthanthestringmodelasimplementedinthePYTHIA[3]eventgeneratoryetstillgivesareasonabledescriptionofcolliderobservables[43].
TotuneHerwig++,andinvestigatethedependencyofob-servablesontheshowerandhadronizationparameters,theProfessorMonteCarlotuningsystem[4]wasused.
Profes-sorusestheRivetanalysisframework[58]andanumberofsimulatedeventsamples,withdifferentMonteCarloparam-eters,toparameterisethedependenceofeachobservable1usedinthetuningontheparametersoftheMonteCarloeventgenerator.
Aheuristicchi-squaredfunctionχ2(p)=OwOb∈O(fb(p)Rb)22b,(1)isconstructedwherepisthesetofparametersbeingtuned,OaretheobservablesusedeachwithweightwO,barethedifferentbinsineachobservabledistributionwithassociatedexperimentalmeasurementRb,errorbandMonteCarlopredictionfb(p).
Weightingofthoseobservablesforwhichagooddescriptionoftheexperimentalresultisimportantisusedinmostcases.
Theparameterisationoftheeventgen-eratorresponse,f(p),isthenusedtominimizetheχ2andndtheoptimumparametervalues.
TherearetenmainfreeparameterswhichaffecttheshowerandhadronizationinHerwig++.
TheseareshowninTable1alongwiththeirdefaultvaluesandallowedranges.
Thegluonmass,GluonMass,isrequiredtoallowthenon-perturbativedecayofgluonsintoqqpairsandcon-trolstheenergyreleaseinthisprocess.
PSplitLight,ClPowLightandClMaxLightcontrolthemassdistri-butionsoftheclustersproducedduringthessionofheavyclusters.
ClSmrLightcontrolsthesmearingofthedirec-tionofhadronscontaininga(anti)quarkfromtheperturba-tiveevolutionaboutthedirectionofthe(anti)quark.
Al-phaMZisstrongcouplingattheZ0bosonmassandcon-trolstheamountofQCDradiationinthepartonshower,whileQmincontrolstheinfraredbehaviourofthestrongcoupling.
pTministheminimumallowedtransversemo-mentuminthepartonshowerandcontrolstheamountofradiationandthescaleatwhichtheperturbativeevolutionterminates.
PwtDIquarkandPwtSquarkaretheproba-bilitiesofselectingadiquark–antidiquarkorssquarkpairfromthevacuumduringclustersplitting,andaffectthepro-ductionofbaryonsandstrangehadronsrespectively.
PreviousexperienceoftuningHerwig++hasfoundthatQmin,GluonMass,ClSmrLightandClPowLighttobeat,andsoitwaschosentoxtheseattheirdefaultval-ues[29].
TodeterminetheallowedvariationoftheseparametersProfessorwasusedtotunethevariablesinTable1totheobservablesandweightsfoundinAppendixAinTables5,6,7and8.
Thedependenceofχ2onthevariousparameters,abouttheminimumχ2value,isthendiagonalized.
Thevariationoftheparametersalongtheeigenvectorsinparameterspaceobtainedcorrespondingtoacertainchange,χ2,inχ2canthenbeusedtopredicttheuncertaintyintheMonteCarlopredictionsforspecicobservables.
1Normallythisiseitheranobservationsuchasamultiplicityorabininameasureddistribution.
Eur.
Phys.
J.
C(2012)72:2178Page3of13Table1Thetenparameterstowhichthejetsubstructureismostsensitivewiththeirdefaultvalues,theallowedrangeofthesevaluesinHerwig++,therangescannedoverandthenewoptimumvaluefoundfromminimizingχ2ParameterDefaultvalueAllowedrangeScannedrangeOptimumvalueQmin0.
935≥00.
500–2.
500FixedatdefaultGluonMass0.
950–10.
75–1.
00FixedatdefaultClSmrLight0.
780–20.
30–3.
00FixedatdefaultClPowLight1.
280–100.
50–4.
00FixedatdefaultpTmin1.
00≥00.
50–1.
500.
88AlphaMZ0.
12≥00.
10–0.
120.
11ClMaxLight3.
250–103.
00–4.
203.
60PSplitLight1.
200–101.
00–2.
000.
90PwtDIquark0.
490–100.
10–0.
500.
33PwtSquark0.
680–100.
50–0.
800.
64Intheory,iftheχ2measurefortheparameterisedgen-eratorresponseisactuallydistributedasatrueχ2,thenachangeinthegoodnessoftofonewillcorrespondtoaonesigmadeviationfromtheminima,i.
e.
thebesttune.
Inprac-tice,eventhebesttunedoesnottthedataideallyandnoristheχ2measureactuallydistributedaccordingtoatrueχ2distribution.
ThismeansthatonecannotjustuseProfessortovarytheparametersabouttheminimatoagivendeviationintheχ2measurewithoutusingsomesubjectiveopiniononthequalityoftheresults.
Wesimulatedonethousandeventsampleswithdifferentrandomlyselectedvaluesoftheparametersweweretuning.
Sixhundredofthesewereusedtointerpolatethegeneratorresponse.
Alltheeventsampleswereusedtoselecttwohun-dredsamplesrandomlytwohundredtimesinordertoassessthesystematicsoftheinterpolationandtuningprocedure.
AcubicinterpolationofthegeneratorresponsewasusedasthishasbeenshowntogiveagooddescriptionoftheMonteCarlobehaviourintheregionofbestgeneratorresponse[4].
TheparameterswerevariedbetweenvaluesshowninTa-ble1.
Thequalityoftheinterpolationwascheckedbycom-paringtheχ2/Ndf,whereNdfisthenumberofobservablebinsusedinthetune,intheallowedparameterrangeonaparameterbyparameterbasisfortheobservablesbycom-paringtheinterpolationresponsewithactualgeneratorre-sponseatthesimulatedparametervalues.
