In this contribution we describe a new model of multiple partonic
interactions that has been implemented in Herwig++. Tuning its two free
parameters we find a good description of CDF underlying event data. We show
extrapolations to the LHC and discuss intrinsic PDF uncertainties.Comment: 4 pages, 2 figures, to appear in the proceedings of the DIS 2008
  workshop, 7-11 April 2008, University College Londo

Bähr, Manuel

Gieseke, Stefan

Seymour, Michael H.

English

arXiv

In this contribution we describe a new model of multiple partonic interactions that has been implemented in Herwig++. Tuning its two free parameters we find a good description of CDF underlying event data. We show extrapolations to the LHC and discuss intrinsic PDF uncertainties

Bahr, Manuel

CERN Document Server

arXiv:0806.4250v1  [hep-ph]  26 Jun 2008M ultiple Interactions in Herwig++M anuelBahr1,Stefan G ieseke1and M ichaelH.Seym our2 1 -InstitutfurTheoretische PhysikUniversitatK arlsruhe,76128 K arlsruhe,G erm any2 -SchoolofPhysicsand Astronom y,University ofM anchester;andPhysicsD epartm ent,CERN,CH-1211 G eneva 23,SwitzerlandIn this contribution we describe a new m odelofm ultiple partonic interactions thathas been im plem ented in Herwig+ + . Tuning its two free param eters we nd a gooddescription ofCD F underlying event data. W e show extrapolations to the LHC anddiscussintrinsic PD F uncertainties.1 IntroductionW ith the advent ofthe Large Hadron Collider (LHC) in the near future it willbecom eincreasingly im portantto gain a detailed understanding ofallsourcesofhadronic activityin a high energy scattering event. An im portantsource ofadditionalsoft jets willbe thepresence ofthe underlying event. From the experim entalpoint ofview, the underlyingeventcontainsallactivity in a hadronic collision thatisnotrelated to the signalparticlesfrom the hard process,e.g.leptons or m issing transverse energy. The additionalparticlesm ay resultfrom the initialstate radiation ofadditionalgluonsorfrom additionalhard (orsoft) scatters that occur during the sam e hadron{hadron collision. Jet m easurem ents areparticularly sensitiveto theunderlying eventbecause,although a jet’senergy isdom inatedby the prim ary hard parton thatinitiated it,jet algorithm sinevitably gathertogetherallotherenergydepositsin itsvicinity,givingan im portantcorrection toitsenergyand internalstructure.In thisnote,based on Refs.[1,2],wewantto focuson the description ofthehard com -ponentoftheunderlying event,which stem sfrom additionalhard scatterswithin the sam eproton. Notonly doesthism odelgive usa sim ple unitarization ofthe hard crosssection,it also allows to give a good description ofthe additionalsubstructure ofthe underlyingevents.Itturnsoutthatm ostactivity in the underlying eventcan be understood in term sofhard m inijets. W e therefore adopt this m odel,based on the m odelJIM M Y [3,4],forournew eventgeneratorHerwig+ + [5]. Thusfar,we do notconsidera description beyondm ultiplehard interactions.An extension ofourm odeltowardssofterinteractionsalong thelinessuggested in [6]isplanned and willalsoallow ustodescribem inim um biasinteractions.Asa rststep,the allowed param eterspaceforsuch m odelsatLHC hasbeen identied inRef.[7].2 Tevatron resultsW e have perform ed a tune ofthe m odelby calculating the total2 againstthe data fromRef.[8]. For this analysis each event is partitioned into three parts,the tow ards, aw ayand transverse regions. These regionsare equalin size in     space and classify whereThis work was supported in part by the EU M arie Curie R esearch Training N etwork M Cnet undercontract M RTN -CT-2006-035606. Preprint:M Cnet/08/04DIS2008particlesarelocated in thisspacewith respectto thehardestjetin theevent.W e com pareour predictions to data for the average num ber ofcharged particles and for the scalarpTsum in each ofthese regions.Figure1:Contourplotsforthe 2 perdegreeoffreedom ofallconsidered observables.Theparam eterspaceforthistuneistwodim ensionaland consists of the pT cutopm inTand theinversehadron radiussquared,2.In Fig.1weshow the2 