Badregionswereremovedandtheinterpolationrepeatedleavingavolumeinthe5-dimensionalparameterspacewheretheinterpolationworkedwell.
Figure1showstheχ2/Ndfdistributionsfortwohun-dredtunesbasedontwohundredrandomlyselectedeventsamplespointsforthecubicinterpolation.
Thespreadofthesevaluesgivesanideaofthesystematicsofthetuningprocessshowingthatwehaveobtainedagoodtforourparameterisationofthegeneratorresponse.
Thelineindicatesthetunewhichisbasedonacubicin-terpolationfromsixhundredeventsamples.
Itisthisinter-polationwhichwasusedtovaryχ2abouttheminimumtoassesstheuncertaintyonthemeasureddistributions.
Dur-ingthetuneitwasdiscoveredthatPSplitLightwasrel-ativelyinsensitivetotheobservablesusedinthetune.
Assuch,PSplitLightwasxedatthedefaultvalueof1.
20duringthetuneandsubsequentχ2variation.
Professorwasusedtovaryχ2abouttheminimumvalue,asdescribedabove,determiningtheallowedrangefortheparameters.
Asveparameterswereeventuallyvaried,thereare10newsamplepoints—oneforeachoftheparametersandone"+"andone""alongeacheigenvectordirectioninparameterspace.
Wefollowtheexamplesetbythepartondistributionfunction(PDF)ttinggroupsindetermininghowmuchtoallowχ2tovary.
OursituationisdifferenttothePDFttersinthatweareusingleading-ordercalculationswithleading-logaccuracyinthepartonshower,wheretheyttonext-to-leadingordercalculationswhichgivesbetteroverallagree-mentwiththeobservablesused.
Generally,PDFgroupsttofullyinclusivevariables,whereaswehavettedtomoreexclusiveprocessesandbynature,thesearemoremodelde-pendent,inparticularhadronization.
InRefs.
[45,46]theseissuesareexploredintermsofPDFsandtheallowedvariationisrelatedtoatolerancepa-rameterT,whereχ2global≤T2.
(2)AtoleranceparameterofT≈10to15isgenerallychosenforthePDFgroups,wheretheyarettingtoaround1300datapoints.
Asourtislikleytohaveahigherχ2thantheirtduetotheaforementionedreasons,andthatwettoagreaternumberofparameters,wewillhaveahighertoler-anceparameter.
Inourt,wehave1665degrees-of-freedomandweexaminedvariouschangesinχ2,whilstconsideringtheeffectsoftheprecisiondatafromLEP.
Avariationofχ2/Ndf=5,equivalenttoT≈90,seems,subjectivelytokeeptheLEPdatawithinreasonablelimitswhileavari-ationofχ2/Ndf=10,i.
e.
T≈130istoolarge.
Any-thinglessT≈40hadverylittlevariationandwasthereforePage4of13Eur.
Phys.
J.
C(2012)72:2178Fig.
1Theχ2/Ndfdistributionsfortheparametersthatwerevariedfromtheirdefaultvalueswhilstdeterminingtheerrortune.
ThescatteroftheresultsgivesarepresentationofthesystematicsoftuningprocedureTable2Thevedirectionscorrespondingtotheerrortuneforaχ2/Ndf=5andthevaluestheparameterstakeineachdirectionParameterDirection12345pTmin0.
880.
880.
880.
880.
840.
930.
870.
900.
890.
87AlphaMZ0.
110.
110.
100.
120.
120.
110.
120.
110.
120.
11ClMaxLight3.
613.
613.
613.
613.
603.
623.
663.
553.
543.
67PwtDIquark0.
460.
230.
330.
330.
330.
330.
330.
330.
330.
33PwtSquark0.
640.
640.
640.
640.
640.
640.
620.
670.
510.
78deemedinappropriate.
Thevaluesforbothχ2/Ndf=5andχ2/Ndf=10areshowninareshowninTables2and3respectively.
TheProfessortunewasthencomparedwiththeinternalHerwig++tuningprocedure[29]asnotallanalysesthatareintheinternalHerwig++tuningsystemareavailableinRivetandsubsequentlyaccessibletoProfessor.
LookingatFig.
4itisfoundthatPSplitLightatavalueof0.
90isfavouredandgivesasignicantreductionintheχ2/Ndf.
Itwasthere-foredecidedtousethevaluesobtainedfromminimisationprocedure,butusingthevalueof0.
90forPSplitLighttomaintainagoodoveralldescriptionofthedata.
ThenewEur.
Phys.
J.
C(2012)72:2178Page5of13Table3Thevedirectionscorrespondingtotheerrortuneforaχ2/Ndf=10andthevaluestheparameterstakeineachdirectionParameterDirection12345pTmin0.
880.
880.
880.
880.
820.
950.
860.
900.
890.
87AlphaMZ0.
110.
110.
100.
120.
120.
100.
120.
100.
120.
11ClMaxLight3.
613.
613.
613.
613.
593.
633.
683.
523.
523.
70PwtDIquark0.
510.
190.
330.
330.
330.
330.
330.
330.
330.
33PwtSquark0.
640.
640.
640.
640.
650.
640.
610.
680.
460.
84Fig.
2ResultsfromtheDELPHI[44]analysisofout-of-planepTwith-respect-tothethrustaxisand1-thrustshowingthenewtuneandtheenvelopescorrespondingtoachangeinχ2/Ndf=5Fig.
3ResultsfromtheDELPHI[44]analysisofoutofplanepTwith-respect-tothethrustaxisand1-thrustshowingthenewtuneandtheenvelopescorrespondingtoachangeinχ2/Ndf=10minimafortheQCDparametersaresummarizedintheTa-ble1.
ExamplesofthenewtuneandtheuncertaintybandareshowninFigs.
2and3fortheout-of-planetransversemomentumandthrustmeasuredbyDELPHI[44].
Theseerrortunevaluescannowbeusedtopredicttheuncertaintyfromthetuningoftheshowerparametersonanyobservable.
Inthenextsectionwewillpresentanexampleofusingthesetunestoestimatetheuncertaintyonthepre-Page6of13Eur.
Phys.
J.
C(2012)72:2178Fig.
4AscanofPSplitLightusingtheinternalHerwig++tuningsystemwiththeotherparametersxedattheirnewtunedvalue.
Fromthetotalχ2/Ndfweseethatavalueof0.
90forPSplitLightisfavouredatthenewtunedparametersdrivenbythemultiplicitiesdictionsforsearchesfortheHiggsbosonusingtheBDRSjetsubstructuremethod.
3JetsubstructureboostedHiggsTheanalysisofRef.
[5]usesanumberofdifferentchannelsfortheproductionoftheHiggsbosondecayingtobbinas-sociationwithanelectroweakgaugeboson,i.
e.
theproduc-tionofh0Z0andh0W±.
Reference[5]usesthefactthattheHiggsbosonpredominantlydecaystobbinajetsubstruc-tureanalysistoextractthesignalofaboostedHiggsbo-sonabovethevariousbackgrounds.
TheirstudyfoundthattheCambridge-Aachenalgorithm[47,48]withradiuspa-rameterR=1.
2gavethebestresultswhencombinedwiththeirjetsubstructuretechnique.
Forourstudy,weusedtheCambridge-AachenalgorithmasimplementedintheFast-Jetpackage[49].
Threedifferenteventselectioncriteriaareused:(a)aleptonpairwith80GeVpminTtoselecteventsforZ0→+;(b)missingtransversemomentum/pT>pminTtoselecteventswithZ0→νν;(c)missingtransversemomentum/pT>30GeVandalep-tonwithpT>30GeVconsistentwiththepresenceofaWbosonwithpT>pminTtoselecteventswithW→ν;wherepminT=200GeV.
InadditionthepresenceofahardjetwithpTj>pminTwithsubstructureisrequired.
ThesubstructureanalysisofRef.
[5]proceedswiththehardjetjwithsomeradiusRj,amassmjandinamass-dropalgorithm:1.
thetwosubjetswhichweremergedtoformthejet,or-deredsuchthatthemassoftherstjetmj1isgreaterthanthatofthesecondjetmj2,areobtained;2.
ifmj1ycut,(3)whereR2j1,j2=(yj1yj2)2+(φj1φj2)2,andpTj1,2,ηj1,2,φj1,2arethetransversemomenta,rapiditiesandaz-imuthalanglesofjets1and2,respectively,thenjisintheheavyparticleregion.
Ifthejetisnotintheheavyparticleregiontheprocedureisrepeatedusingtherstjet.
Thisalgorithmrequiresthatj1,2areb-taggedandtakesμ=0.
67andycut=0.
09.
Auniformb-taggingefciencyof60%wasusedwithauniformmistaggingprobabilityof2%.
Theheavyjetselectedbythisprocedureisconsid-eredtobetheHiggsbosoncandidatejet.
Finally,thereisalteringprocedureontheHiggsbosoncandidatejet,j.
Thejet,j,isresolvedonanerscalebysettinganewra-diusRlt=min(0.
3,Rbb/2),wherefromthepreviousmass-dropcondition,Rbb=R2j1,j2.
ThethreehardestsubjectsofthislteringprocessaretakentobetheHiggsbosondecayproducts,wherethetwohardestarerequiredtobeb-tagged.
Allthreeanalysesrequirethat:afterthereconstructionofthevectorboson,therearenoadditionalleptonswithpseudorapidity|η|30GeV;otherthantheHiggsbosoncandidate,therearenoad-ditionalb-taggedjetswithpseudorapidity|η|50GeV.
Inaddition,duetotopcontamination,criterion(c)re-quiresthatotherthantheHiggsbosoncandidate,therearenoadditionaljetswith|η|30GeV.
Forallevents,thecandidateHiggsbosonjetshouldhavepT>pminT.
TheanalyseswereimplementedusingtheRivetsys-tem[58].
TheplotsshowninFig.
5usetheleading-ordermatrixelementsfortheproductionanddecayofHiggsbosonbuttheW,Zandtop[50]havematrixelementcorrectionsfortheirdecays.
TheplotsshowninFig.
6haveleading-orderttproduction,leading-ordervectorbosonplusjetproduc-tion(withthesamematrixelementcorrectionsastheLOmatrixelements)buttheNLOvectorbosonpairproduc-tion[51]andNLOvectorandHiggsbosonassociatedpro-duction[52].
Inadditionwehaveimplementedthecorrec-tionstothedecayh0→bbinthePOWHEGscheme,asde-scribedinAppendixB.
ThesignalsignicancesareoutlinedinTable4.
Eur.
Phys.
J.
C(2012)72:2178Page7of13Fig.
5ResultsforthereconstructedHiggsbosonmassdistributionusingleading-ordermatrixelements.
ASMHiggsbosonwasassumedwithamassof115GeV.
Inadditiontothefullresultthecontributionfromtopquarkpairproduction(tt),theproductionofW±(W+Jet)andZ0(Z+Jet)bosonsinassociationwithahardjet,vectorbosonpairproduction(VV)andtheproductionofavectorbosoninassociationwiththeHiggsboson(V+Higgs),areshownFig.