contourforde-scribing allsix observables. W e have usedtheM RST 2001LO [9]PDFsbuiltin toHer-wig+ + forthis plot,and discussthe PDF-dependence in the nextsection. Forthese,and allsubsequentplots,we use Herwig+ +version 2.2.1,with allparam eters at theirdefaultvaluesexceptthetwo wearetuningand,in the nextsection,the PDF choice.The description ofthe Tevatron data istrulysatisfactoryfortheentirerangeofcon-sidered values ofpm inT. For each point onthe x-axis we can nd a point on the y-axis to give a reasonable t. Neverthelessan optim um can be found between 3 and 4G eV.The strong and constant correlationbetween pm inTand 2 isdueto thefactthatasm allerhadron radiuswillalwaysbalanceagainstalargerpT cuto asfarastheunderlyingeventactivity isconcerned. Asa defaulttune we use pm inT= 3:4 G eV and 2 = 1:5 G eV2,which resultsin an overall2=N dof of1.3.2.1 P D F uncertaintiesForprecision studies itisim portantto quantify the extentto which hard scattering crosssectionsareuncertain dueto uncertaintiesin thePDFs.Aswehavealready m entioned,jetcross sections are particularly sensitive to the am ountofunderlying event activity,whichintroduces an additionaldependence on the PDF in our m odel. In particular, it relieson the partonic scattering crosssections down to sm alltransverse m om enta,which probem om entum fractionsassm allasx  10  7 attheLHC and x  10  6 attheTevatron,wherethe PDFs are only indirectly constrained by data. O ne willhave m easured the am ountof underlying event activity at the LHC by the tim e precision m easurem ents are beingm ade,so one m ight think that the size ofthe underlying event correction willbe known.However,in practice,jetcrosssection correctionsdepend signicantly on rare uctuationsand correlationsin the underlying event,so the correction m ustbe represented by a m odeltuned to data,rather than by a single num ber m easured from data. This willthereforeentailin principle a retuning ofthe param etersoftheunderlying eventm odelforeach newPDF.Thiswould m ake the quantication ofPDF errorson a given jetcrosssection,orofextracting a new PDF setfrom jetdata,m uch m orecom plicated than a sim plereweightingofthe hard scattering crosssection.In thissection we explorethe extentto which thiseectisim portant,by studying howthe predictions with xed param eters vary as one varies the PDF.To quantify the eectDIS2008ofthe uncertaintieswithin a given PDF set,we haveused the errorsetsprovided with theCTEQ 6 fam ily,and the form ulaX =120@N pXi= 1X (S+i)  X (S i)21A1=2from Ref.[10]. Here,X isthe observable ofinterestand X (Si)are the predictionsforXbased on the PDF setsSifrom the eigenvectorbasis.Number of points10 210 310 410relative pdf uncertainty [%] -110110210 / ndf 2χ 3.632 / 9k         20.95± 300.3 P         0.1831± 4.045 transverseawaytowards , TVT Run1, 35 GeV < pt < 36 GeVchN2/N + P2kf(N) = Figure2:RelativePDF uncertaintyin percentforthem ultiplicity observables.Thedierentcurvesshow the resultsforthe threedierentregions dened in the experim entalanalysis.ThePDFsused areCTEQ 6M [10]and itscor-responding errorsets.The tresultshown asa solid line is forthe transverse region. Alsoshown asalightdashed lineisthetassum inga purely statisticalerror.W ehavestudied therelativePDF uncer-tainty,i.e.X =X (S 0),asa function ofthenum berofpointsused foreach X (Si).W eshow the resultin Fig.2 forone bin corre-sponding to 35  36 G eV ofthe leading jetfor the m ultiplicity observables. The nalstatisticsare obtained from 20M fully gen-eratedeventsforeachPDF setandthevalueon thex axisisthenum berofeventsfallingwithin thisbin.W eseethatwith these20Mevents, we have stillnot com pletely elim -inated the statisticaluncertainties. How-ever,a departure from the straightline ona log{log plot that would be expected forpure statisticalerrors, 1=pN ,is clearlyobserved. W e use this to extract the truePDF uncertainty,P ,by tting a curve ofthe formf(N )=rk2N+ P 2to thesedata.In perform ingthetwegetareliable resultalready fora m oderate num -ber of events. Using our t, we have aclear indication that the PDF uncertaintyisaround 4% forthe m ultiplicity and 4.5%forthe psumTin the transverseregion.Itisnote-worthy thatthedierencebetween thecentralvaluesoftheM RST and CTEQPDF sets(shown in Ref.