6ResultsforthereconstructedHiggsbosonmassdistributionusingleading-ordermatrixelementsfortopquarkpairproduction(tt),andtheproductionofW±(W+Jet)andZ0(Z+Jet)bosonsinassociationwithahardjet.
Thenext-to-leading-ordercorrectionsareincludedforvectorbosonpairproduction(VV)andtheproductionofavectorbosoninassociationwiththeHiggsboson(V+Higgs)aswellasinthedecayoftheHiggsboson,h0→bb.
ASMHiggsbosonwasassumedwithamassof115GeVTheuncertaintiesduetotheMonteCarlosimulationareshownasbandsinFigs.
7and8.
Astherearecorrelationsbe-tweenthedifferentprocessestheuncertaintyisdeterminedforthesumofallprocesses.
Whilstitwouldbepossibletoshowtheenvelopefortheindividualprocesses,thiswouldnotofferanyinformationontheenvelopeforthesumofthePage8of13Eur.
Phys.
J.
C(2012)72:2178Fig.
7ResultsforthereconstructedHiggsbosonmassdistributionusingleading-ordermatrixelements.
ASMHiggsbosonwasassumedwithamassof115GeV.
TheenvelopeshowstheuncertaintyfromtheMonteCarlosimulationFig.
8ResultsforthereconstructedHiggsbosonmassdistributionusingleading-ordermatrixelementsfortopquarkpairproduction,andtheproductionofW±andZ0bosonsinassociationwithahardjet.
Thenext-to-leading-ordercorrectionsareincludedforvectorbosonpairproductionandtheproductionofavectorbosoninassociationwiththeHiggsbosonaswellasinthedecayoftheHiggsboson,h0→bb.
ASMHiggsbosonwasassumedwithamassof115GeV.
TheenvelopeshowstheuncertaintyfromtheMonteCarlosimulationEur.
Phys.
J.
C(2012)72:2178Page9of13Table4Thesignicanceofthedifferentprocessesfortheleading-andnext-to-leading-ordermatrixelements.
Thesignicanceiscalcu-latedusingallmassesintherange112–120GeVSignicanceProcessOrderS√BHerwig++defaultS√BHerwig++tuneZ0→l+lLO1.
171.
24+0.
360.
11NLO1.
571.
96+0.
290.
30Z0→ννLO2.
182.
89+0.
190.
60NLO2.
954.
04+0.
250.
90W→lνLO1.
882.
32+0.
150.
27NLO2.
633.
20+0.
290.
36TotalLO2.
983.
71+0.
290.
53NLO4.
095.
20+0.
430.
81processeswhichistheresultofinterest.
Inadditiontheun-certaintyonthesignicanceisshowninTable4.
4ConclusionsMonteCarlosimulationsareanessentialtoolintheanalysisofmoderncolliderexperiments.
Whilesignicantefforthasbeendevotedtothetuningoftheparameterstoproduceabestttherehasbeenmuchlesseffortunderstandingtheuncertaintiesintheseresults.
InthispaperwehaveproducedasetoftuneswhichcanbeusedtoassessthisuncertaintyusingtheHerwig++MonteCarloeventgenerator.
Wethenusedthesetunestoassesstheuncertaintiesonthemass-dropanalysisofRef.
[5]usingHerwig++withbothleading-andnext-to-leading-ordermatrixelementsinclud-ingaPOWHEGsimulationofthedecayh0→bb.
Wendthatwhilethejetsubstructuretechniquehassig-nicantpotentialasaHiggsbosondiscoverychannel,weneedtobecondentofourtunestoinvestigatethiswithMonteCarlosimulations.
TheerrortunesandprocedureherecannowbeusedinotheranalyseswheretheuncertaintyduetotheMonteCarlosimulationisimportant.
AcknowledgementsWearegratefultoalltheothermembersoftheHerwig++collaborationandHendrikHoethforvaluablediscussionsandtheauthorsofRef.
[5]forhelpinreproducingtheirresults.
WeacknowledgetheuseoftheUKGridforParticlePhysicsinproducingtheresults.
ThisworkwassupportedbytheScienceandTechnologyFacilitiesCouncil.
DWacknowledgessupportbytheSTFCstudentshipST/F007299/1.
OpenAccessThisarticleisdistributedunderthetermsoftheCre-ativeCommonsAttributionLicensewhichpermitsanyuse,distribu-tion,andreproductioninanymedium,providedtheoriginalauthor(s)andthesourcearecredited.
AppendixA:ObservablesandweightsusedtotuneHerwig++TheweightsandobservablesusedintheProfessortuningsystemareoutlinedinTables5,6,7and8.
Table5Observablesusedinthetuningandassociatedweightsforobservablestakenfrom[53]ObservableWeightK±(892)spectrum1.
0ρspectrum1.
0ω(782)spectrum1.
0Ξspectrum1.
0K0(892)spectrum1.
0φspectrum1.
0Σ±(1385)spectrum1.
0γspectrum1.
0K±spectrum1.
0ObservableWeightΛ0spectrum1.
0π0spectrum1.
0pspectrum1.
0ηspectrum1.
0Ξ0(1530)spectrum1.
0π±spectrum1.
0ηspectrum1.
0K0spectrum1.
0Table6Observablesusedinthetuningandassociatedweightsforobservablestakenfrom[44]ObservableWeightSphericity,S1.
0Energy-energycorrelation,EEC1.
0Aplanarity,A2.
0Meanout-of-planep⊥inGeVw.
r.
t.
thrustaxesvs.
xp1.
0Meanchargedmultiplicity150.
0Meanp⊥inGeVvs.
xp1.
0Planarity,P1.
0Thrustmajor,M1.
0Oblateness=Mm1.
0Out-of-planep⊥inGeVw.
r.
t.
sphericityaxes1.
0Dparameter1.
01Thrust1.
0Out-of-planep⊥inGeVw.
r.
t.
thrustaxes1.
0Logofscaledmomentum,log(1/xp)1.
0In-planep⊥inGeVw.
r.
t.
sphericityaxes1.
0In-planep⊥inGeVw.
r.
t.
thrustaxes1.
0Thrustminor,m2.
0Cparameter1.
0Scaledmomentum,xp=|p|/|pbeam|1.
0Page10of13Eur.
Phys.
J.
C(2012)72:2178Table7Multiplicitiesusedinthetuningandassociatedweightsforobservablestakenfrom[59]ObservableWeightMeanρ0(770)multiplicity10.
0Mean++(1232)multiplicity10.
0MeanK+(892)multiplicity10.
0MeanΣ0multiplicity10.
0MeanΛ0bmultiplicity10.
0MeanK+multiplicity10.
0MeanΞ0(1530)multiplicity10.
0MeanΛ(1520)multiplicity10.
0MeanD+s(2112)multiplicity10.
0MeanΣ(1385)multiplicity10.
0Meanf1(1420)multiplicity10.
0Meanφ(1020)multiplicity10.
0MeanK02(1430)multiplicity10.
0MeanΩmultiplicity10.
0MeanΣ±(1385)multiplicity10.
0Meanψ(2S)multiplicity10.
0MeanD+(2010)multiplicity10.
0MeanBmultiplicity10.
0Meanπ0multiplicity10.
0Meanηmultiplicity10.
0Meana+0(980)multiplicity10.
0MeanD+s1multiplicity10.
0Meanρ+(770)multiplicity10.
0MeanΞmultiplicity10.
0Meanω(782)multiplicity10.
0MeanΥ(1S)multiplicity10.
0ObservableWeightMeanχc1(3510)multiplicity10.
0MeanD+multiplicity10.
0MeanΣ+multiplicity10.
0Meanf1(1285)multiplicity10.
0Meanf2(1270)multiplicity10.
0MeanJ/ψ(1S)multiplicity10.
0MeanB+umultiplicity10.
0MeanBmultiplicity10.
0MeanΛ+cmultiplicity10.
0MeanD0multiplicity10.
0Meanf2(1525)multiplicity10.
0MeanΣ±multiplicity10.
0MeanD+s2multiplicity10.
0MeanK0(892)multiplicity10.
0MeanΣmultiplicity10.
0Meanπ+multiplicity10.
0Meanf0(980)multiplicity10.
0MeanΣ+(1385)multiplicity10.
0MeanD+smultiplicity10.
0Meanpmultiplicity10.
0MeanB0smultiplicity10.
0MeanK0multiplicity10.
0MeanB+,B0dmultiplicity10.
0MeanΛmultiplicity10.
0Meanη(958)multiplicity10.
0Table8Observablesusedinthetuningandassociatedweightsforobservablestakenfrom[60]ObservableWeightbquarkfragmentationfunctionf(xweakB)7.
0Meanofbquarkfragmentationfunctionf(xweakB)3.
0AppendixB:Simulationofh0→bbusingthePOWHEGmethodTheNLOdifferentialdecayrateinthePOWHEG[39]ap-proachisdσ=B(Φm)dΦBNLORpminT+NLORpminTR(Φm,Φ1)B(Φm)dΦ1,(4)whereB(Φm)=B(Φm)+V(Φm)+R(Φm,Φ1)iDi(Φm,Φ1)dΦ1.
(5)HereB(Φm)istheleading-orderBorndifferentialdecayrate,V(Φm)theregularizedvirtualcontribution,Di(Φm,Φ1)thecountertermsregularizingtherealemissionandR(Φm,Φ1)therealemissioncontribution.
Theleading-orderprocesshasmoutgoingpartons,withassociatedphasespaceΦm.
ThevirtualandBorncontributionsdependonlyonthism-bodyphasespace.
Therealemissionphasespace,Φm+1,isfactorisedintothem-bodyphasespaceandthephasespace,Φ1,describingtheradiationofanextrapar-ton.
TheSudakovformfactorinthePOWHEGmethodisNLOR=expdΦ1R(Φm,Φ1)B(Φm)θkT(Φm,Φ1)pT,(6)Eur.
Phys.
J.
C(2012)72:2178Page11of13Fig.
9Thetworeal-emissionprocessescontributingtotheNLOdecayratewherekT(Φm,Φ1)isthetransversemomentumoftheemit-tedparton.
InordertoimplementthedecayoftheHiggsbosoninthePOWHEGschemeinHerwig++weneedtogeneratetheBorncongurationaccordingtoEq.
(5)andthesubsequenthardestemissionaccordingtoEq.
(6).
Thegenerationofthetruncatedandvetoedpartonshowersfromthesecongura-tionsthenproceedsasdescribedinRefs.
[29,52,54,55].
Thevirtualcontributionforh0→bbwascalculatedinRef.
[56].
Thecorrespondingrealemissioncontribution,seeFig.
9,is|MR|2=|M2|2CF8παsM2H(14μ2)*2+1xq1xq+(8μ46μ2+1)(1xq)(1xq)214μ211xq2μ214μ21(1xq)2+(xqxq),(7)whereM2istheleading-ordermatrixelement,CF=43,mqisthemassofthebottomquark,MHisthemassoftheHiggsboson,μ=mqMHandxi=2EiMH.