[2])islargerthan theuncertaintyon each,atabout10% .Although,aswehavealready m entioned,theunderlying eventwillhavealready been m easured beforem aking precision m easurem entsorusing jetcrosssectionsto extractPDFs,a m odeltunedto thatunderlying eventm easurem entwillhave to be used and its tuning willdepend onthe PDF set. W e consideran uncertainty of5{10% large enough to warrantfurtherstudyin thisdirection.3 LH C extrapolationForcalculating theLHC extrapolationsweleftthe M PIparam etersattheirdefaultvalues,i.e.the tto Tevatron CDF data. In Ref.[11]a com parison ofdierentpredictionsforanDIS2008analysism odelled on theCDF onediscussed earlierwaspresented.Asa benchm ark observ-able the charged particle m ultiplicity in the transverse region was used. Allexpectationsreached a plateau in thisobservable forpljetT> 10 G eV.O urprediction forthisobservablealso reached a roughly constantplateau within thisregion. The heightofthisplateau canbe used forcom parison. In Ref.[11]PYTHIA 6.214 [12]ATLAS tune reached a heightof 6:5,PYTHIA 6.214 CDF Tune A of 5 and PHO JET 1.12 [13]of 3. O ur m odelreachesa heightof 5 and seem sto be close to the PYTHIA 6.214 CDF tune,althoughourm odelparam eterswerekeptconstantattheirvaluesextracted from thetto Tevatrondata.W e have seen already in the previous section that our t results in a at valley ofparam eterpoints,which allgiveaverygood description ofthedata.W ewillbriey estim atethe spread ofourLHC expectations,using only param etersetsfrom thisvalley.The rangeofpredictions thatwe deduce willbe the range thatcan be expected assum ing no energydependence on our m ain param eters. Therefore,early m easurem ents could shed light onthe potentialenergy dependenceofthe inputparam etersby sim ply com paring rstdata tothese predictions. W e extracted the average value ofthe two transverse observables for agiven param eterset in the region 20 G eV < pljetT< 30 G eV. W e did that for the best tpointsatthree dierentvaluesforpm inT,nam ely 2 G eV,3.4 G eV and 4.5 G eV.LHC predictions hN chgitransv hpsumTitransv[G eV]TVT bestt 5:1 0:3 5:0 0:5R eferences[1] Slides:http://indico.cern.ch/contributionD isplay.py?contribId= 225& sessionId= 13& confId= 24657.[2] M anuelBahr,Stefan G ieseke,and M ichaelH .Seym our.Sim ulation ofm ultiple partonic interactionsinH erwig+ + .arX iv:0803.3633 [hep-ph].2008.[3] J.M .Butterworth,Jerey R .Forshaw,and M .H .Seym our.M ultiparton interactions in photoproduc-tion atH ER A .Z.Phys.,C72:637{646,1996.[4] J. M . Butterworth and M . H . Seym our. Jim m y4 M anual. D ownloadable underhttp://projects.hepforge.org/jim m y/.[5] M .Bahretal.H erwig+ + Physics and M anual.arX iv:0803.0883 [hep-ph].2008.[6] I. Borozan and M . H . Seym our. A n eikonal m odel for m ultiparticle production in hadron hadroninteractions. JH EP,09:015,2002.[7] M anuelBahr, Jonathan M .Butterworth, and M ichaelH .Seym our. The U nderlying Event and theTotalCrossSection from Tevatron to the LH C.arX iv:0806.2949 [hep-ph].2008.[8] A nthony A llen A olderetal.Charged jetevolution and theunderlying eventin pp collisionsat1.8TeV .Phys.Rev.,D 65:092002,2002.[9] A lan D .M artin,R .G .R oberts,W .J.Stirling,and R .S.Thorne. M R ST2001: Partons and alpha(s)from precise deep inelastic scattering and Tevatron jetdata. Eur.Phys.J.,C23:73{87,2002.[10] J.Pum plin etal.N ew generation ofparton distributionswith uncertainties from globalQ CD analysis.JH EP,07:012,2002.[11] S.A lekhin et al. H ER A and the LH C -A workshop on the im plications ofH ER A for LH C physics:Proceedings PartA .arX iv:hep-ph/0601012. 2005.[12] Torbjorn Sjostrand,LeifLonnblad,and Stephen M renna.PY TH IA 6.2:Physicsand m anual.arX iv:hep-ph/0108264. 2001.[13] R .Engel. Photoproduction within the two com ponent dualparton m odel.1.A m plitudes and cross-sections. Z.Phys.,C66:203{214,1995.DIS2008

Multiple Interactions in Herwig++

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