WeusetheCatani–Seymoursubtractionscheme[57]wherethecountertermsareDi=CF8παSs|M2|211xj*2(12μ2)2xixj14μ2x2j4μ2xj2μ212μ2*2+xi1xj2μ2+2μ21xj,(8)whereforDi,iistheemittingpartonandjisthespectatorparton.
Inpractice,asthecountertermscanbecomenegativeinsomeregions,weuseR(Φm,Φ1)iDi(Φm,Φ1)=iR(Φm,Φ1)|Di(Φm,Φ1)|j|Dj(Φm,Φ1)|Di(Φm,Φ1).
(9)WehavealsoregulatedsingularitiesinthevirtualtermV(Φm)withtheintegratedcountertermsfromtheCatani–SeymoursubtractionschemeallowingustogeneratetheBorncongurationaccordingtoB(Φm).
ThehardestemissionforeachlegisgeneratedaccordingtoNLOiR=expM2H16π2(14μ2)12*dx1dx2dφR(Φm+1)B(Φm)|Di|j|Dj|*θkT(Φm,Φ1)pT.
(10)Howeverthisformisnotsuitableforthegenerationofthehardestemission.
InsteadweperformaJacobiantransfor-mationandusethetransversemomentum,pT,rapidity,y,andazimuthalangle,φ,oftheradiatedgluontodenethephasespaceΦ1.
ThemomentaoftheHiggsbosondecayproductsarep1=MH2x1;x⊥cos(φ),x⊥sin(φ),±x21x2⊥4μ2,(11a)p2=MH2x2;0,0,x224μ2,(11b)p3=MH2x3;x⊥cos(φ),x⊥sin(φ),±x23x2⊥,(11c)wherepartons1,2,3aretheradiatingbottomquark,spec-tatorantibottomquarkandradiatedgluon,respectively.
Theenergyfractionsxi=2EiMHandx⊥=2pTMH.
Usingtheconser-vationofmomentuminthez-directionandx1+x2+x3=2Page12of13Eur.
Phys.
J.
C(2012)72:2178givesx2⊥=(2x1x2)2(2+2x1+2x2x2x1x22)2x224μ2.
(12)Togetherwiththedenition,x3=x⊥coshy,weobtaintheJacobianx1x2pTy=x⊥MHx⊥(x224μ2)32(x1x22μ2(x1+x2)+x22x2),(13)forthetransformationoftheradiationvariables.
WecanthengeneratetheadditionalradiationaccordingtoEq.
(10)usingthevetoalgorithm[3].
ToachievethisweuseanoverestimateoftheintegrandintheSudakovformfactor,f(pT)=cpT,wherecisasuitableconstant.
WerstgenerateanemissionaccordingtooverR(pT)=exppmaxTpTymaxymindpTdycpT,(14)usingthisoverestimate,whereymax=cosh1(MH2pminT),ymin=ymax,pmaxTisthemaximumpossibletransversemomen-tumofthegluonandpminTisaparametersetinthemodel,takentobe1GeV.
ThetrialvalueofthetransversemomentumisobtainedbysolvingR=overR,whereRisarandomnumberin[0,1],i.
e.
pT=pmaxTR1c(ymaxymin).
(15)OncethetrialpThasbeengenerated,yandφarealsogen-erateduniformlybetween[ymin,ymax]and[0,2π],respec-tively.
Theenergyfractionsofthepartonsareobtainedusingthedenitionx3=x⊥coshy,x1=12(x31)x2⊥23x32+x2⊥2x3x2⊥x23±x23x2⊥(x31)4μ2+x31μ2x2⊥(16)andx2usingenergyconservation.
Astherearetwosolu-tionsforx1bothsolutionsmustbekeptandusedtocal-culatetheweightforaparticulartrialpT.
Thesignsofthez-componentsofthemomentaarexedbythesignoftherapidityandmomentumconservation.
Anymomentumcon-gurationsoutsideofthephysicallyallowedphasespacearerejectedandanewsetofvariablesgenerated.
Themomen-tumcongurationisacceptedwithaprobabilitygivenbytheratioofthetrueintegrandtotheoverestimatedvalue.
Ifthecongurationisrejected,theprocedurecontinueswithpmaxTsettotherejectedpTuntilthetrialvalueofpTisacceptedorfallsbelowtheminimumallowedvalue,pminT.
Thispro-ceduregeneratestheradiationvariablescorrectlyasshowninRef.
[3].
Thisprocedureisusedtogenerateatrialemissionfromboththebottomandantibottom.
Thehardestpotentialemis-sionisthenselectedwhichcorrectlygenerateseventsac-cordingtoEq.
(10)usingthiscompetitionalgorithm.
References1.
P.
Z.
Skands,TuningMonteCarlogenerators:thePerugiatunes.
Phys.
Rev.
D82,074018(2010).
arXiv:1005.
34572.
B.
Cooper,J.
Katzy,M.
Mangano,A.
Messina,L.
Mijovicetal.
,MonteCarlotuninginthepresenceofmatching.
arXiv:1109.
52953.
T.
Sjstrand,S.
Mrenna,P.
Skands,PYTHIA6.
4PhysicsandManual.
J.
HighEnergyPhys.
05,026(2006).
hep-ph/06031754.
A.
Buckley,H.
Hoeth,H.
Lacker,H.
Schulz,J.
E.
vonSeggern,SystematiceventgeneratortuningfortheLHC.
Eur.
Phys.
J.
C65,331–357(2010).
arXiv:0907.
29735.
J.
M.
Butterworth,A.
R.
Davison,M.
Rubin,G.
P.
Salam,Jetsub-structureasanewHiggssearchchannelattheLHC.
Phys.
Rev.
Lett.
100,242001(2008).
arXiv:0802.
24706.
S.
D.
Ellis,C.
K.
Vermilion,J.
R.
Walsh,Techniquesforimprovedheavyparticlesearcheswithjetsubstructure.
Phys.
Rev.
D80,051501(2009).
arXiv:0903.
50817.
S.
D.
Ellis,C.
K.
Vermilion,J.
R.
Walsh,Recombinationalgorithmsandjetsubstructure:pruningasatoolforheavyparticlesearches.
Phys.
Rev.
D81,094023(2010).
arXiv:0912.
00338.
G.
D.
Kribs,A.
Martin,T.
S.
Roy,M.
Spannowsky,DiscoveringtheHiggsbosoninnewphysicseventsusingjetsubstructure.
Phys.
Rev.
D81,111501(2010).
arXiv:0912.
47319.
G.
D.
Kribs,A.
Martin,T.
S.
Roy,M.
Spannowsky,DiscoveringHiggsbosonsoftheMSSMusingjetsubstructure.
Phys.
Rev.
D82,095012(2010).
arXiv:1006.
165610.
G.
D.
Kribs,A.
Martin,T.
S.
Roy,Higgsdiscoverythroughtop-partnersusingjetsubstructure.
arXiv:1012.
286611.
J.
M.
Butterworth,J.
R.
Ellis,A.
R.
Raklev,G.
P.
Salam,Discoveringbaryon-numberviolatingneutralinodecaysattheLHC.
Phys.
Rev.
Lett.
103,241803(2009).
arXiv:0906.
072812.
CDFCollaboration,T.
Aaltonenetal.
,Studyofsubstructureofhightransversemomentumjetsproducedinproton–antiprotoncollisionsat√s=1.
96TeV.
arXiv:1106.
595213.
Y.
Bai,J.
Shelton,Compositeoctetsearcheswithjetsubstructure.
arXiv:1107.
356314.
C.
K.
Vermilion,JetsubstructureattheLargeHadronCollider:harder,better,faster,stronger.
arXiv:1101.
1335.
PhDthesis15.
T.
Plehn,G.
P.
Salam,M.
Spannowsky,FatjetsforalightHiggs.
Phys.
Rev.
Lett.
104,111801(2010).
arXiv:0910.
547216.
M.
H.
Seymour,Searchesfornewparticlesusingconeandclus-terjetalgorithms:acomparativestudy.
Z.
Phys.
C62,127–138(1994)17.
A.
Abdesselam,E.
B.
Kuutmann,U.
Bitenc,G.
Brooijmans,J.
But-terworthetal.
,Boostedobjects:aprobeofbeyondthestandardmodelphysics.
Eur.
Phys.
J.
C71,1661(2011).
arXiv:1012.
541218.
I.
Feige,M.
Schwartz,I.
Stewart,J.
Thaler,Precisionjetsubstruc-turefromboostedeventshapes.
arXiv:1204.
389819.
A.
Altheimer,S.
Arora,L.
Asquith,G.
Brooijmans,J.
Butter-worthetal.
,JetsubstructureattheTevatronandLHC:newre-sults,newtools,newbenchmarks.
J.
Phys.
G39,063001(2012).
arXiv:1201.
000820.
S.
Yang,Q.
-S.
Yan,SearchingforheavychargedHiggsbosonwithjetsubstructureattheLHC.
J.
HighEnergyPhys.
1202,074(2012).
arXiv:1111.
4530Eur.
Phys.
J.
C(2012)72:2178Page13of1321.
J.
M.
Butterworth,B.
E.
Cox,J.
R.
Forshaw,WWscatteringattheCERNLHC.
Phys.
Rev.
D65,096014(2002).
hep-ph/020109822.
J.
M.
Butterworth,J.
R.
Ellis,A.
R.
Raklev,Reconstructingsparticlemassspectrausinghadronicdecays.
J.
HighEnergyPhys.
05,033(2007).
hep-ph/070215023.
Measurementofjetmassandsubstructureforinclusivejetsins=7TeVppcollisionswiththeatlasexperiment.
Tech.
Rep.
ATLAS-CONF-2011-073,CERN,Geneva,May201124.
AtlassensitivitytothestandardmodelHiggsinthehwandhzchannelsathightransversemomenta.
Tech.
Rep.
ATL-PHYS-PUB-2009-088,CERN,Geneva,August200925.
Studyofjetsubstructureinppcollisionsat7TeVincms.
Tech.
Rep.
CMSPASJME10-013,CERN,Geneva,March201126.
G.
Corcellaetal.
,HERWIG6:aneventgeneratorforhadronemis-sionreactionswithinterferinggluons(includingsupersymmetricprocesses).
J.
HighEnergyPhys.
01,010(2001).
hep-ph/001136327.
G.
Corcellaetal.
,HERWIG6.
5releasenote.
hep-ph/021021328.
J.
M.
Butterworth,J.
R.
Forshaw,M.
H.
Seymour,Multi-partonin-teractionsinphotoproductionatHERA.
Z.
Phys.
C72,637–646(1996).
hep-ph/960137129.
M.
Bhretal.
,Herwig++physicsandmanual.
Eur.
Phys.
J.
C58,639–707(2008).
arXiv:0803.
088330.
K.
Arnold,L.
d'Errico,S.
Gieseke,D.
Grellscheid,K.
Hamiltonetal.
,Herwig++2.
6releasenote.
arXiv:1205.
490231.
G.
Marchesini,B.
R.
Webber,SimulationofQCDcoherenceinheavyquarkproductionanddecay.
Nucl.
Phys.
B330,261(1990)32.
S.
Gieseke,P.
Stephens,B.
Webber,NewformalismforQCDpartonshowers.
J.
HighEnergyPhys.
12,045(2003).
hep-ph/031008333.
M.
Bhr,S.
Gieseke,M.
H.
Seymour,Simulationofmultiplepar-tonicinteractionsinHerwig++.
arXiv:0803.
363334.
M.
Bhr,J.
M.
Butterworth,M.
H.
Seymour,TheunderlyingeventandthetotalcrosssectionfromTevatrontotheLHC.
arXiv:0806.
294935.
S.
Gieseke,C.
Rhr,A.
Siodmok,ColourreconnectionsinHer-wig++.
arXiv:1206.
004136.
S.
Gieseke,C.
Rhr,A.
Siodmok,MultiplepartonicinteractiondevelopmentsinHerwig++.
arXiv:1110.
267537.
G.
Aadetal.
(ATLASCollaboration),Jetmassandsubstructureofinclusivejetsin√s=7TeVppcollisionswiththeATLASexper-iment.
J.
HighEnergyPhys.
1205,128(2012).
arXiv:1203.
460638.
G.
Aadetal.
(ATLASCollaboration),ATLASmeasurementsofthepropertiesofjetsforboostedparticlesearches.
arXiv:1206.
536939.
P.
Nason,AnewmethodforcombiningNLOQCDwithshowerMonteCarloalgorithms.
J.
HighEnergyPhys.
11,040(2004).
hep-ph/040914640.
S.
Frixione,P.
Nason,C.
Oleari,MatchingNLOQCDcompu-tationswithpartonshowersimulations:thePOWHEGmethod.
J.
HighEnergyPhys.
11,070(2007).
arXiv:0709.
209241.
B.
R.
Webber,AQCDmodelforjetfragmentationincludingsoftgluoninterference.
Nucl.
Phys.
B238,492(1984)42.
D.
Amati,G.
Veneziano,Preconnementasapropertyofpertur-bativeQCD.
Phys.
Lett.
B83,87(1979)43.
A.
Buckleyetal.
,General-purposeeventgeneratorsforLHCphysics.
arXiv:1101.
259944.
P.
Abreuetal.
(DELPHICollaboration),Tuningandtestoffrag-mentationmodelsbasedonidentiedparticlesandprecisioneventshapedata.
Z.
Phys.
C73,11–60(1996)45.
J.
Pumplin,D.
Stump,R.
Brock,D.
Casey,J.
Hustonetal.
,Uncertaintiesofpredictionsfrompartondistributionfunc-tions,2:theHessianmethod.
Phys.
Rev.
D65,014013(2001).
hep-ph/010103246.
J.
Pumplin,D.
Stump,W.
Tung,Multivariatettingandtheerrormatrixinglobalanalysisofdata.
Phys.
Rev.
D65,014011(2001).
hep-ph/000819147.
Y.
L.
Dokshitzer,G.
D.
Leder,S.
Moretti,B.
R.
Webber,Betterjetclusteringalgorithms.
J.
HighEnergyPhys.
08,001(1997).
hep-ph/970732348.
M.
Wobisch,MeasurementandQCDanalysisofjetcrosssec-tionsindeep-inelasticpositronprotoncollisionsats(1/2)=300GeV.
DESY-THESIS-2000-04949.
M.
Cacciari,G.
P.
Salam,DispellingtheN3mythforthektjet-nder.
Phys.
Lett.
B641,57–61(2006).
hep-ph/051221050.
K.
Hamilton,P.
Richardson,AsimulationofQCDradiationintopQuarkDecays.
J.
HighEnergyPhys.
02,069(2007).
hep-ph/061223651.
K.
Hamilton,Apositive-weightnext-to-leadingordersimulationofweakbosonpairproduction.
J.
HighEnergyPhys.
1101,009(2011).
arXiv:1009.
539152.
K.
Hamilton,P.
Richardson,J.
Tully,Apositive-weightnext-to-leadingorderMonteCarlosimulationforHiggsbosonproduction.
J.
HighEnergyPhys.
04,116(2009).
arXiv:0903.
434553.
R.
Barateetal.
(ALEPHCollaboration),Studiesofquantumchro-modynamicswiththeALEPHdetector.
Phys.
Rep.
294,1–165(1998)54.
K.
Hamilton,P.
Richardson,J.
Tully,Apositive-weightnext-to-leadingorderMonteCarlosimulationofDrell–Yanvectorbosonproduction.
arXiv:0806.
029055.
L.
D'Errico,P.
Richardson,Apositive-weightnext-to-leading-orderMonteCarlosimulationofdeepinelasticscatteringandHiggsbosonproductionviavectorbosonfusioninHerwig++.
arXiv:1106.
298356.
E.
Braaten,J.
P.
Leveille,Higgsbosondecayandtherunningmass.
Phys.
Rev.
D22,715(1980)57.
S.
Catani,S.
Dittmaier,M.
H.
Seymour,Z.
Trócsányi,Thedipoleformalismfornext-to-leadingorderQCDcalculationswithmas-sivepartons.
Nucl.
Phys.
B627,189–265(2002).
hep-ph/020103658.
A.
Buckley,J.
Butterworth,L.
Lonnblad,H.
Hoeth,J.
Monk,etal.
,Rivetusermanual.
arXiv:1003.
069459.
C.
Amsler,etal.
(ParticleDataGroup),Reviewofparticlephysics.
Phys.
Lett.
B667,1–1340(2008).
doi:10.
1016/j.
physletb.
2008.
07.
01860.
G.
Barker,E.
Ben-Haim,M.
Feindt,U.
Kerzel,P.
Roudeau,L.
Ramler,A.
Savoy-Navarro,Astudyoftheb-quarkfragmenta-tionfunctionwiththeDELPHIdetectoratLEPI.
DELPHI-2002-069-CONF-603,CERN,Geneva,July2002